Results 11  20
of
101
A Rosetta stone for quantum mechanics with an introduction to quantum computation
, 2002
"... Abstract. The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading ..."
Abstract

Cited by 24 (10 self)
 Add to MetaCart
(Show Context)
Abstract. The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading
A quantum computer only needs one universe
 In Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, chapter 8
, 2003
"... The nature of quantum computation is discussed. It is argued that, in terms of the amount of information manipulated in a given time, quantum and classical computation are equally efficient. Quantum superposition does not permit quantum computers to “perform many computations simultaneously ” except ..."
Abstract

Cited by 22 (0 self)
 Add to MetaCart
(Show Context)
The nature of quantum computation is discussed. It is argued that, in terms of the amount of information manipulated in a given time, quantum and classical computation are equally efficient. Quantum superposition does not permit quantum computers to “perform many computations simultaneously ” except in a highly qualified and to some extent misleading sense. Quantum computation is therefore not well described by interpretations of quantum mechanics which invoke the concept of vast numbers of parallel universes. Rather, entanglement makes available types of computation process which, while not exponentially larger than classical ones, are unavailable to classical systems. The essence of quantum computation is that it uses entanglement to generate and manipulate a physical representation of the correlations between logical entities, without the need to completely represent the logical entities themselves.
Toward a software architecture for quantum computing design tools
 Proceedings of the 2nd International Workshop on Quantum Programming Languages (QPL
, 2004
"... Compilers and computeraided design tools are essential for finegrained control of nanoscale quantummechanical systems. A proposed fourphase design flow assists with computations by transforming a quantum algorithm from a highlevel language program into precisely scheduled physical actions. Quan ..."
Abstract

Cited by 21 (3 self)
 Add to MetaCart
Compilers and computeraided design tools are essential for finegrained control of nanoscale quantummechanical systems. A proposed fourphase design flow assists with computations by transforming a quantum algorithm from a highlevel language program into precisely scheduled physical actions. Quantum computers have the potential to solve certain computational problems—for example, factoring composite numbers or comparing an unknown image against a large database— more efficiently than modern computers. They are also indispensable in controlling quantummechanical systems in emergent nanotechnology applications, such as secure optical communication, in which modern computers cannot natively operate on quantum data. Despite convincing laboratory demonstrations of
Level reduction and the quantum threshold theorem
 PH.D. THESIS, CALTECH, 2007, EPRINT ARXIV:QUANTPH/0703230
, 2007
"... ..."
(Show Context)
Graphbased Simulation of Quantum Computation in the Density Matrix Representation
 Journal of Quantum Information and Computation
, 2005
"... Quantummechanical phenomena are playing an increasing role in information processing, as transistor sizes approach the nanometer level, and quantum circuits and data encoding methods appear in the securest forms of communication. Simulating such phenomena efficiently is exceedingly difficult becaus ..."
Abstract

Cited by 17 (3 self)
 Add to MetaCart
Quantummechanical phenomena are playing an increasing role in information processing, as transistor sizes approach the nanometer level, and quantum circuits and data encoding methods appear in the securest forms of communication. Simulating such phenomena efficiently is exceedingly difficult because of the vast size of the quantum state space involved. A major complication is caused by errors (noise) due to unwanted interactions between the quantum states and the environment. Consequently, simulating quantum circuits and their associated errors using the density matrix representation is potentially significant in many applications, but is well beyond the computational abilities of most classical simulation techniques in both time and memory resources. The size of a density matrix grows exponentially with the number of qubits simulated, rendering arraybased simulation techniques that explicitly store the density matrix intractable. In this work, we propose a new technique aimed at efficiently simulating quantum circuits that are subject to errors. In particular, we describe new graphbased algorithms implemented in the simulator QuIDDPro/D. While previously reported graphbased simulators operate in terms of the statevector representation, these new algorithms use the density matrix representation. To gauge the improvements offered by QuIDDPro/D, we compare its simulation performance with an optimized arraybased simulator called QCSim. Empirical results, generated by both simulators on a set of quantum circuit benchmarks involving error correction, reversible logic, communication, and quantum search, show that the graphbased approach far outperforms the arraybased approach.
Probabilistic model–checking of quantum protocols
 DCM 2006: PROCEEDINGS OF THE 2ND INTERNATIONAL WORKSHOP ON DEVELOPMENTS IN COMPUTATIONAL MODELS
, 2005
"... We establish fundamental and general techniques for formal verification of quantum protocols. Quantum protocols are novel communication schemes involving the use of quantummechanical phenomena for representation, storage and transmission of data. As opposed to quantum computers, quantum communicati ..."
Abstract

Cited by 17 (6 self)
 Add to MetaCart
We establish fundamental and general techniques for formal verification of quantum protocols. Quantum protocols are novel communication schemes involving the use of quantummechanical phenomena for representation, storage and transmission of data. As opposed to quantum computers, quantum communication systems can and have been implemented using presentday technology; therefore, the ability to model and analyse such systems rigorously is of primary importance. While current analyses of quantum protocols use a traditional mathematical approach and require considerable understanding of the underlying physics, we argue that automated verification techniques provide an elegant alternative. We demonstrate these techniques through the use of prism, a probabilistic modelchecking tool. Our approach is conceptually simpler than existing proofs, and allows us to disambiguate protocol definitions and assess their properties. It also facilitates detailed analyses of actual implemented systems. We illustrate our techniques by modelling a selection of quantum protocols (namely superdense coding, quantum teleportation, and quantum error correction) and verifying their basic correctness properties. Our results provide a foundation for further work on modelling and analysing larger systems such as those used for quantum cryptography, in which basic protocols are used as components.
Checking Equivalence of Quantum Circuits and States
, 2007
"... Quantum computing promises exponential speedups for important simulation and optimization problems. It also poses new CAD problems that are similar to, but more challenging, than the related problems in classical (nonquantum) CAD, such as determining if two states or circuits are functionally equiv ..."
Abstract

Cited by 17 (0 self)
 Add to MetaCart
(Show Context)
Quantum computing promises exponential speedups for important simulation and optimization problems. It also poses new CAD problems that are similar to, but more challenging, than the related problems in classical (nonquantum) CAD, such as determining if two states or circuits are functionally equivalent. While differences in classical states are easy to detect, quantum states, which are represented by complexvalued vectors, exhibit subtle differences leading to several notions of equivalence. This provides flexibility in optimizing quantum circuits, but leads to difficult new equivalencechecking issues for simulation and synthesis. We identify several different equivalencechecking problems and present algorithms for practical benchmarks, including quantum communication and search circuits, which are shown to be very fast and robust for hundreds of qubits.
Secure assisted quantum computation
 Quantum Information and Computation
, 2005
"... Suppose Alice wants to perform some computation that could be done quickly on a quantum computer, but she cannot do universal quantum computation. Bob can do universal quantum computation and claims he is willing to help, but Alice wants to be sure that Bob cannot learn her input, the result of her ..."
Abstract

Cited by 16 (0 self)
 Add to MetaCart
(Show Context)
Suppose Alice wants to perform some computation that could be done quickly on a quantum computer, but she cannot do universal quantum computation. Bob can do universal quantum computation and claims he is willing to help, but Alice wants to be sure that Bob cannot learn her input, the result of her calculation, or perhaps even the function she is trying to compute. We describe a simple, efficient protocol by which Bob can help Alice perform the computation, but there is no way for him to learn anything about it. We also discuss techniques for Alice to detect whether Bob is honestly helping her or if he is introducing errors. 1
Quantum computers that can be simulated classically in polynomial time
 In: Proceedings of the ThirtyThird Annual ACM Symposium on Theory of Computing. ACM
, 2001
"... A model of quantum computation based on unitary matrix operations was introduced by Feynman and Deutsch. It has been asked whether the power of this model exceeds that of classical Turing machines. We show here that a signi cant class of these quantum computations can be simulated classically in p ..."
Abstract

Cited by 13 (0 self)
 Add to MetaCart
(Show Context)
A model of quantum computation based on unitary matrix operations was introduced by Feynman and Deutsch. It has been asked whether the power of this model exceeds that of classical Turing machines. We show here that a signi cant class of these quantum computations can be simulated classically in polynomial time. In particular we show that twobit operations characterized by 4 4 matrices in which the sixteen entries obey a set of ve polynomial relations can be composed according to certain rules to yield a class of circuits that can be simulated classically in polynomial time. This contrasts with the known universality of twobit operations, and demonstrates that eÆcient quantum computation of restricted classes is reconcilable with the Polynomial Time Turing Hypothesis. In other words it is possible that quantum phenomena can be used in a scalable fashion to make computers but that they do not have superpolynomial speedups compared to Turing machines for any problem. The techniques introduced bring the quantum computational model within the realm of algebraic complexity theory. In a manner consistent will one view of quantum physics, the wave function is simulated deterministically, and randomization arises only in the course of making measurements. The results generalize the quantum model in that they do not require the matrices to be unitary. In a dierent direction these techniques also yield deterministic polynomial time algorithms for the decision and parity problems for certain classes of readtwice Boolean formulae. All our results are based on the use of gates that are dened in terms of their graph matching properties. 1. BACKGROUND The now classical theory of computational complexity is based on the computational model proposed by Turing[30] augmented in two ways: On the one hand random oper