martes, 16 de junio de 2009
Aula Circular Classroom
Professional identity crisis: race, class, gender, and success at ... - Resultado de la Búsqueda de libros de Google
de Carrie Yang Costello - 2005 - Social Science - 264 páginas
Yet this effect was denied by social welfare professors, who presented their circular classroom arrangements as liberating and egalitarian. ...
books.google.es/books?isbn=0826515053...
ESTÁ MUY BUENO porque habla en pag. 86 bien del circulo en el aula...
Teaching communication: theory, research, and methods - Resultado de la Búsqueda de libros de Google
de Anita L. Vangelisti, John Augustine Daly ... - 1999 - Language Arts & Disciplines - 564 páginas
Thus, a u-shaped or a circular classroom arrangement is recommended for facilitating classroom discussion among the greatest number of students (Patterson, ...
books.google.es/books?isbn=0805828362...
Children's Social Competence in Context: The Contributions of ... - Resultado de la Búsqueda de libros de Google
de Barry H. Schneider - 1993 - Social Science - 202 páginas
He introduced the metaphor of a "circular classroom"— as opposed to the traditional "square" or rectangular arrangement of pupils in rows— as a way of ...
books.google.es/books?isbn=0080377637...
A companion to Socrates - Resultado de la Búsqueda de libros de Google
de Sara Ahbel-Rappe, Rachana Kamtekar - 2006 - Philosophy - 533 páginas
That the conversation takes place among students most of the time in Socratic teaching is enabled through the face-to-face, circular classroom seating. ...
books.google.es/books?isbn=1405108630...
eStream - Increasing the use of Streaming Media in school ...
- [ Traducir esta página ]
... time) in which you may find direct references to the French circular classroom, I will send the copy to both of you via your email address, very best. ...
estream.schule.at/?url=&cid=2&forumid=estream&folder=&modul=foren&forumurl...id... - En caché - Páginas similares
» The great journalism education debate | The Journalism Iconoclast
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In the decentralized Socratic circular classroom, the teacher asks questions instead of making statements. The role of the teacher is to direct the flow of ...
patthorntonfiles.com/blog/2008/08/27/the-great-journalism-education-debate/ - En caché - Páginas similares
Curriculum development in the postmodern era - Resultado de la Búsqueda de libros de Google
de Patrick Slattery - 2006 - Education - 330 páginas
... 1993), and the medicine wheel in Native American tradition (Regnier, 1992) in order to establish a theoretical basis for the circular classroom milieu. ...
books.google.es/books?isbn=0415953383...
Euclidean ideals « Rationale Thoughts
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They usually consisted of a long rant, a.k.a. a lecture, followed by an even longer emotionally super-charged and circular classroom discussion. ...
rtnl.wordpress.com/2006/12/20/24/ - En caché - Páginas similares
INTERGENERACIONAL
IN STAMFORD, STUDY SPANS GENERATIONS - The New York Times
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19 Apr 1987 ... In a large circular classroom, where the youngsters wear jeans and sneakers and the elderly wear dresses and suits, the two groups learn not ...
www.nytimes.com/1987/04/19/nyregion/in-stamford-study-spans-generations.html - En caché - Páginas similares
de Carrie Yang Costello - 2005 - Social Science - 264 páginas
Yet this effect was denied by social welfare professors, who presented their circular classroom arrangements as liberating and egalitarian. ...
books.google.es/books?isbn=0826515053...
ESTÁ MUY BUENO porque habla en pag. 86 bien del circulo en el aula...
Teaching communication: theory, research, and methods - Resultado de la Búsqueda de libros de Google
de Anita L. Vangelisti, John Augustine Daly ... - 1999 - Language Arts & Disciplines - 564 páginas
Thus, a u-shaped or a circular classroom arrangement is recommended for facilitating classroom discussion among the greatest number of students (Patterson, ...
books.google.es/books?isbn=0805828362...
Children's Social Competence in Context: The Contributions of ... - Resultado de la Búsqueda de libros de Google
de Barry H. Schneider - 1993 - Social Science - 202 páginas
He introduced the metaphor of a "circular classroom"— as opposed to the traditional "square" or rectangular arrangement of pupils in rows— as a way of ...
books.google.es/books?isbn=0080377637...
A companion to Socrates - Resultado de la Búsqueda de libros de Google
de Sara Ahbel-Rappe, Rachana Kamtekar - 2006 - Philosophy - 533 páginas
That the conversation takes place among students most of the time in Socratic teaching is enabled through the face-to-face, circular classroom seating. ...
books.google.es/books?isbn=1405108630...
eStream - Increasing the use of Streaming Media in school ...
- [ Traducir esta página ]
... time) in which you may find direct references to the French circular classroom, I will send the copy to both of you via your email address, very best. ...
estream.schule.at/?url=&cid=2&forumid=estream&folder=&modul=foren&forumurl...id... - En caché - Páginas similares
» The great journalism education debate | The Journalism Iconoclast
- [ Traducir esta página ]
In the decentralized Socratic circular classroom, the teacher asks questions instead of making statements. The role of the teacher is to direct the flow of ...
patthorntonfiles.com/blog/2008/08/27/the-great-journalism-education-debate/ - En caché - Páginas similares
Curriculum development in the postmodern era - Resultado de la Búsqueda de libros de Google
de Patrick Slattery - 2006 - Education - 330 páginas
... 1993), and the medicine wheel in Native American tradition (Regnier, 1992) in order to establish a theoretical basis for the circular classroom milieu. ...
books.google.es/books?isbn=0415953383...
Euclidean ideals « Rationale Thoughts
- [ Traducir esta página ]
They usually consisted of a long rant, a.k.a. a lecture, followed by an even longer emotionally super-charged and circular classroom discussion. ...
rtnl.wordpress.com/2006/12/20/24/ - En caché - Páginas similares
INTERGENERACIONAL
IN STAMFORD, STUDY SPANS GENERATIONS - The New York Times
- [ Traducir esta página ]
19 Apr 1987 ... In a large circular classroom, where the youngsters wear jeans and sneakers and the elderly wear dresses and suits, the two groups learn not ...
www.nytimes.com/1987/04/19/nyregion/in-stamford-study-spans-generations.html - En caché - Páginas similares
QIS Quantum Information Science MIT
2008 - 2009 (academic year)
:: Wed 9/3/08, 3:00 pm in Mallinckrodt M213 (12 Oxford st, across from science center) (special seminar)
Alexandra Olaya-Castro
Energy Transfer in a photosynthetic core complex: Exploiting quantum coherence and static disorder
Photosynthetic structures are finely tuned to capture solar light efficiently and transfer it to molecular reaction centres for conversion into chemical energy with 950r more efficiency. How photosynthetic structures achieve such a high-efficiency is still a long-standing question in science. Fundamental breakthroughs towards answering this question have recently been achieved. In particular, direct evidence of long-lasting electronic coherence during excitation transfer in photosynthetic complexes has been obtained. In this talk I will discuss our recent work on the energy transfer efficiency in a photosynthetic core where a light harvesting antenna is connected to a reaction centre as in purple bacteria. By using a quantum jump approach, we demonstrate that in the presence of quantum coherent energy transfer and energetic disorder, the transfer efficiency from the antenna to the reaction centre depends intimately on the quantum superposition properties of the initial state. This indicates that initial state properties could be used as an efficiency control parameter. Our results open up experimental possibilities to investigate and exploit such coherent phenomena in artificial and natural systems capable of harvesting light.
:: Thu 9/4/08, 3:00 pm in 24-307 (special seminar)
Paola Cappellaro (Harvard)
Coherent Control of Quantum Information Devices
The development of new technologies at scales approaching the quantum regime is driving new theoretical and experimental research on control in quantum systems. The implementation of quantum control would have an enormous impact on a wide range of fields, in particular in quantum information processing and precision metrology. In this talk Dr. Cappellaro will present the application of coherent control techniques to the electronic and nuclear spins associated with Nitrogen-Vacancy (NV) centers in diamond. These systems have emerged as excellent candidates for quantum information processing, since they can be optically polarized and detected, and present good coherence properties even at room temperature. She will first show how this solid state system can be used as the building block of a scalable architecture for quantum computation or communication,then present a novel approach to magnetometry, based on NV centers, that takes advantage of coherent control techniques and the confinement of the sensing spins into a sample of nanometer dimensions. The resulting magnetic sensor is projected to yield an unprecedented combination of ultra-high sensitivity and spatial resolution, with the potential of exciting applications in bioscience, materials science, and single electronic and nuclear spin detection.
:: Mon 9/8/08, 4:15 pm in 36-428 (QIP seminar)
Sergey Bravyi (IBM)
Additive quantum codes with geometrically local generators
(Link To Video)
We study properties of additive quantum error-correcting codes (QECC) that permit a local description on a regular D-dimensional lattice. Specifically, we assume that the stabilizer group of a code has a set of local generators such that support of any generator can be bounded by a rectangular box of size $r=O(1)$. Our first result concerns the optimal scaling of the distance $d$ with the linear size of the lattice $L$. We establish an upper bound $dle r L^{D-1}$ which is tight for $D=1,2$. We also prove a bound $d=O(1)$ for one-dimensional subsystem codes assuming that the gauge group of a code has a set of local generators. Secondly we analyze suitability of various QECCs for building a self-correcting quantum memory. Any additive QECC with geometrically local generators can be naturally converted to a local Hamiltonian that penalizes states violating the stabilizer conditions. A degenerate ground state of this Hamiltonian corresponds to the logical subspace of a code. We prove that for $D=1,2$ the height of an energy barrier separating different logical states is upper bounded by a constant independent of the lattice size $L$. This result demonstrates that a self-correcting quantum memory cannot be build using additive QECC in dimensions $D=1,2$.
:: Mon 10/6/08, 4:15 pm in 36-428 (QIP seminar)
Hassidim,Avinatan (MIT)
Quantum Multi Prover Interactive Proofs with Communicating Provers
(Link To Video)
Quantum Multi Prover Interactive Proofs (QMIP) can provide us with important insights to the capabilities of entanglement. The talk will present some known models and insights they give. We introduce a variant of the model, where the provers do not share entanglement, the communication between the verifier and the provers is quantum, but the provers are unlimited in the classical communication between them. At first, this model may seem very weak, as provers who exchange information seem to be equivalent in power to a simple prover. This in fact is not the case - we show that any language in NEXP can be recognized in this model efficiently, with just two provers and two rounds of communication, with a constant completeness-soundness gap. The main idea is not to bound the information the provers exchange with each other, as in the classical case, but rather to prove that any ``cheating'' strategy employed by the provers has constant probability to diminish the entanglement between the verifier and the provers by a constant amount. Detecting such reduction gives us the soundness proof. Similar ideas and techniques may help help with other models of Quantum MIP, including the dual question, of non communicating provers with unlimited entanglement.
:: Mon 10/20/08, 4:15 in 36-428 (QIP seminar)
Kenneth Brown (Georgia Institute of Technology)
Quantum Simulations and Errors
(Link To Video)
A quantum simulation is a map of the dynamics of a target quantum system onto a control quantum system. A quantum computer is a control quantum system that can simulate any target quantum system. In this talk, we describe two cases of quantum simulations in the presence of errors. In the first case, we examine a control quantum system that simulates the target system in an interaction picture. Although the control system simulates the dynamics, it does not simulate the thermodynamics of the target system. This is an important distinction when the target system represents a Hamiltonian with proposed error-correcting properties. In the second case, we use a model of a fault-tolerant quantum architecture to evaluate the resource cost of evaluating the ground state energy of the target quantum system. The resources are compared to performing Shor's algorithm on the same model. Simulations of modest accuracy on 10's of qubits are found to have comparable cost, in the product of computational time and space (KQ), to the factoring of 1024 bit numbers.
:: Wed 10/22/08, 3:00 in 36-428 (special seminar)
William Oliver (MIT Lincoln Laboratory)
Quantum Computation with Superconducting Artificial Atoms
(Link To Video)
In this talk, we will present an overview of our superconductive quantum computing effort. In collaboration with Lincoln�s Solid State Division (Division 8) and the MIT campus, we have fabricated superconductive artificial atoms, actively cooled them to near absolute zero, and demonstrated new broadband spectroscopy techniques along with the more conventional Rabi, Ramsey, and spin-echo metrics to characterize their coherence. These artificial atoms form the fundamental building blocks, �qubits,� of a quantum information processor. We have developed and simulated a universal set of gate operations capable of low error rates to control these qubits. Today, we are working to improve single-qubit coherence while coupling these qubits into more complicated circuit elements. The talk will present a review of our progress and future work.
:: Mon 11/17/08, 4:15 in 36-428 (QIP seminar)
Aliferis,Panos (IBM)
Fault-tolerant quantum computing against highly biased noise
(Link To Video)
Experimentalists in quantum computing observe that in many of their systems noise is biased---i.e., loss of phase coherence in the computational basis occurs faster than relaxation to the lowest energy eigenstate or leakage outside the computational subspace. I will discuss a scheme for fault-tolerant quantum computation that is especially designed to protect against biased noise. The scheme is particularly effective when the noise bias is very high, with dephasing dominating other types of noise by three orders of magnitude or more. To illustrate how this scheme could be relevant for future experiments, I will discuss the design of a universal set of biased-noise operations for the superconducting flux qubit investigated at the IBM labs.
:: Mon 11/24/08, 4:15 in 36-428 (QIP seminar)
Verstraete,Frank
The complexity of simulating quantum many-body systems
(Link To Video)
The theory of entanglement and of quantum computational complexity is providing valuable new insights into the problem of simulating strongly correlated quantum many-body systems. We will discuss recent progress in that field.
:: Mon 12/1/08, 4:15 in 36-428 (QIP seminar)
Wootters,William (Williams College)
The Entanglement Cost of a Nonlocal Measurement
(Link To Video)
For a joint measurement on a pair of spatially separated quantum objects, one can ask how much entanglement is needed to carry out the measurement using only local operations and classical communication. In this talk I focus on a particular orthogonal measurement on two qubits with partially entangled eigenstates, for which we can find upper and lower bounds on the entanglement cost. The lower bound implies that the entanglement required to perform the measurement is strictly greater than the average entanglement of the eigenstates. I also consider other examples, including a simple two-qubit product- state measurement that cannot be performed locally.
:: Mon 12/8/08, 4:15 in 36-428 (QIP seminar)
Zeng,Bei (MIT)
Quantum Error Correction via Codes Over GF(3)
(Link To Video)
``Quantum Error Correction via Codes Over GF(4)" is one of the seminal papers in quantum coding theory. This 1996 work transforms the problem of finding binary quantum-error-correcting codes into the problem of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Ever since then, these codes, called additive codes or stabilizer codes, have dominated the research on quantum coding theory. There is now a rich theory of stabilizer codes, and a thorough understanding of their properties. Nevertheless, there are a few known examples of nonadditive codes which outperform any possible stabilzer code. In previous work, my colleagues and I introduced the codeword stabilized quantum codes framework for understanding additive and nonadditive codes. This has allowed us to find, using exhaustive or random search, good new nonadditive codes. However, these new codes have no obvious structure to generalize to other cases. A systematical understanding of constructing nonadditive quantum codes is still lacking. In this talk, we introduce the idea of constructing binary quantum- error-correcting codes via classical codes over the field GF(3). Quantum codes directly constructed this way are nonadditive codes adapted to the amplitude damping channel. These codes have higher performance than all the previous codes for the amplitude damping channel. We then further generalize this GF(3) idea to the case of constructing 'usual' binary quantum codes for the depolarizing channel, which leads to a systematical way of constructing good nonadditive codes that outperform best additive codes. Using this method, many good new codes are found. Particularly, we construct families of good nonadditive codes which not only ourperform any additive codes, but also asymptotically achieve the quantum Hamming bound. Generalization to nonbinary case is straightforward and families of good nonadditive nonbinary quantum codes are found. What is more, our new method can also be used to construct additive codes, and additive codes with better parameters than previous known are found. Based on joint work with Markus Grassl, Peter Shor, Graeme Smith, and John Smolin.
:: Thu 1/8/09, 4:15 in 36-428 (QIP seminar)
Eban,Elad (Hebrew University)
Interactive Proofs for Quantum Computation
The widely held belief that BQP strictly contains BPP raises fundamental questions: Upcoming generations of quantum computers might already be too large to be simulated classically. Is it possible to experimentally test that these systems perform as they should, if we cannot efficiently compute predictions for their behavior? Vazirani has asked [Vaz07]: If computing predictions for Quantum Mechanics requires exponential resources, is Quantum Mechanics a falsifiable theory? In cryptographic settings, an untrusted future company wants to sell a quantum computer or perform a delegated quantum computation. Can the customer be convinced of correctness without the ability to compare results to predictions? To provide answers to these questions, we define Quantum Prover Interactive Proofs (QPIP).Whereas in standard Interactive Proofs [GMR85] the prover is computationally unbounded, here our prover is in BQP, representing a quantum computer. The verifier models our current computational capabilities: it is a BPP machine, with access to few qubits. Our main theorem can be roughly stated as: "Any language in BQP has a QPIP, and moreover, a fault tolerant one". We provide two proofs. The simpler one uses a new (possibly of independent interest) quantum authentication scheme (QAS) based on random Clifford elements. This QPIP however, is not fault tolerant. Our second protocol uses polynomial codes QAS due to Ben-Or, CrŽepeau, Gottesman, Hassidim, and Smith [BOCG+06],combined with quantum fault tolerance and secure multiparty quantum computation techniques. A slight modification of our constructions makes the protocol "blind": the quantum computation and input remain unknown to the prover. After we have derived the results, we have learnt that Broadbent, Fitzsimons, and Kashefi [BFK08] have independently derived "universal blind quantum computation" using completely different methods (measurement based quantum computation). Their construction implicitly implies similar implications.
:: Tue 1/20/09, 4:15 in 36-428 (QIP seminar)
Sattath,Or (Hebrew University)
The Pursuit For Uniqueness: Extending Valiant-Vazirani Theorem to the Probabilistic and Quantum Settings
In 1985, Valiant-Vazirani showed [VV85] that solving NP with the promise that "yes" instances have only one witness, is powerful enough to solve the entire NP class (under randomized reductions).We are interested in extending this result to the quantum setting. We prove extensions to the classes Merlin-Arthur (MA) and Quantum- Classical-Merlin-Arthur (QCMA) [AN02].Our results have implications on the complexity of approximating the ground state energy of a quantum local Hamiltonian with a unique ground state and an inverse polynomial spectral gap. We show that the estimation, within polynomial accuracy, of the ground state energy of poly-gapped 1-D local Hamiltonians is QCMA-hard, under randomized reductions. This is in strong contrast to the case of constant gapped 1-D Hamiltonians, which is in NP [Has07]. Moreover, it shows that unless QCMA can be reduced to NP by randomized reductions, there is no classical description of the ground state of every poly-gapped local Hamiltonian which allows the efficient calculation of expectation values.Finally, we conjecture that an analogous result to the class Quantum Merlin-Arthur(QMA) is impossible. This is formulated by separating between the two relavant classes, QMA and its "unique" version UQMA, using the definition by Aaronson and Kuperberg [AK06] of quantum oracles.
:: Mon 2/2/09, 11:45 in 4-331
Guifre Vidal (University of Queensland)
Recent Progress in Entanglement Renormalization
Entanglement Renormalization (ER) has been proposed as a real space renormalization group transformation for quantum lattice systems in D spatial dimensions [Phys. Rev. Lett. 99, 220405 (2007)]. Its main novelty is the use of disentanglers, namely unitary transformations that act accross a spin block boundary, to remove short-range entanglement from the system's ground state. In this talk I will first review the basic concepts underlying ER and then present a summary of the most recent results. Specifically, I intend to describe the simulation of lattice systems at a quantum critical point by exploiting scale invariance; and the simulation of two dimensional lattice systems that are beyond the reach of Monte Carlo sampling techniques, including spin models of frustrated antiferromagnets.
:: Mon 2/9/09, 4:30 in 4-237 (QIP seminar)
Matthew Hastings (Los Alamos National Laboratory)
A counter-example to additivity: using entanglement to boost communication capacity
Suppose Alice is using a noisy quantum channel to send classical information to Bob. For example, she might send single photons over a fiber optic line. How should she do this? In particular, should she use entanglement or should she send unentangled input states? The additivity conjecture in quantum information theory states that it is never useful for her to use entanglement. In fact, there are several related additivity conjectures, depending on the use of entanglement for different tasks. I will present a counter-example to one of these conjectures, the minimum output entropy conjecture, implying that all of these conjectures are false, and that in some circumstances Alice can increase the communication capacity by using entangled states.
:: Tue 2/17/09, 4:15 in 36-428 (QIP seminar)
Roland,Jeremie (NEC Laboratories America)
The communication complexity of non-signaling distributions
We study a model of communication complexity that encompasses many well-studied problems, including classical and quantum communication complexity, the complexity of simulating distributions arising from bipartite measurements of shared quantum states, and XOR games. In this model, Alice gets an input x, Bob gets an input y, and their goal is to each produce an output a,b distributed according to some pre-specified joint distribution p(a,b|x,y). Our results apply to any non-signaling distribution, that is, those where Alice's marginal distribution does not depend on Bob's input, and vice versa, therefore our techniques apply to any communication problem that can be reduced to a non-signaling distribution, including quantum distributions, Boolean and non-Boolean functions, most relations, partial (promise) problems, in the two-player and multipartite settings. We give elementary proofs and very intuitive interpretations of the recent lower bounds of Linial and Shraibman, which we generalize to the problem of simulating any non-signaling distribution. The lower bounds we obtain are also expressed as linear programs (or SDPs for quantum communication). We show that the dual formulations have a striking interpretation, since they coincide with maximum violations of Bell and Tsirelson inequalities. The dual expressions are closely related to the winning probability of XOR games. We show that as in the case of Boolean functions, the gap between the quantum and classical lower bounds is at most linear in size of the support of the distribution, and does not depend on the size of the inputs. This translates into a bound on the gap between maximal Bell and Tsirelson inequalities, which was previously known only for the case of Boolean outcomes with uniform marginals. Finally, we give an exponential upper bound on quantum and classical communication complexity in the simultaneous messages model, for any non-signaling distribution. One consequence of this is a simple proof that any quantum distribution can be approximated with a constant number of bits of communication. Joint work with:Julien Degorre, Marc Kaplan and Sophie Laplante
:: Mon 3/16/09, 4:15 in 36-428 (QIP seminar)
Aaronson,Scott (MIT)
The Power of Quantum Advice
I'll describe a powerful new result about quantum advice: namely, given any state rho on n qubits, there exists a local Hamiltonian H on poly(n) qubits (e.g., a sum of two-qubit interactions), such that *any* ground state of H can be used to simulate rho on all circuits of a fixed polynomial size. In terms of complexity classes, this implies that BQP/qpoly is contained in QMA/poly, superseding the previous result that BQP/qpoly is contained in PP/poly. Indeed, we can exactly characterize the /qpoly operator, as equivalent in power to *untrusted* quantum advice combined with trusted *classical* advice. The proof of this theorem relies on my previous result about the learnability of quantum states, as well as a new combinatorial result called the "majority-certificates lemma" that might be of independent interest. Joint work with Andrew Drucker.
:: Mon 3/30/09, 4:15 in 36-428 (QIP seminar)
Frederick Strauch (Williams College)
Quantum walks in the wild: perfect quantum state transfer with superconducting qubits
Superconducting quantum bits are artificial atoms that can be wired up into complex structures. I will present a theoretical proposal to implement perfect quantum state transfer between any two nodes of a hypercube network. This example of novel quantum transport in an artificial solid has many applications for quantum computing. It would also provide an experimental simulation of a continuous-time quantum walk with exponential speedup over the corresponding classical walk. This speedup is found to be remarkably robust to both decoherence and diagonal disorder, but only for certain (inefficient) representations of the hypercube.
:: Mon 4/13/09, 4:15 in 36-428 (QIP seminar)
Debbie Leung (University of Waterloo)
Continuity of quantum channel capacities
Many capacities of a quantum channel are given by expressions that involve asymptotically large number of uses of the channel, thus, there is no a priori reason for the capacities to be continuous. In this talk, we prove that the ability to transmit classical data, private classical data, quantum data are all continuous.
:: Mon 4/27/09, 4:15 in 34-401B (QIP seminar)
Smith,Graeme (IBM)
Quantum Communication With Zero-Quantum-Capacity Channels
Besides transmitting ordinary classical information, some quantum channels can faithfully transmit intact quantum states. A channel's capacity for such coherent transmission, its quantum capacity, is of central importance in quantum information theory as it measures the optimum performance of quantum error-correcting codes. I will show that two quantum channels, each of zero quantum capacity, can nevertheless achieve a positive quantum capacity when used together. This result contrasts sharply with the classical setting, where the capacity of a channel is independent of what other channels are available. This uniquely quantum effect unveils a rich structure in the theory of quantum communications and shows that there are several kinds of quantum information, the ability to transmit each of which is necessary but not sufficient for faithful quantum communication.
:: Mon 5/4/09, 4:15 in 36-428 (QIP seminar)
Broadbent,Anne (IQC)
Universal Blind Quantum Computation
We present a protocol which allows a client to have a server carry out a quantum computation for her such that the client's inputs, outputs and computation remain perfectly private, and where she does not require any quantum computational power or memory. The client only needs to be able to prepare single qubits randomly chosen from a finite set and send them to the server, who has the balance of the required quantum computational resources. Our protocol is interactive: after the initial preparation of quantum states, the client and server use two-way classical communication which enables the client to drive the computation, giving single- qubit measurement instructions to the server, depending on previous measurement outcomes. Our protocol works for inputs and outputs that are either classical or quantum. We give an authentication protocol that allows the client to detect an interfering server; our scheme can also be made fault-tolerant.
:: Tue 5/5/09, 4:00 in 26-214
Girvin,Steven (Yale)
Demonstration of entanglement on demand and two-qubit quantum algorithms in circuit QED
The 'circuit QED' architecture consists of Josephson junction qubits placed inside a coplanar waveguide microwave resonator. This talk will present an introduction to the quantum optics of these novel electrical circuits and describe recent experiments in the Schoelkopf lab at Yale. With the help of a controlled phase gate based on precision control and shaping of microwave pulses, it is now possible to achieve two-qubit entanglement on demand with concurrence up to 94% and to run the Grover search and Deutsch-Josza quantum algorithms with fidelities exceeding 80%. This success is based on a qubit design with long coherence times and the ability to simultaneously readout the state of two qubits (so far still with low fidelity).
:: Mon 5/11/09, 4:15 in 36-428 (QIP seminar)
Jordan,Stephen (Caltech)
Permutational Quantum Computation
In topological quantum computation the geometric details of a particle trajectory are irrelevant; only the topology matters. This is one reason for the inherent fault tolerance of topological quantum computation. I will describe a model in which this idea is taken one step further. Even the topology is irrelevant. The computation is determined solely by the permutation of the particles. Unlike topological quantum computation, which requires anyons, permutational quantum computations can in principle be performed by permuting ordinary spin-1/2 particles. It seems possible that permutational quantum computation is less powerful than standard quantum computation (BQP). Nevertheless I will present algorithms for this model which provide apparent exponential speedup over classical algorithms.
:: Mon 5/18/09, 4:15 in 36-428 (QIP seminar)
Navascues,Miguel (Imperial College London)
The power of symmetric extensions for entanglement detection
In this talk, I will analyze the speed of convergence of algorithms for entanglement detection based on PPT (Positive Partial Transpose) symmetric extensions, as conceived by Doherty et al. [1]. I will show that the states defined in [1] can be made separable just by partially depolarizing one of the parts. While the amount of necessary noise to induce separability on states that admit a plain N-symmetric extension decreases as O(1/N), the corresponding perturbation for states arising from PPT N-symmetric extensions decreases at least as O(1/N^2). I will use these results to estimate and compare the time and space complexity of both algorithms. Finally, I will consider the power of the PPT criterion alone: I will show how to derive upper bounds on the maximum possible distance between a PPT entangled state and the set of separable states by means of a simple construction. [1] A. C. Doherty, P. A. Parrilo and F. M. Spedalieri, Phys. Rev. A 69, 022308 (2004).
:: Wed 9/3/08, 3:00 pm in Mallinckrodt M213 (12 Oxford st, across from science center) (special seminar)
Alexandra Olaya-Castro
Energy Transfer in a photosynthetic core complex: Exploiting quantum coherence and static disorder
Photosynthetic structures are finely tuned to capture solar light efficiently and transfer it to molecular reaction centres for conversion into chemical energy with 950r more efficiency. How photosynthetic structures achieve such a high-efficiency is still a long-standing question in science. Fundamental breakthroughs towards answering this question have recently been achieved. In particular, direct evidence of long-lasting electronic coherence during excitation transfer in photosynthetic complexes has been obtained. In this talk I will discuss our recent work on the energy transfer efficiency in a photosynthetic core where a light harvesting antenna is connected to a reaction centre as in purple bacteria. By using a quantum jump approach, we demonstrate that in the presence of quantum coherent energy transfer and energetic disorder, the transfer efficiency from the antenna to the reaction centre depends intimately on the quantum superposition properties of the initial state. This indicates that initial state properties could be used as an efficiency control parameter. Our results open up experimental possibilities to investigate and exploit such coherent phenomena in artificial and natural systems capable of harvesting light.
:: Thu 9/4/08, 3:00 pm in 24-307 (special seminar)
Paola Cappellaro (Harvard)
Coherent Control of Quantum Information Devices
The development of new technologies at scales approaching the quantum regime is driving new theoretical and experimental research on control in quantum systems. The implementation of quantum control would have an enormous impact on a wide range of fields, in particular in quantum information processing and precision metrology. In this talk Dr. Cappellaro will present the application of coherent control techniques to the electronic and nuclear spins associated with Nitrogen-Vacancy (NV) centers in diamond. These systems have emerged as excellent candidates for quantum information processing, since they can be optically polarized and detected, and present good coherence properties even at room temperature. She will first show how this solid state system can be used as the building block of a scalable architecture for quantum computation or communication,then present a novel approach to magnetometry, based on NV centers, that takes advantage of coherent control techniques and the confinement of the sensing spins into a sample of nanometer dimensions. The resulting magnetic sensor is projected to yield an unprecedented combination of ultra-high sensitivity and spatial resolution, with the potential of exciting applications in bioscience, materials science, and single electronic and nuclear spin detection.
:: Mon 9/8/08, 4:15 pm in 36-428 (QIP seminar)
Sergey Bravyi (IBM)
Additive quantum codes with geometrically local generators
(Link To Video)
We study properties of additive quantum error-correcting codes (QECC) that permit a local description on a regular D-dimensional lattice. Specifically, we assume that the stabilizer group of a code has a set of local generators such that support of any generator can be bounded by a rectangular box of size $r=O(1)$. Our first result concerns the optimal scaling of the distance $d$ with the linear size of the lattice $L$. We establish an upper bound $dle r L^{D-1}$ which is tight for $D=1,2$. We also prove a bound $d=O(1)$ for one-dimensional subsystem codes assuming that the gauge group of a code has a set of local generators. Secondly we analyze suitability of various QECCs for building a self-correcting quantum memory. Any additive QECC with geometrically local generators can be naturally converted to a local Hamiltonian that penalizes states violating the stabilizer conditions. A degenerate ground state of this Hamiltonian corresponds to the logical subspace of a code. We prove that for $D=1,2$ the height of an energy barrier separating different logical states is upper bounded by a constant independent of the lattice size $L$. This result demonstrates that a self-correcting quantum memory cannot be build using additive QECC in dimensions $D=1,2$.
:: Mon 10/6/08, 4:15 pm in 36-428 (QIP seminar)
Hassidim,Avinatan (MIT)
Quantum Multi Prover Interactive Proofs with Communicating Provers
(Link To Video)
Quantum Multi Prover Interactive Proofs (QMIP) can provide us with important insights to the capabilities of entanglement. The talk will present some known models and insights they give. We introduce a variant of the model, where the provers do not share entanglement, the communication between the verifier and the provers is quantum, but the provers are unlimited in the classical communication between them. At first, this model may seem very weak, as provers who exchange information seem to be equivalent in power to a simple prover. This in fact is not the case - we show that any language in NEXP can be recognized in this model efficiently, with just two provers and two rounds of communication, with a constant completeness-soundness gap. The main idea is not to bound the information the provers exchange with each other, as in the classical case, but rather to prove that any ``cheating'' strategy employed by the provers has constant probability to diminish the entanglement between the verifier and the provers by a constant amount. Detecting such reduction gives us the soundness proof. Similar ideas and techniques may help help with other models of Quantum MIP, including the dual question, of non communicating provers with unlimited entanglement.
:: Mon 10/20/08, 4:15 in 36-428 (QIP seminar)
Kenneth Brown (Georgia Institute of Technology)
Quantum Simulations and Errors
(Link To Video)
A quantum simulation is a map of the dynamics of a target quantum system onto a control quantum system. A quantum computer is a control quantum system that can simulate any target quantum system. In this talk, we describe two cases of quantum simulations in the presence of errors. In the first case, we examine a control quantum system that simulates the target system in an interaction picture. Although the control system simulates the dynamics, it does not simulate the thermodynamics of the target system. This is an important distinction when the target system represents a Hamiltonian with proposed error-correcting properties. In the second case, we use a model of a fault-tolerant quantum architecture to evaluate the resource cost of evaluating the ground state energy of the target quantum system. The resources are compared to performing Shor's algorithm on the same model. Simulations of modest accuracy on 10's of qubits are found to have comparable cost, in the product of computational time and space (KQ), to the factoring of 1024 bit numbers.
:: Wed 10/22/08, 3:00 in 36-428 (special seminar)
William Oliver (MIT Lincoln Laboratory)
Quantum Computation with Superconducting Artificial Atoms
(Link To Video)
In this talk, we will present an overview of our superconductive quantum computing effort. In collaboration with Lincoln�s Solid State Division (Division 8) and the MIT campus, we have fabricated superconductive artificial atoms, actively cooled them to near absolute zero, and demonstrated new broadband spectroscopy techniques along with the more conventional Rabi, Ramsey, and spin-echo metrics to characterize their coherence. These artificial atoms form the fundamental building blocks, �qubits,� of a quantum information processor. We have developed and simulated a universal set of gate operations capable of low error rates to control these qubits. Today, we are working to improve single-qubit coherence while coupling these qubits into more complicated circuit elements. The talk will present a review of our progress and future work.
:: Mon 11/17/08, 4:15 in 36-428 (QIP seminar)
Aliferis,Panos (IBM)
Fault-tolerant quantum computing against highly biased noise
(Link To Video)
Experimentalists in quantum computing observe that in many of their systems noise is biased---i.e., loss of phase coherence in the computational basis occurs faster than relaxation to the lowest energy eigenstate or leakage outside the computational subspace. I will discuss a scheme for fault-tolerant quantum computation that is especially designed to protect against biased noise. The scheme is particularly effective when the noise bias is very high, with dephasing dominating other types of noise by three orders of magnitude or more. To illustrate how this scheme could be relevant for future experiments, I will discuss the design of a universal set of biased-noise operations for the superconducting flux qubit investigated at the IBM labs.
:: Mon 11/24/08, 4:15 in 36-428 (QIP seminar)
Verstraete,Frank
The complexity of simulating quantum many-body systems
(Link To Video)
The theory of entanglement and of quantum computational complexity is providing valuable new insights into the problem of simulating strongly correlated quantum many-body systems. We will discuss recent progress in that field.
:: Mon 12/1/08, 4:15 in 36-428 (QIP seminar)
Wootters,William (Williams College)
The Entanglement Cost of a Nonlocal Measurement
(Link To Video)
For a joint measurement on a pair of spatially separated quantum objects, one can ask how much entanglement is needed to carry out the measurement using only local operations and classical communication. In this talk I focus on a particular orthogonal measurement on two qubits with partially entangled eigenstates, for which we can find upper and lower bounds on the entanglement cost. The lower bound implies that the entanglement required to perform the measurement is strictly greater than the average entanglement of the eigenstates. I also consider other examples, including a simple two-qubit product- state measurement that cannot be performed locally.
:: Mon 12/8/08, 4:15 in 36-428 (QIP seminar)
Zeng,Bei (MIT)
Quantum Error Correction via Codes Over GF(3)
(Link To Video)
``Quantum Error Correction via Codes Over GF(4)" is one of the seminal papers in quantum coding theory. This 1996 work transforms the problem of finding binary quantum-error-correcting codes into the problem of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Ever since then, these codes, called additive codes or stabilizer codes, have dominated the research on quantum coding theory. There is now a rich theory of stabilizer codes, and a thorough understanding of their properties. Nevertheless, there are a few known examples of nonadditive codes which outperform any possible stabilzer code. In previous work, my colleagues and I introduced the codeword stabilized quantum codes framework for understanding additive and nonadditive codes. This has allowed us to find, using exhaustive or random search, good new nonadditive codes. However, these new codes have no obvious structure to generalize to other cases. A systematical understanding of constructing nonadditive quantum codes is still lacking. In this talk, we introduce the idea of constructing binary quantum- error-correcting codes via classical codes over the field GF(3). Quantum codes directly constructed this way are nonadditive codes adapted to the amplitude damping channel. These codes have higher performance than all the previous codes for the amplitude damping channel. We then further generalize this GF(3) idea to the case of constructing 'usual' binary quantum codes for the depolarizing channel, which leads to a systematical way of constructing good nonadditive codes that outperform best additive codes. Using this method, many good new codes are found. Particularly, we construct families of good nonadditive codes which not only ourperform any additive codes, but also asymptotically achieve the quantum Hamming bound. Generalization to nonbinary case is straightforward and families of good nonadditive nonbinary quantum codes are found. What is more, our new method can also be used to construct additive codes, and additive codes with better parameters than previous known are found. Based on joint work with Markus Grassl, Peter Shor, Graeme Smith, and John Smolin.
:: Thu 1/8/09, 4:15 in 36-428 (QIP seminar)
Eban,Elad (Hebrew University)
Interactive Proofs for Quantum Computation
The widely held belief that BQP strictly contains BPP raises fundamental questions: Upcoming generations of quantum computers might already be too large to be simulated classically. Is it possible to experimentally test that these systems perform as they should, if we cannot efficiently compute predictions for their behavior? Vazirani has asked [Vaz07]: If computing predictions for Quantum Mechanics requires exponential resources, is Quantum Mechanics a falsifiable theory? In cryptographic settings, an untrusted future company wants to sell a quantum computer or perform a delegated quantum computation. Can the customer be convinced of correctness without the ability to compare results to predictions? To provide answers to these questions, we define Quantum Prover Interactive Proofs (QPIP).Whereas in standard Interactive Proofs [GMR85] the prover is computationally unbounded, here our prover is in BQP, representing a quantum computer. The verifier models our current computational capabilities: it is a BPP machine, with access to few qubits. Our main theorem can be roughly stated as: "Any language in BQP has a QPIP, and moreover, a fault tolerant one". We provide two proofs. The simpler one uses a new (possibly of independent interest) quantum authentication scheme (QAS) based on random Clifford elements. This QPIP however, is not fault tolerant. Our second protocol uses polynomial codes QAS due to Ben-Or, CrŽepeau, Gottesman, Hassidim, and Smith [BOCG+06],combined with quantum fault tolerance and secure multiparty quantum computation techniques. A slight modification of our constructions makes the protocol "blind": the quantum computation and input remain unknown to the prover. After we have derived the results, we have learnt that Broadbent, Fitzsimons, and Kashefi [BFK08] have independently derived "universal blind quantum computation" using completely different methods (measurement based quantum computation). Their construction implicitly implies similar implications.
:: Tue 1/20/09, 4:15 in 36-428 (QIP seminar)
Sattath,Or (Hebrew University)
The Pursuit For Uniqueness: Extending Valiant-Vazirani Theorem to the Probabilistic and Quantum Settings
In 1985, Valiant-Vazirani showed [VV85] that solving NP with the promise that "yes" instances have only one witness, is powerful enough to solve the entire NP class (under randomized reductions).We are interested in extending this result to the quantum setting. We prove extensions to the classes Merlin-Arthur (MA) and Quantum- Classical-Merlin-Arthur (QCMA) [AN02].Our results have implications on the complexity of approximating the ground state energy of a quantum local Hamiltonian with a unique ground state and an inverse polynomial spectral gap. We show that the estimation, within polynomial accuracy, of the ground state energy of poly-gapped 1-D local Hamiltonians is QCMA-hard, under randomized reductions. This is in strong contrast to the case of constant gapped 1-D Hamiltonians, which is in NP [Has07]. Moreover, it shows that unless QCMA can be reduced to NP by randomized reductions, there is no classical description of the ground state of every poly-gapped local Hamiltonian which allows the efficient calculation of expectation values.Finally, we conjecture that an analogous result to the class Quantum Merlin-Arthur(QMA) is impossible. This is formulated by separating between the two relavant classes, QMA and its "unique" version UQMA, using the definition by Aaronson and Kuperberg [AK06] of quantum oracles.
:: Mon 2/2/09, 11:45 in 4-331
Guifre Vidal (University of Queensland)
Recent Progress in Entanglement Renormalization
Entanglement Renormalization (ER) has been proposed as a real space renormalization group transformation for quantum lattice systems in D spatial dimensions [Phys. Rev. Lett. 99, 220405 (2007)]. Its main novelty is the use of disentanglers, namely unitary transformations that act accross a spin block boundary, to remove short-range entanglement from the system's ground state. In this talk I will first review the basic concepts underlying ER and then present a summary of the most recent results. Specifically, I intend to describe the simulation of lattice systems at a quantum critical point by exploiting scale invariance; and the simulation of two dimensional lattice systems that are beyond the reach of Monte Carlo sampling techniques, including spin models of frustrated antiferromagnets.
:: Mon 2/9/09, 4:30 in 4-237 (QIP seminar)
Matthew Hastings (Los Alamos National Laboratory)
A counter-example to additivity: using entanglement to boost communication capacity
Suppose Alice is using a noisy quantum channel to send classical information to Bob. For example, she might send single photons over a fiber optic line. How should she do this? In particular, should she use entanglement or should she send unentangled input states? The additivity conjecture in quantum information theory states that it is never useful for her to use entanglement. In fact, there are several related additivity conjectures, depending on the use of entanglement for different tasks. I will present a counter-example to one of these conjectures, the minimum output entropy conjecture, implying that all of these conjectures are false, and that in some circumstances Alice can increase the communication capacity by using entangled states.
:: Tue 2/17/09, 4:15 in 36-428 (QIP seminar)
Roland,Jeremie (NEC Laboratories America)
The communication complexity of non-signaling distributions
We study a model of communication complexity that encompasses many well-studied problems, including classical and quantum communication complexity, the complexity of simulating distributions arising from bipartite measurements of shared quantum states, and XOR games. In this model, Alice gets an input x, Bob gets an input y, and their goal is to each produce an output a,b distributed according to some pre-specified joint distribution p(a,b|x,y). Our results apply to any non-signaling distribution, that is, those where Alice's marginal distribution does not depend on Bob's input, and vice versa, therefore our techniques apply to any communication problem that can be reduced to a non-signaling distribution, including quantum distributions, Boolean and non-Boolean functions, most relations, partial (promise) problems, in the two-player and multipartite settings. We give elementary proofs and very intuitive interpretations of the recent lower bounds of Linial and Shraibman, which we generalize to the problem of simulating any non-signaling distribution. The lower bounds we obtain are also expressed as linear programs (or SDPs for quantum communication). We show that the dual formulations have a striking interpretation, since they coincide with maximum violations of Bell and Tsirelson inequalities. The dual expressions are closely related to the winning probability of XOR games. We show that as in the case of Boolean functions, the gap between the quantum and classical lower bounds is at most linear in size of the support of the distribution, and does not depend on the size of the inputs. This translates into a bound on the gap between maximal Bell and Tsirelson inequalities, which was previously known only for the case of Boolean outcomes with uniform marginals. Finally, we give an exponential upper bound on quantum and classical communication complexity in the simultaneous messages model, for any non-signaling distribution. One consequence of this is a simple proof that any quantum distribution can be approximated with a constant number of bits of communication. Joint work with:Julien Degorre, Marc Kaplan and Sophie Laplante
:: Mon 3/16/09, 4:15 in 36-428 (QIP seminar)
Aaronson,Scott (MIT)
The Power of Quantum Advice
I'll describe a powerful new result about quantum advice: namely, given any state rho on n qubits, there exists a local Hamiltonian H on poly(n) qubits (e.g., a sum of two-qubit interactions), such that *any* ground state of H can be used to simulate rho on all circuits of a fixed polynomial size. In terms of complexity classes, this implies that BQP/qpoly is contained in QMA/poly, superseding the previous result that BQP/qpoly is contained in PP/poly. Indeed, we can exactly characterize the /qpoly operator, as equivalent in power to *untrusted* quantum advice combined with trusted *classical* advice. The proof of this theorem relies on my previous result about the learnability of quantum states, as well as a new combinatorial result called the "majority-certificates lemma" that might be of independent interest. Joint work with Andrew Drucker.
:: Mon 3/30/09, 4:15 in 36-428 (QIP seminar)
Frederick Strauch (Williams College)
Quantum walks in the wild: perfect quantum state transfer with superconducting qubits
Superconducting quantum bits are artificial atoms that can be wired up into complex structures. I will present a theoretical proposal to implement perfect quantum state transfer between any two nodes of a hypercube network. This example of novel quantum transport in an artificial solid has many applications for quantum computing. It would also provide an experimental simulation of a continuous-time quantum walk with exponential speedup over the corresponding classical walk. This speedup is found to be remarkably robust to both decoherence and diagonal disorder, but only for certain (inefficient) representations of the hypercube.
:: Mon 4/13/09, 4:15 in 36-428 (QIP seminar)
Debbie Leung (University of Waterloo)
Continuity of quantum channel capacities
Many capacities of a quantum channel are given by expressions that involve asymptotically large number of uses of the channel, thus, there is no a priori reason for the capacities to be continuous. In this talk, we prove that the ability to transmit classical data, private classical data, quantum data are all continuous.
:: Mon 4/27/09, 4:15 in 34-401B (QIP seminar)
Smith,Graeme (IBM)
Quantum Communication With Zero-Quantum-Capacity Channels
Besides transmitting ordinary classical information, some quantum channels can faithfully transmit intact quantum states. A channel's capacity for such coherent transmission, its quantum capacity, is of central importance in quantum information theory as it measures the optimum performance of quantum error-correcting codes. I will show that two quantum channels, each of zero quantum capacity, can nevertheless achieve a positive quantum capacity when used together. This result contrasts sharply with the classical setting, where the capacity of a channel is independent of what other channels are available. This uniquely quantum effect unveils a rich structure in the theory of quantum communications and shows that there are several kinds of quantum information, the ability to transmit each of which is necessary but not sufficient for faithful quantum communication.
:: Mon 5/4/09, 4:15 in 36-428 (QIP seminar)
Broadbent,Anne (IQC)
Universal Blind Quantum Computation
We present a protocol which allows a client to have a server carry out a quantum computation for her such that the client's inputs, outputs and computation remain perfectly private, and where she does not require any quantum computational power or memory. The client only needs to be able to prepare single qubits randomly chosen from a finite set and send them to the server, who has the balance of the required quantum computational resources. Our protocol is interactive: after the initial preparation of quantum states, the client and server use two-way classical communication which enables the client to drive the computation, giving single- qubit measurement instructions to the server, depending on previous measurement outcomes. Our protocol works for inputs and outputs that are either classical or quantum. We give an authentication protocol that allows the client to detect an interfering server; our scheme can also be made fault-tolerant.
:: Tue 5/5/09, 4:00 in 26-214
Girvin,Steven (Yale)
Demonstration of entanglement on demand and two-qubit quantum algorithms in circuit QED
The 'circuit QED' architecture consists of Josephson junction qubits placed inside a coplanar waveguide microwave resonator. This talk will present an introduction to the quantum optics of these novel electrical circuits and describe recent experiments in the Schoelkopf lab at Yale. With the help of a controlled phase gate based on precision control and shaping of microwave pulses, it is now possible to achieve two-qubit entanglement on demand with concurrence up to 94% and to run the Grover search and Deutsch-Josza quantum algorithms with fidelities exceeding 80%. This success is based on a qubit design with long coherence times and the ability to simultaneously readout the state of two qubits (so far still with low fidelity).
:: Mon 5/11/09, 4:15 in 36-428 (QIP seminar)
Jordan,Stephen (Caltech)
Permutational Quantum Computation
In topological quantum computation the geometric details of a particle trajectory are irrelevant; only the topology matters. This is one reason for the inherent fault tolerance of topological quantum computation. I will describe a model in which this idea is taken one step further. Even the topology is irrelevant. The computation is determined solely by the permutation of the particles. Unlike topological quantum computation, which requires anyons, permutational quantum computations can in principle be performed by permuting ordinary spin-1/2 particles. It seems possible that permutational quantum computation is less powerful than standard quantum computation (BQP). Nevertheless I will present algorithms for this model which provide apparent exponential speedup over classical algorithms.
:: Mon 5/18/09, 4:15 in 36-428 (QIP seminar)
Navascues,Miguel (Imperial College London)
The power of symmetric extensions for entanglement detection
In this talk, I will analyze the speed of convergence of algorithms for entanglement detection based on PPT (Positive Partial Transpose) symmetric extensions, as conceived by Doherty et al. [1]. I will show that the states defined in [1] can be made separable just by partially depolarizing one of the parts. While the amount of necessary noise to induce separability on states that admit a plain N-symmetric extension decreases as O(1/N), the corresponding perturbation for states arising from PPT N-symmetric extensions decreases at least as O(1/N^2). I will use these results to estimate and compare the time and space complexity of both algorithms. Finally, I will consider the power of the PPT criterion alone: I will show how to derive upper bounds on the maximum possible distance between a PPT entangled state and the set of separable states by means of a simple construction. [1] A. C. Doherty, P. A. Parrilo and F. M. Spedalieri, Phys. Rev. A 69, 022308 (2004).
Summer School in Quantum Information Processing
Summer School in Quantum Information Processing
May 14 - 18, 2001
ABSTRACTS
Audio of the Lectures
Charles Bennett (IBM)
Degrees of Knowledge of a Quantum State
It is possible to "know" or "possess" a quantum state in infinitely many physically inequivalent ways, ranging from complete classical knowledge, through possession of of a single specimen of the state, to weaker and less compactly embodiable forms such as the ability to simulate the outcome of a single measurement on the state. We study the transformations of these degrees of knowledge, including "remote state preparation", in which a sender with complete classical knowledge of a state enables a receiver to create a single specimen of it in his lab.
Gilles Brassard ( Université de Montréal )
Quantum Cryptography
For ages, mathematicians have searched for a system that would allow two people to exchange messages in absolute secrecy. Around the middle of last century, Shannon proved that this dream is possible if and only if the legitimate participants share a random secret key as long as the message they wish to transmit. But Shannon's theorem did not take account of the quantum world in which we live. When information is appropriately encoded as quantum states, any attempt from an eavesdropper to access it yields partial information at best and entails a probability of spoiling it irreversibly. This unavoidable disturbance can be detected by the legitimate users. This phenomenon can be exploited to implement a cryptographic system that is unconditionally secure even against an eavesdropper with unlimited computing power and technology, with no need for a long shared secret key. This can be accomplished by the use of very faint pulses of polarized light that consist on the average of less than one photon. Alternatively, entanglement can be harnessed to the same cause. Sophisticated prototypes have been built in several countries, including England, Switzerland and the United States. In particular, the Swiss prototype work over 23 kilometres of ordinary optical fibre deployed beneath Lake Geneva. Another prototype, built at the Los Alamos National Laboratory, implements quantum cryptography on a free line-of-sight optical path, without any need for a waveguide. In the first lecture, I shall describe the basics of quantum cryptography and discuss the (in)security of some current prototypes. No prior knowledge of classical cryptography will be assumed.
The second lecture will concentrate on more theoretical issues. What advantages can there be to entanglement-based quantum cryptography? How can entanglement purification and quantum error correcting codes come to the rescue? But the main topic of the second lecture will concern quantum cryptography beyond the transmission of confidential information. Are there other tasks of a cryptographic nature that could benefit from quantum mechanics? For many years, the chief candidate was bit commitment, a primitive that would allow one person to commit to the value of a bit in a way that this value remains concealed until that person wishes to reveal it, at which time it is not possible to reveal a bit different from what had been sealed in the commitment. In particular, this primitive could be used to implement perfect zero-knowledge protocols and protect private information while it is being used to reach public decisions. It is obvious that unconditionally secure bit commitment cannot exist according to the laws of classical physics. Yet, hopes were high that a quantum version of this powerful primitive was possible, but they were striken down five years ago. Despite this setback, quantum mechanics does provide powerful tools for cryptography. For example, it allows for a coin tossing protocol in which neither party can make the coin fall on their chosen side with a probability better than 75%. Also, it allows for the computationally-secure distributed computation of functions on secret inputs under the only assumption that (quantum) one-way functions exist. (This assumption is believed to be too weak in a classical setting.) I shall discuss these results as well as other more recent work on quantum authentication, the secret transmission of quantum information, quantum digital signatures, etc.
We end with a speculation that the foundations of quantum mechanics can be laid on the understanding of which information processing tasks are possible (such as unconditionally secure confidential communication) and which are not (such as unconditionally secure bit commitment). Could it be that if God had wanted to provide His creatures with confidential communication but not with the ability to compute on secret data, then He had no choice but to invent quantum mechanics? Wouldn't that be a nicer foundation for quantum mechanics than the current cumbersome axioms?
Richard Cleve (Calgary)
Bell's theorem and Communication Complexity
A distributed information processing task is one where two or more physically separated parties each receive some input data and they are required to compute some quantities based on this data. A simple two-party example is where each party receives a binary string and their goal is to determine whether or not the strings are identical. It is clear that this particular task cannot be accomplished without some communication occuring between the parties. In comunication complexity, the amount of communication required to perform distributed information processing tasks is quantified.
Bells Theorem concerns distributed information processing tasks that, in terms of classical information, require communication, but which can be performed without any communication in the presence of quantum entanglement.
We explain Bell's Theorem and address the more general question of when quantum information can be used to reduce the communication complexity of distributed information processing tasks.
Peter Høyer (Calgary)
Introduction to Quantum Algorithms
This talk introduces to algorithms that are designed to run on quantum computers. We refer to such algorithms as quantum algorithms. Most known quantum algorithms share 2 characteristics: they are developed in the so-called black box model, and they are based on amplitude amplification and Fourier transforms. The black box model, which I introduce, will be discussed in detail by Ronald de Wolf later this week. I discuss and analyse some of the simplest quantum algorithms, most of which will be extended and generalized by Michele Mosca and Alain Tapp on Tuesday morning. No familiarity with quantum computation other than having actively attended Michael Nielsen's lectures is assumed.
Emanuel Knill (Los Alamos)
Fault-tolerant Quantum Error Correction
Scalable quantum computation requires robustness against errors. Robustness can be realized by using quantum error correction. I will give an elementary introduction to quantum error correction based on the notions of subsystems and error detection. The assumptions for scalable quantum computation will be stated and techniques for establishing threshold accuracies demonstrated.
1st lecture slides, and 2nd lecture slides ,
Please do not to print them! If you do, you'll get 40+ pages, most of which are virtually the same.
Raymond Laflamme (Los Alamos)
NMR Quantum Information Processing (pdf-slides)
Nuclear magnetic resonance (NMR) provides an experimental setting to explore physical implementations of quantum information processing (QIP). I will introduce the basic background for understanding applications of NMR to QIP and explain their current successes, limitations and potential. NMR spectroscopy is well known for its wealth of diverse coherent manipulations of spin dynamics. Ideas and instrumentation from liquid state NMR spectroscopy have been used to experiment with QIP. This approach has carried the field to a complexity of about 10 qubits, a small number for quantum computation but large enough for observing and better understanding the complexity of the quantum world. While liquid state NMR is the only present-day technology about to reach this number of qubits, further increases in complexity will require new methods. I will sketch one direction leading towards a scalable quantum computer using spin 1/2 particles. The next step in this program is a solid state NMR-based QIP capable of reaching 10-30 qubits.
Physical Implementations of Quantum Information Processors (pdf slides)
Quantum Information Processing (QIP) has been an active area of research bringing together many disciplines from the engineering to pure sciences. In my talk I will describe how some of the ideas of quantum information processing can be implemented using a variety of physical devices. Although today's devices are a small step towards what is needed for useful (QIP) they show that at least small quantum systems can reasonable controlled. I will stress the importance for better quantum control, a necessary requirement for scalability. I will also put forward the idea of common benchmarking methods to compare the achievements of the various physical devices. I will conclude with speculations of where the field might go in the future.
Daniel Lidar (Toronto)
Ion Trap and Quantum Dot Implementations
Certain electronic states in a trapped ion can be used as a qubit, and qubits can be coupled by collective vibrations of all ions. Ion traps are currently the most advanced experimentally implemented quantum computer systems, after NMR. Logic gates and decoherence avoidance has been demonstrated using 2 ions, and entanglement has been achieved involving 4 ions. The first half of this lecture will be a theoretical introduction to the Cirac-Zoller scheme for quantum computing using trapped ions, and a survey of the latest experiments. The second half will be devoted to a theoretical introduction to the quantum dots quantum computer proposal. The spin states of an excess electron trapped in a quantum dot can serve as a qubit, while qubits can be coupled through an exchange interaction between neighboring dots. The quantum dots implementation is considered to be one of the more promising scalable solid-state proposals for a quantum computer.
Michele Mosca (Waterloo)
Quantum Algorithms (click here for talk)
This talk will describe the most powerful known quantum algorithms. I will use the approach in [CEMM] http://xxx.lanl.gov/abs/quant-ph/9708016 , much of which is based on the approach of Kitaev in http://xxx.lanl.gov/abs/quant-ph/9511026 .
The task of approximating a phase rotation can be formulated as a computational problem; I will show how the quantum Fourier transform can be used to perform this approximation. I will show how such phase rotations can be produced as a result of an eigenvalue "kicked back" by a computation involving an auxiliary register. Lastly I will show how efficient eigenvalue estimation leads to efficient quantum factorization; this approach complements the original approach of Shor, and when reformulated as done in CEMM produces the same quantum network.
I will summarize the application of these methods to the Hidden Subgroup Problem, and the Hidden Affine Function problem.
Michael Nielsen (Queensland)
Introduction to quantum mechanics and quantum information science
In these lectures I introduce the basic notions of quantum mechanics, illustrated through simple examples drawn from quantum computation and quantum information. The only prerequisite is a grasp of basic linear algebra. No previous acquantaince with quantum mechanics is necessary.
1st Lecture slides in pdf format or Postscript
2nd Lecture slides in pdf format or Postscript
3rd Lecture slides in pdf format or Postscript
Peter Shor (AT&T)
Quantum Computing
Quantum computers are hypothetical devices which use the principles of quantum mechanics to perform computations. For some difficult computational problems, including the cryptographically important problems of prime factorization and finding discrete logarithms, the best algorithms known for classical computers are exponentially slower than the algorithms known for quantim computers. Although they have not yet been built, quantum computers do not appear to violate any fundamental principles of physics. I will explain how quantum mechanics provides this extra computational power, and outline the factoring algorithm.
Capacities of Quantum Channels
The classical theorem of Shannon from 1948 gives a simple formula for how much information can be sent through a communication channel. When we try to extend this formula to the quantum regime, we find that there is no longer a unique way to define channel capacity. We can define one capacity of a channel for transmitting classical information, and another for transmitting quantum information. To further complicate the situation, these quantum channel capacities will sometimes be changed by giving the sender and receiver additional capabilities which do not change the classical capacity (e.g., shared entanglement or a back channel from the receiver to the sender). However, there do seem to be a small number of interesting quantum channel capacities, and many of them seem to be quantifiable by analogs of Shannon's formula. We survey these capacities, and give proven and conjectured analogs of Shannon's formula for many of them.
Newsletter article
Aephraim Steinberg (Toronto)
Experiments with Entangled Photons
Much of the power of quantum mechanical systems for handling information stems from the unusual sorts of correlations, or "entanglement," which may exist between quantum particles. Entangled photons have long been a topic of intense experimental investigation. At first, this was in order to address foundational questions about locality and determinism, through the famous Einstein-Podolsky-Rosen "paradox" and Bell's inequalities. More recently, these states have been applied in a variety of quantum information schemes. At the moment, photons appear to be ideal carriers of information, for use in cryptography and teleportation, but have certain weaknesses which make them less attractive for use in quantum computers. Nevertheless, entangled photon states are likely to be important in any future quantum- information technology. I will try to introduce the basic quantum-mechanical concepts which govern the behaviour of photons, by describing a number of important and surprising experiments in the field. We will see some of the practical issues which arise in this physical implementation of quantum information, and touch upon the prospects for the direct application of photons in quantum computation.
Alain Tapp (Waterloo)
Quantum Searching and Generalizations
In 1996 Lov Grover gave the foundation of an exciting new algorithm for quantum computers. One of the most important classes of problems in computer science is the class NP. Roughly speaking it addresses all the problems that can be stated the following way. We have a function F:{0,1}^n -> {0,1} and an efficient classical algorithm that computes it. The problem is to find x such that F(x)=1. Sometimes there is an efficient solution to this problem but in general it is very hard.There are literally hundreds of problems that can be put in this hard class, from areas including optimization, scheduling, cryptography, theorem proving, combinatorics, etc. The most efficient algorithms that can solve this problem have a running time proportional to the number of possible inputs x which is in O(2^n). Grover sketched an algorithm that solves the general problem in a time proportional to the square root of the number of inputs x, which is in O(2^(n/2)). In this talk I will discuss the generalization of Grover's algorithm discussed by Boyer, Brassard, Hoyer and Tapp. I will also present the algorithm proposed by Brassard, Hoyer, Mosca and Tapp that probabilistically counts the number of solution.
Barbara Terhal (IBM)
Simulating Physical Systems of a Quantum Computer
One of the greatest and earliest mentioned promises of a quantum computer lies in its ability to simulate physical systems. In order to realize this promise, one must analyze how the structure and the dynamics of physical quantum systems can be mapped onto the architecture of a quantum computer.
I will treat various types of quantum systems for which it has been found that they can be efficiently simulated on a quantum computer. These are tensorproduct systems with local degrees of freedom, some continuous conjugate variable systems, some 'unphysical' Hamiltonians and fermionic quantum systems.
References:
* M.A. Nielsen and I.L. Chuang, "Quantum Computation and Quantum Information," Cambridge University Press (2000).
Simulating systems with small local degrees of freedom:
* R.P. Feynman, Simulating Physics with Computers, Int. J. Theor. Phys. 21 (1982), 467-488.
* S. Lloyd, Universal Quantum Simulators, Science 273 (1996), 1073.
Simulating the Schrödinger equation for systems with conjugate variables:
* C. Zalka, Simulating quantum systems on a quantum computer, Proc. R. Soc. London A 454 (1998), 313-322.
* S. Wiesner, Simulations of Many-Body Quantum Systems by a Quantum Computer, quant-ph/9603028.
Simulating fermionic quantum systems:
* D.S. Abrams and S. Lloyd, Simulation of Many-Body Fermi Systems on a Universal Quantum Computer, Phys. Rev. Lett. 79 (1997), 2586-2589.
* S. Bravyi and A. Kitaev, Fermionic qantum computation, quant-ph/0003137.
* G. Ortiz, J.E. Gubernatis, E. Knill and R. Laflamme, Quantum Algorithms for Fermionic Simulations, quant-ph/0012334.
Further reading:
Simulating noisy systems, thermal equilibration and calculating correlations functions:
* B.M. Terhal and D.P. DiVincenzo, The problem of equilibriation and the computation of correlation functions on a quantum computer, Phys. Rev. A. 61 (2000), 022301/1-22.
Umesh Vazirani (Berkeley)
How Powerful is Adiabatic Quantum Computation?
Recently, Farhi et al. have proposed a novel paradigm for the design of quantum algorithms - via quantum adiabatic evolution. We analyze the computational power and limitations of such adiabatic quantum algorithms. Joint work with Wim van Dam and Mike Mosca.
John Watrous (Calgary)
Quantum Interactive Proof Systems
Interactive proof systems were first introduced in 1985, both as a natural extension of the class NP and as a model for various cryptographic situations. An interactive proof system consists of two interacting parties: a computationally unbounded prover and a polynomial-time verifier. The prover attempts to prove to the verifier that a given input string satisfies some property, while the verifier tries to determine the validity of this proof.
Quantum interactive proof systems are interactive proof systems in which the prover and verifier may perform quantum computations and exchange quantum messages. In this talk I will survey some of the known facts about quantum interactive proof systems, and discuss some of the tools that are helpful for analyzing their properties.
Ronald de Wolf (CWI and University of Amsterdam)
Quantum Lower Bounds
Few quantum algorithms are known to date, and virtually all of them make use of "queries" in some form or other. In the query or "black-box" model of computation, an N-bit input x is given as a black-box that returns the i-th bit of the input x when queried on i. The aim is then to compute some function f(x) of the input, using as few queries as possible. A quantum computer has the advantage that it can query many i-s in superposition. The quantum algorithms of Deutsch and Jozsa, Simon, Grover, and Shor's period-finding can all be cast in this model and provably require far fewer queries than their classical counterparts. It thus appears that the notion of query complexity captures a significant part of the power of quantum computing, and it makes sense to look at the limits of quantum computers in this model. In the last 3 years, significant progress has been made with respect to lower bounds on query complexity of quantum algorithms (in contrast to proving lower bounds on circuit complexity of quantum algorithms, which immediately runs into P vs NP type problems). In this talk we will survey the main lower bounds on quantum query complexity that have been obtained. We focus on two general methods: (1) the "polynomial method" of Beals, Buhrman, Cleve, Mosca, de Wolf, which in particular implies that exponential quantum-classical separations only occur for "promise problems", and (2) the "quantum adversary method" of Ambainis
May 14 - 18, 2001
ABSTRACTS
Audio of the Lectures
Charles Bennett (IBM)
Degrees of Knowledge of a Quantum State
It is possible to "know" or "possess" a quantum state in infinitely many physically inequivalent ways, ranging from complete classical knowledge, through possession of of a single specimen of the state, to weaker and less compactly embodiable forms such as the ability to simulate the outcome of a single measurement on the state. We study the transformations of these degrees of knowledge, including "remote state preparation", in which a sender with complete classical knowledge of a state enables a receiver to create a single specimen of it in his lab.
Gilles Brassard ( Université de Montréal )
Quantum Cryptography
For ages, mathematicians have searched for a system that would allow two people to exchange messages in absolute secrecy. Around the middle of last century, Shannon proved that this dream is possible if and only if the legitimate participants share a random secret key as long as the message they wish to transmit. But Shannon's theorem did not take account of the quantum world in which we live. When information is appropriately encoded as quantum states, any attempt from an eavesdropper to access it yields partial information at best and entails a probability of spoiling it irreversibly. This unavoidable disturbance can be detected by the legitimate users. This phenomenon can be exploited to implement a cryptographic system that is unconditionally secure even against an eavesdropper with unlimited computing power and technology, with no need for a long shared secret key. This can be accomplished by the use of very faint pulses of polarized light that consist on the average of less than one photon. Alternatively, entanglement can be harnessed to the same cause. Sophisticated prototypes have been built in several countries, including England, Switzerland and the United States. In particular, the Swiss prototype work over 23 kilometres of ordinary optical fibre deployed beneath Lake Geneva. Another prototype, built at the Los Alamos National Laboratory, implements quantum cryptography on a free line-of-sight optical path, without any need for a waveguide. In the first lecture, I shall describe the basics of quantum cryptography and discuss the (in)security of some current prototypes. No prior knowledge of classical cryptography will be assumed.
The second lecture will concentrate on more theoretical issues. What advantages can there be to entanglement-based quantum cryptography? How can entanglement purification and quantum error correcting codes come to the rescue? But the main topic of the second lecture will concern quantum cryptography beyond the transmission of confidential information. Are there other tasks of a cryptographic nature that could benefit from quantum mechanics? For many years, the chief candidate was bit commitment, a primitive that would allow one person to commit to the value of a bit in a way that this value remains concealed until that person wishes to reveal it, at which time it is not possible to reveal a bit different from what had been sealed in the commitment. In particular, this primitive could be used to implement perfect zero-knowledge protocols and protect private information while it is being used to reach public decisions. It is obvious that unconditionally secure bit commitment cannot exist according to the laws of classical physics. Yet, hopes were high that a quantum version of this powerful primitive was possible, but they were striken down five years ago. Despite this setback, quantum mechanics does provide powerful tools for cryptography. For example, it allows for a coin tossing protocol in which neither party can make the coin fall on their chosen side with a probability better than 75%. Also, it allows for the computationally-secure distributed computation of functions on secret inputs under the only assumption that (quantum) one-way functions exist. (This assumption is believed to be too weak in a classical setting.) I shall discuss these results as well as other more recent work on quantum authentication, the secret transmission of quantum information, quantum digital signatures, etc.
We end with a speculation that the foundations of quantum mechanics can be laid on the understanding of which information processing tasks are possible (such as unconditionally secure confidential communication) and which are not (such as unconditionally secure bit commitment). Could it be that if God had wanted to provide His creatures with confidential communication but not with the ability to compute on secret data, then He had no choice but to invent quantum mechanics? Wouldn't that be a nicer foundation for quantum mechanics than the current cumbersome axioms?
Richard Cleve (Calgary)
Bell's theorem and Communication Complexity
A distributed information processing task is one where two or more physically separated parties each receive some input data and they are required to compute some quantities based on this data. A simple two-party example is where each party receives a binary string and their goal is to determine whether or not the strings are identical. It is clear that this particular task cannot be accomplished without some communication occuring between the parties. In comunication complexity, the amount of communication required to perform distributed information processing tasks is quantified.
Bells Theorem concerns distributed information processing tasks that, in terms of classical information, require communication, but which can be performed without any communication in the presence of quantum entanglement.
We explain Bell's Theorem and address the more general question of when quantum information can be used to reduce the communication complexity of distributed information processing tasks.
Peter Høyer (Calgary)
Introduction to Quantum Algorithms
This talk introduces to algorithms that are designed to run on quantum computers. We refer to such algorithms as quantum algorithms. Most known quantum algorithms share 2 characteristics: they are developed in the so-called black box model, and they are based on amplitude amplification and Fourier transforms. The black box model, which I introduce, will be discussed in detail by Ronald de Wolf later this week. I discuss and analyse some of the simplest quantum algorithms, most of which will be extended and generalized by Michele Mosca and Alain Tapp on Tuesday morning. No familiarity with quantum computation other than having actively attended Michael Nielsen's lectures is assumed.
Emanuel Knill (Los Alamos)
Fault-tolerant Quantum Error Correction
Scalable quantum computation requires robustness against errors. Robustness can be realized by using quantum error correction. I will give an elementary introduction to quantum error correction based on the notions of subsystems and error detection. The assumptions for scalable quantum computation will be stated and techniques for establishing threshold accuracies demonstrated.
1st lecture slides, and 2nd lecture slides ,
Please do not to print them! If you do, you'll get 40+ pages, most of which are virtually the same.
Raymond Laflamme (Los Alamos)
NMR Quantum Information Processing (pdf-slides)
Nuclear magnetic resonance (NMR) provides an experimental setting to explore physical implementations of quantum information processing (QIP). I will introduce the basic background for understanding applications of NMR to QIP and explain their current successes, limitations and potential. NMR spectroscopy is well known for its wealth of diverse coherent manipulations of spin dynamics. Ideas and instrumentation from liquid state NMR spectroscopy have been used to experiment with QIP. This approach has carried the field to a complexity of about 10 qubits, a small number for quantum computation but large enough for observing and better understanding the complexity of the quantum world. While liquid state NMR is the only present-day technology about to reach this number of qubits, further increases in complexity will require new methods. I will sketch one direction leading towards a scalable quantum computer using spin 1/2 particles. The next step in this program is a solid state NMR-based QIP capable of reaching 10-30 qubits.
Physical Implementations of Quantum Information Processors (pdf slides)
Quantum Information Processing (QIP) has been an active area of research bringing together many disciplines from the engineering to pure sciences. In my talk I will describe how some of the ideas of quantum information processing can be implemented using a variety of physical devices. Although today's devices are a small step towards what is needed for useful (QIP) they show that at least small quantum systems can reasonable controlled. I will stress the importance for better quantum control, a necessary requirement for scalability. I will also put forward the idea of common benchmarking methods to compare the achievements of the various physical devices. I will conclude with speculations of where the field might go in the future.
Daniel Lidar (Toronto)
Ion Trap and Quantum Dot Implementations
Certain electronic states in a trapped ion can be used as a qubit, and qubits can be coupled by collective vibrations of all ions. Ion traps are currently the most advanced experimentally implemented quantum computer systems, after NMR. Logic gates and decoherence avoidance has been demonstrated using 2 ions, and entanglement has been achieved involving 4 ions. The first half of this lecture will be a theoretical introduction to the Cirac-Zoller scheme for quantum computing using trapped ions, and a survey of the latest experiments. The second half will be devoted to a theoretical introduction to the quantum dots quantum computer proposal. The spin states of an excess electron trapped in a quantum dot can serve as a qubit, while qubits can be coupled through an exchange interaction between neighboring dots. The quantum dots implementation is considered to be one of the more promising scalable solid-state proposals for a quantum computer.
Michele Mosca (Waterloo)
Quantum Algorithms (click here for talk)
This talk will describe the most powerful known quantum algorithms. I will use the approach in [CEMM] http://xxx.lanl.gov/abs/quant-ph/9708016 , much of which is based on the approach of Kitaev in http://xxx.lanl.gov/abs/quant-ph/9511026 .
The task of approximating a phase rotation can be formulated as a computational problem; I will show how the quantum Fourier transform can be used to perform this approximation. I will show how such phase rotations can be produced as a result of an eigenvalue "kicked back" by a computation involving an auxiliary register. Lastly I will show how efficient eigenvalue estimation leads to efficient quantum factorization; this approach complements the original approach of Shor, and when reformulated as done in CEMM produces the same quantum network.
I will summarize the application of these methods to the Hidden Subgroup Problem, and the Hidden Affine Function problem.
Michael Nielsen (Queensland)
Introduction to quantum mechanics and quantum information science
In these lectures I introduce the basic notions of quantum mechanics, illustrated through simple examples drawn from quantum computation and quantum information. The only prerequisite is a grasp of basic linear algebra. No previous acquantaince with quantum mechanics is necessary.
1st Lecture slides in pdf format or Postscript
2nd Lecture slides in pdf format or Postscript
3rd Lecture slides in pdf format or Postscript
Peter Shor (AT&T)
Quantum Computing
Quantum computers are hypothetical devices which use the principles of quantum mechanics to perform computations. For some difficult computational problems, including the cryptographically important problems of prime factorization and finding discrete logarithms, the best algorithms known for classical computers are exponentially slower than the algorithms known for quantim computers. Although they have not yet been built, quantum computers do not appear to violate any fundamental principles of physics. I will explain how quantum mechanics provides this extra computational power, and outline the factoring algorithm.
Capacities of Quantum Channels
The classical theorem of Shannon from 1948 gives a simple formula for how much information can be sent through a communication channel. When we try to extend this formula to the quantum regime, we find that there is no longer a unique way to define channel capacity. We can define one capacity of a channel for transmitting classical information, and another for transmitting quantum information. To further complicate the situation, these quantum channel capacities will sometimes be changed by giving the sender and receiver additional capabilities which do not change the classical capacity (e.g., shared entanglement or a back channel from the receiver to the sender). However, there do seem to be a small number of interesting quantum channel capacities, and many of them seem to be quantifiable by analogs of Shannon's formula. We survey these capacities, and give proven and conjectured analogs of Shannon's formula for many of them.
Newsletter article
Aephraim Steinberg (Toronto)
Experiments with Entangled Photons
Much of the power of quantum mechanical systems for handling information stems from the unusual sorts of correlations, or "entanglement," which may exist between quantum particles. Entangled photons have long been a topic of intense experimental investigation. At first, this was in order to address foundational questions about locality and determinism, through the famous Einstein-Podolsky-Rosen "paradox" and Bell's inequalities. More recently, these states have been applied in a variety of quantum information schemes. At the moment, photons appear to be ideal carriers of information, for use in cryptography and teleportation, but have certain weaknesses which make them less attractive for use in quantum computers. Nevertheless, entangled photon states are likely to be important in any future quantum- information technology. I will try to introduce the basic quantum-mechanical concepts which govern the behaviour of photons, by describing a number of important and surprising experiments in the field. We will see some of the practical issues which arise in this physical implementation of quantum information, and touch upon the prospects for the direct application of photons in quantum computation.
Alain Tapp (Waterloo)
Quantum Searching and Generalizations
In 1996 Lov Grover gave the foundation of an exciting new algorithm for quantum computers. One of the most important classes of problems in computer science is the class NP. Roughly speaking it addresses all the problems that can be stated the following way. We have a function F:{0,1}^n -> {0,1} and an efficient classical algorithm that computes it. The problem is to find x such that F(x)=1. Sometimes there is an efficient solution to this problem but in general it is very hard.There are literally hundreds of problems that can be put in this hard class, from areas including optimization, scheduling, cryptography, theorem proving, combinatorics, etc. The most efficient algorithms that can solve this problem have a running time proportional to the number of possible inputs x which is in O(2^n). Grover sketched an algorithm that solves the general problem in a time proportional to the square root of the number of inputs x, which is in O(2^(n/2)). In this talk I will discuss the generalization of Grover's algorithm discussed by Boyer, Brassard, Hoyer and Tapp. I will also present the algorithm proposed by Brassard, Hoyer, Mosca and Tapp that probabilistically counts the number of solution.
Barbara Terhal (IBM)
Simulating Physical Systems of a Quantum Computer
One of the greatest and earliest mentioned promises of a quantum computer lies in its ability to simulate physical systems. In order to realize this promise, one must analyze how the structure and the dynamics of physical quantum systems can be mapped onto the architecture of a quantum computer.
I will treat various types of quantum systems for which it has been found that they can be efficiently simulated on a quantum computer. These are tensorproduct systems with local degrees of freedom, some continuous conjugate variable systems, some 'unphysical' Hamiltonians and fermionic quantum systems.
References:
* M.A. Nielsen and I.L. Chuang, "Quantum Computation and Quantum Information," Cambridge University Press (2000).
Simulating systems with small local degrees of freedom:
* R.P. Feynman, Simulating Physics with Computers, Int. J. Theor. Phys. 21 (1982), 467-488.
* S. Lloyd, Universal Quantum Simulators, Science 273 (1996), 1073.
Simulating the Schrödinger equation for systems with conjugate variables:
* C. Zalka, Simulating quantum systems on a quantum computer, Proc. R. Soc. London A 454 (1998), 313-322.
* S. Wiesner, Simulations of Many-Body Quantum Systems by a Quantum Computer, quant-ph/9603028.
Simulating fermionic quantum systems:
* D.S. Abrams and S. Lloyd, Simulation of Many-Body Fermi Systems on a Universal Quantum Computer, Phys. Rev. Lett. 79 (1997), 2586-2589.
* S. Bravyi and A. Kitaev, Fermionic qantum computation, quant-ph/0003137.
* G. Ortiz, J.E. Gubernatis, E. Knill and R. Laflamme, Quantum Algorithms for Fermionic Simulations, quant-ph/0012334.
Further reading:
Simulating noisy systems, thermal equilibration and calculating correlations functions:
* B.M. Terhal and D.P. DiVincenzo, The problem of equilibriation and the computation of correlation functions on a quantum computer, Phys. Rev. A. 61 (2000), 022301/1-22.
Umesh Vazirani (Berkeley)
How Powerful is Adiabatic Quantum Computation?
Recently, Farhi et al. have proposed a novel paradigm for the design of quantum algorithms - via quantum adiabatic evolution. We analyze the computational power and limitations of such adiabatic quantum algorithms. Joint work with Wim van Dam and Mike Mosca.
John Watrous (Calgary)
Quantum Interactive Proof Systems
Interactive proof systems were first introduced in 1985, both as a natural extension of the class NP and as a model for various cryptographic situations. An interactive proof system consists of two interacting parties: a computationally unbounded prover and a polynomial-time verifier. The prover attempts to prove to the verifier that a given input string satisfies some property, while the verifier tries to determine the validity of this proof.
Quantum interactive proof systems are interactive proof systems in which the prover and verifier may perform quantum computations and exchange quantum messages. In this talk I will survey some of the known facts about quantum interactive proof systems, and discuss some of the tools that are helpful for analyzing their properties.
Ronald de Wolf (CWI and University of Amsterdam)
Quantum Lower Bounds
Few quantum algorithms are known to date, and virtually all of them make use of "queries" in some form or other. In the query or "black-box" model of computation, an N-bit input x is given as a black-box that returns the i-th bit of the input x when queried on i. The aim is then to compute some function f(x) of the input, using as few queries as possible. A quantum computer has the advantage that it can query many i-s in superposition. The quantum algorithms of Deutsch and Jozsa, Simon, Grover, and Shor's period-finding can all be cast in this model and provably require far fewer queries than their classical counterparts. It thus appears that the notion of query complexity captures a significant part of the power of quantum computing, and it makes sense to look at the limits of quantum computers in this model. In the last 3 years, significant progress has been made with respect to lower bounds on query complexity of quantum algorithms (in contrast to proving lower bounds on circuit complexity of quantum algorithms, which immediately runs into P vs NP type problems). In this talk we will survey the main lower bounds on quantum query complexity that have been obtained. We focus on two general methods: (1) the "polynomial method" of Beals, Buhrman, Cleve, Mosca, de Wolf, which in particular implies that exponential quantum-classical separations only occur for "promise problems", and (2) the "quantum adversary method" of Ambainis
cita: La educacion cientifica
4
Gil Perez, Daniel; Gavidia Catalan, Valentin; Vilches Peña, Amparo; Martinez Torregrosa, Joaquin. La educacion cientifica ante las actuales transformaciones cientifico-tecnologicas. Didáctica de las Ciencias Experimentales y Sociales. 1998, , 12: 43-63
Gil Perez, Daniel; Gavidia Catalan, Valentin; Vilches Peña, Amparo; Martinez Torregrosa, Joaquin. La educacion cientifica ante las actuales transformaciones cientifico-tecnologicas. Didáctica de las Ciencias Experimentales y Sociales. 1998, , 12: 43-63
More IQS, Less IQ
Conductism, based in reductionism as IQ, is going astray as we wellcome the systemic revolution ahead.
IQS (Intensactive Quantum Science) is fed by theories that complement (inclusive) all the IQ story. If all people are different, because their genetics and their life-experience, and if Multiple Inteligence is sprouting more and more, with many other systemic theories, IQ would be considered as a "Semantic Island", where only one kind of inteligence is included.
IQS (Intensactive Quantum Science) is fed by theories that complement (inclusive) all the IQ story. If all people are different, because their genetics and their life-experience, and if Multiple Inteligence is sprouting more and more, with many other systemic theories, IQ would be considered as a "Semantic Island", where only one kind of inteligence is included.
And the Guay Gueby Gueb?
The Guay Gueby Gueb is also a symbiont growing inside these three holons (see previous post): 1)Google, 2)Internet and 3)Knowledge Society.
In this "bacterium" we call Guay Gueby Gueb, processes flow at a special rate, because the openness and freedom in cooperation. In this way GGGueb has learned very much from two colective experiences: The ong I.S.M.A., as an open-actor/ress community; and the experience, from 2006, in the first "Gueby" developped when the survival of Los Baños del Carmen, an old forested-sea-balneary in the city of Málaga, were in question. We needed an internet tool to share among the "Asamblea Balne" and Salvador Espada chose the "GMAIL" format. Easy to use, efficient as bikes, and powerfull for our aims.
With time, that Gueby experience of "asambleabalneATgmail.com" increased and reproduced, giving birth to other Guebys of the same format, to following experimentation in this easy way. We used and use GMAIL as blog, mailinglits, chat, wihi...and so on. Of course some profesional-minded internautas was looking without interest to our guebys. But today we can say that the experience have matured enough to consider the gueby-networking (including wikis and blogs too) as a platform that explain, by its use and by its "fluid structure" our success building this IQS
In this "bacterium" we call Guay Gueby Gueb, processes flow at a special rate, because the openness and freedom in cooperation. In this way GGGueb has learned very much from two colective experiences: The ong I.S.M.A., as an open-actor/ress community; and the experience, from 2006, in the first "Gueby" developped when the survival of Los Baños del Carmen, an old forested-sea-balneary in the city of Málaga, were in question. We needed an internet tool to share among the "Asamblea Balne" and Salvador Espada chose the "GMAIL" format. Easy to use, efficient as bikes, and powerfull for our aims.
With time, that Gueby experience of "asambleabalneATgmail.com" increased and reproduced, giving birth to other Guebys of the same format, to following experimentation in this easy way. We used and use GMAIL as blog, mailinglits, chat, wihi...and so on. Of course some profesional-minded internautas was looking without interest to our guebys. But today we can say that the experience have matured enough to consider the gueby-networking (including wikis and blogs too) as a platform that explain, by its use and by its "fluid structure" our success building this IQS
Internet is a Eucaryotic Cell. Google a Endosymbiont
Internet is a network created in our knowledge society.
Systemicaly can be compared to a Eucaryotic Cell. As that, Internet interacts with ecosystem (nowledge society) creating and growing within itself autopoyeticaly.
Google maybe a mitochondrion, inside Internet, inside Knowledge-Society-Ecosystem.
As a mitochondrion, Google is also changing in autopoyesis, fed by and feeding the Eucaryotic Cell (Internet) within where Google is developping.
To speak of Google is to speak abut a big corporation that works mainly by zeronomics (zero-cost economics), as so many internet-based companies.
Systemicaly can be compared to a Eucaryotic Cell. As that, Internet interacts with ecosystem (nowledge society) creating and growing within itself autopoyeticaly.
Google maybe a mitochondrion, inside Internet, inside Knowledge-Society-Ecosystem.
As a mitochondrion, Google is also changing in autopoyesis, fed by and feeding the Eucaryotic Cell (Internet) within where Google is developping.
To speak of Google is to speak abut a big corporation that works mainly by zeronomics (zero-cost economics), as so many internet-based companies.
Zero Knowledge... Looks fine!
10.
John Watrous: Zero Knowledge In Our Quantum Future | SCS | UW
- [ Traducir esta página ]
9 Feb 2007 ... John Watrous: Zero Knowledge In Our Quantum Future ... Professor Watrous joined Waterloo's School of Computer Science in July, 2006. ... proof or zero-knowledge protocol is an interactive method for one party to prove to ...
www.cs.uwaterloo.ca/about/features/2007/watrous - En caché - Páginas similares
John Watrous: Zero Knowledge In Our Quantum Future | SCS | UW
- [ Traducir esta página ]
9 Feb 2007 ... John Watrous: Zero Knowledge In Our Quantum Future ... Professor Watrous joined Waterloo's School of Computer Science in July, 2006. ... proof or zero-knowledge protocol is an interactive method for one party to prove to ...
www.cs.uwaterloo.ca/about/features/2007/watrous - En caché - Páginas similares
What is a symbiopoyetic blog
This blog, as others, is a experimental blog.
In a experimental blog, according to networking or systemic approach, its (symbiopoyetic) construction, step by step, is maintained in the blog.
For example here we have made different search in the web that are included as different posts.
Actualy we try to prepare a paper for "Futures"@ Elsevier. The title will probably be the same of this blog.
As ideas are coming in free way on our mind, we are writing with the confidence from our experience in this way.
When working in transdiciplinary grounds, any idea can be of importance. The two complementary processes present in a trandiciplinary mind are: Integration-And-Desintegration.
In the level of this text this double-and-complementary-process imply to try to include a critical mass of interesting convincing ideas in order to be accepted by the editors.
The draft style of many of our texts in internet are symtomps of the open process of integration and desintegration that rules our transdisiciplinary or polymathic endeavour.
In a experimental blog, according to networking or systemic approach, its (symbiopoyetic) construction, step by step, is maintained in the blog.
For example here we have made different search in the web that are included as different posts.
Actualy we try to prepare a paper for "Futures"@ Elsevier. The title will probably be the same of this blog.
As ideas are coming in free way on our mind, we are writing with the confidence from our experience in this way.
When working in transdiciplinary grounds, any idea can be of importance. The two complementary processes present in a trandiciplinary mind are: Integration-And-Desintegration.
In the level of this text this double-and-complementary-process imply to try to include a critical mass of interesting convincing ideas in order to be accepted by the editors.
The draft style of many of our texts in internet are symtomps of the open process of integration and desintegration that rules our transdisiciplinary or polymathic endeavour.
Futures. The journal of policy, planning and futures studies
Futures® is an international, refereed, multidisciplinary journal concerned with medium and long-term futures of cultures and societies, science and technology, economics and politics, environment and the planet and individuals and humanity. Covering methods and practices of futures studies, the journal seeks to examine possible and alternative futures of all human endeavours. Futures® seeks to promote divergent and pluralistic visions, ideas and opinions about the future. The editors do not necessarily agree with the views expressed in the pages of Futures®.
entrepreneurial:
I wonders looking the particle (meme) "neurial" in this word. I will try to add a etymological search...
entrepreneurial:
English definition | in French | in Italian | in Portuguese
conjugator | in context | images
entrepreneurial empresarial
entrepreneurial nm emprendedor
Forum discussions with the word(s) "entrepreneurial" in the title:
entrepreneurial
entrepreneurial
entrepreneurial birth/ mortality - financial
Entrepreneurial companies
entrepreneurial spirit
entrepreneurial venture
entrepreneurial ventures
I am a person with entrepreneurial spirit - grammar
wildly entrepreneurial and fiercely independent in spirit
* Ask in the forums yourself.
* Visit the Spanish-English Forum.
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entrepreneurial
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TransMeme
A "transmeme" is a special kind of nomadic "gene" (gyn) fertilizing symbiopoyeticaly different fields of knowledge.
One research-group may be considered a memetic organism.
After years of systemic "invasion" of systemic-thinking-and-practise in more and more societal spaces, we can defend that "systems-thinking has won".
At non-university education, different reforms have produced "a fresh air" of systemic thinking and learning.
At entrepreneurial level, systems science is also well extended. Corporations are networking organism interrelated with other population of networks.
But it is at university level where hiperspecialization seemed to habe obscured the good systemic records we have from the other societal levels.
What happens in universities? Ous (systemic) opinion is that universities actualy offers "the two faces of the coin". It is evident, when we criticaly approach to the static and hierarchical structure of the conventional classroom, that system thinking is not very extended in universities. But universities are organisms very diverse among themselves. The same we could say about the "invasion" of Information and Communication Technologies. According to the university "x" or "y", we will find a different level of university "invasion".
The point here, independently of these argument, it is that the extended development of many systemic theories in many fields of knowledge, has produced according to our opinion a critical mass of systemic theories.
These systemic theories are a kind of "gyn" or "transmeme", because their mere existence augures a high-speed contagion among many other "distant" disciplines.
We must take in account the native digital revolution that is increasing every year. Nowadays life of Native-Digital is marked by a literal embodiment in these new technologies. In that way our results were predictable because all these technologies function as networks. By this reason, all these Native Digital generations modulates their life to the system thinking and action approach embeded in all these technologies.
By this reason we have no problem at all with the Inmigrant Digital population that, susprisingly, are still in the process of partial incorporation to these technologies. Among these Inmigrant Digital are many university teacher whose research is closest to lineal-thinking than system-thinking.
So, this systemic revolution has been produced, in symbiosis, by different societal grups of actors/actress. In the "archipelago" of today scientific tribal endeavour, we assist to a significant sprouting of systemic theories.
By their integrative character, systemic theories may be applied to many other fields of knowledge. The sucessive interaction within different systemic theories increase mutually their power "to jump" or "surfing" accross many fields of knowledge. This contagion among disciplines by systemic theories act as "reticular-bossoms".
One research-group may be considered a memetic organism.
After years of systemic "invasion" of systemic-thinking-and-practise in more and more societal spaces, we can defend that "systems-thinking has won".
At non-university education, different reforms have produced "a fresh air" of systemic thinking and learning.
At entrepreneurial level, systems science is also well extended. Corporations are networking organism interrelated with other population of networks.
But it is at university level where hiperspecialization seemed to habe obscured the good systemic records we have from the other societal levels.
What happens in universities? Ous (systemic) opinion is that universities actualy offers "the two faces of the coin". It is evident, when we criticaly approach to the static and hierarchical structure of the conventional classroom, that system thinking is not very extended in universities. But universities are organisms very diverse among themselves. The same we could say about the "invasion" of Information and Communication Technologies. According to the university "x" or "y", we will find a different level of university "invasion".
The point here, independently of these argument, it is that the extended development of many systemic theories in many fields of knowledge, has produced according to our opinion a critical mass of systemic theories.
These systemic theories are a kind of "gyn" or "transmeme", because their mere existence augures a high-speed contagion among many other "distant" disciplines.
We must take in account the native digital revolution that is increasing every year. Nowadays life of Native-Digital is marked by a literal embodiment in these new technologies. In that way our results were predictable because all these technologies function as networks. By this reason, all these Native Digital generations modulates their life to the system thinking and action approach embeded in all these technologies.
By this reason we have no problem at all with the Inmigrant Digital population that, susprisingly, are still in the process of partial incorporation to these technologies. Among these Inmigrant Digital are many university teacher whose research is closest to lineal-thinking than system-thinking.
So, this systemic revolution has been produced, in symbiosis, by different societal grups of actors/actress. In the "archipelago" of today scientific tribal endeavour, we assist to a significant sprouting of systemic theories.
By their integrative character, systemic theories may be applied to many other fields of knowledge. The sucessive interaction within different systemic theories increase mutually their power "to jump" or "surfing" accross many fields of knowledge. This contagion among disciplines by systemic theories act as "reticular-bossoms".
Infimonikal Semantics
Infimonikal Semantics simplifies from three to two, or one, the number of memes in interaction, building in that way a new "transmeme" that after a time of neurosemantic practise, is sprouting in our minds as a waterfall plenty of new transdisciplinary ideas...
InteRactive Quantum Science for ¿Future?
La Web
Resultados 1 - 10 de aproximadamente 66.000 de Interactive Quantum Science for ¿Future?. (0,11 segundos)
Resultados de la búsqueda
1.
Amazon.com: Interactive Quantum Mechanics: Siegmund Brandt, Hans ...
- [ Traducir esta página ]
Interactive Quantum Mechanics and over 300000 other books are available for Amazon .... Physics for Future Presidents: The Science Behind the Headlines ...
www.amazon.com/Interactive-Quantum-Mechanics-Siegmund-Brandt/dp/0387002316 - En caché - Páginas similares
2.
Canada's Perimeter Institute “Quantum to Cosmos” Festival, On-site ...
- [ Traducir esta página ]
15 Jun 2009 ... Science-Inspired Movies and Related Presentations ... “The Quantum Tamers: Revealing Our Weird & Wired Future” ... Quartet by composer Kotoka Suzuki, for string quartet, interactive video, dancers, and quantum computer. ...
www.alphagalileo.org/ViewItem.aspx?ItemId=58586&CultureCode=en - hace 20 horas - Páginas similares
3.
Compound Semiconductors 2004: Compound Semiconductors for Quantum ...
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9 Apr 2008 ... Novel research trends were observed in quantum structures, such as quantum wires and dots, which are promising for future developments in ... device physics, materials science, chemistry and electronic and electrical engineering. ... This textbook features an interactive textbook community where you ...
www.nanoscienceworks.org/publications/books/6/9780750310178 - En caché - Páginas similares
4.
Theory Seminar: Interactive Proofs For Quantum Computations ...
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Computer Science Department. Technion - Israel Institute of Technology ... In cryptographic settings, an untrusted future company wants to sell a quantum ... to these questions, we define Quantum Prover Interactive Proofs (QPIP). ...
www.cs.technion.ac.il/events/2009/691/ - En caché - Páginas similares
5.
Quantum Information Science Workshop / April 23 - 25 2009 / Vienna VA
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Our protocol is interactive: after the initial preparation of quantum states, ... considerations are likely to impose on future progress in this area. ...
www.eas.caltech.edu/qis2009/abstracts.html - En caché - Páginas similares
6.
Open Directory - Science: Physics: Quantum Mechanics: Resources
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3 Mar 2009 ... Interactive Quantum Mechanics - A group of shockwave applets which allow ... How Stuff Works: Teleportation - A fascinating look at a future ...
www.dmoz.org/Science/Physics/Quantum_Mechanics/Resources/ - En caché - Páginas similares
7.
Quantum Information Science
- [ Traducir esta página ]
Future advances in quantum information science will require the combined ..... It is an open question to put the work on quantum interactive proofs in the ...
www.nsf.gov/pubs/2000/nsf00101/nsf00101.htm - En caché - Páginas similares
8.
Newswise Science News | Perimeter Institute's “Quantum to Cosmos ...
- [ Traducir esta página ]
12 Jun 2009 ... For 10 exciting days this October, Perimeter Institute's 10th anniversary science celebration “Quantum to Cosmos: Ideas for the Future” will ...
www.newswise.com/articles/view/553337/?sc=rssn - Páginas similares
9.
Home of the Future -- Interactive Computing Experts Design New ...
- [ Traducir esta página ]
1 Nov 2007 ... Home of the Future Interactive Computing Experts Design New Devices For .... Until now it has only been seen in science ... > read more ...
www.sciencedaily.com/videos/2007/1101-home_of_the_future.htm - En caché - Páginas similares
10.
Science - Physics - Quantum Mechanics - Resources - Kronig Penney ...
- [ Traducir esta página ]
A fascinating look at a future technology and how it could be used to beam . ... Interactive Quantum Mechanics (Popularity: ) ...
www.sciencecentral.com/category/103845 - En caché - Páginas similares
Resultados 1 - 10 de aproximadamente 66.000 de Interactive Quantum Science for ¿Future?. (0,11 segundos)
Resultados de la búsqueda
1.
Amazon.com: Interactive Quantum Mechanics: Siegmund Brandt, Hans ...
- [ Traducir esta página ]
Interactive Quantum Mechanics and over 300000 other books are available for Amazon .... Physics for Future Presidents: The Science Behind the Headlines ...
www.amazon.com/Interactive-Quantum-Mechanics-Siegmund-Brandt/dp/0387002316 - En caché - Páginas similares
2.
Canada's Perimeter Institute “Quantum to Cosmos” Festival, On-site ...
- [ Traducir esta página ]
15 Jun 2009 ... Science-Inspired Movies and Related Presentations ... “The Quantum Tamers: Revealing Our Weird & Wired Future” ... Quartet by composer Kotoka Suzuki, for string quartet, interactive video, dancers, and quantum computer. ...
www.alphagalileo.org/ViewItem.aspx?ItemId=58586&CultureCode=en - hace 20 horas - Páginas similares
3.
Compound Semiconductors 2004: Compound Semiconductors for Quantum ...
- [ Traducir esta página ]
9 Apr 2008 ... Novel research trends were observed in quantum structures, such as quantum wires and dots, which are promising for future developments in ... device physics, materials science, chemistry and electronic and electrical engineering. ... This textbook features an interactive textbook community where you ...
www.nanoscienceworks.org/publications/books/6/9780750310178 - En caché - Páginas similares
4.
Theory Seminar: Interactive Proofs For Quantum Computations ...
- [ Traducir esta página ]
Computer Science Department. Technion - Israel Institute of Technology ... In cryptographic settings, an untrusted future company wants to sell a quantum ... to these questions, we define Quantum Prover Interactive Proofs (QPIP). ...
www.cs.technion.ac.il/events/2009/691/ - En caché - Páginas similares
5.
Quantum Information Science Workshop / April 23 - 25 2009 / Vienna VA
- [ Traducir esta página ]
Our protocol is interactive: after the initial preparation of quantum states, ... considerations are likely to impose on future progress in this area. ...
www.eas.caltech.edu/qis2009/abstracts.html - En caché - Páginas similares
6.
Open Directory - Science: Physics: Quantum Mechanics: Resources
- [ Traducir esta página ]
3 Mar 2009 ... Interactive Quantum Mechanics - A group of shockwave applets which allow ... How Stuff Works: Teleportation - A fascinating look at a future ...
www.dmoz.org/Science/Physics/Quantum_Mechanics/Resources/ - En caché - Páginas similares
7.
Quantum Information Science
- [ Traducir esta página ]
Future advances in quantum information science will require the combined ..... It is an open question to put the work on quantum interactive proofs in the ...
www.nsf.gov/pubs/2000/nsf00101/nsf00101.htm - En caché - Páginas similares
8.
Newswise Science News | Perimeter Institute's “Quantum to Cosmos ...
- [ Traducir esta página ]
12 Jun 2009 ... For 10 exciting days this October, Perimeter Institute's 10th anniversary science celebration “Quantum to Cosmos: Ideas for the Future” will ...
www.newswise.com/articles/view/553337/?sc=rssn - Páginas similares
9.
Home of the Future -- Interactive Computing Experts Design New ...
- [ Traducir esta página ]
1 Nov 2007 ... Home of the Future Interactive Computing Experts Design New Devices For .... Until now it has only been seen in science ... > read more ...
www.sciencedaily.com/videos/2007/1101-home_of_the_future.htm - En caché - Páginas similares
10.
Science - Physics - Quantum Mechanics - Resources - Kronig Penney ...
- [ Traducir esta página ]
A fascinating look at a future technology and how it could be used to beam . ... Interactive Quantum Mechanics (Popularity: ) ...
www.sciencecentral.com/category/103845 - En caché - Páginas similares
IntenSactive Quantum Science for: Future?
(from universidadplanetaria)
A preliminary search:
La Web
Resultados 1 - 2 de aproximadamente 0 de Intensactive Quantum Science for ¿Future?. (0,23 segundos)
Resultados de la búsqueda
1.
Quizás quiso decir: Interactive Quantum Science for ¿Future? 2 resultados principales mostrados
2.
Amazon.com: Interactive Quantum Mechanics: Siegmund Brandt, Hans ...
- [ Traducir esta página ]
Interactive Quantum Mechanics and over 300000 other books are available for Amazon .... Physics for Future Presidents: The Science Behind the Headlines ...
www.amazon.com/Interactive-Quantum-Mechanics-Siegmund-Brandt/dp/0387002316 - En caché - Páginas similares
3.
Canada's Perimeter Institute “Quantum to Cosmos” Festival, On-site ...
- [ Traducir esta página ]
15 Jun 2009 ... Science-Inspired Movies and Related Presentations ... “The Quantum Tamers: Revealing Our Weird & Wired Future” ... Quartet by composer Kotoka Suzuki, for string quartet, interactive video, dancers, and quantum computer. ...
www.alphagalileo.org/ViewItem.aspx?ItemId=58586&CultureCode=en - hace 19 horas - Páginas similares
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5.
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* Intente usar otras palabras.
* Intente usar palabras más generales.
* Intente usar menos palabras.
Quizás quiso buscar: Interactive Quantum Science for ¿Future?
A preliminary search:
La Web
Resultados 1 - 2 de aproximadamente 0 de Intensactive Quantum Science for ¿Future?. (0,23 segundos)
Resultados de la búsqueda
1.
Quizás quiso decir: Interactive Quantum Science for ¿Future? 2 resultados principales mostrados
2.
Amazon.com: Interactive Quantum Mechanics: Siegmund Brandt, Hans ...
- [ Traducir esta página ]
Interactive Quantum Mechanics and over 300000 other books are available for Amazon .... Physics for Future Presidents: The Science Behind the Headlines ...
www.amazon.com/Interactive-Quantum-Mechanics-Siegmund-Brandt/dp/0387002316 - En caché - Páginas similares
3.
Canada's Perimeter Institute “Quantum to Cosmos” Festival, On-site ...
- [ Traducir esta página ]
15 Jun 2009 ... Science-Inspired Movies and Related Presentations ... “The Quantum Tamers: Revealing Our Weird & Wired Future” ... Quartet by composer Kotoka Suzuki, for string quartet, interactive video, dancers, and quantum computer. ...
www.alphagalileo.org/ViewItem.aspx?ItemId=58586&CultureCode=en - hace 19 horas - Páginas similares
4.
5.
Resultados de: Intensactive Quantum Science for ¿Future?
Su búsqueda - Intensactive Quantum Science for ¿Future? - no produjo ningún documento.
Sugerencias:
* Asegúrese de que todas las palabras estén escritas correctamente.
* Intente usar otras palabras.
* Intente usar palabras más generales.
* Intente usar menos palabras.
Quizás quiso buscar: Interactive Quantum Science for ¿Future?
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