Quantum algorithms revisited
TLDR
In this article, a common pattern underpinning quantum algorithms can be identified when quantum computation is viewed as multiparticle interference, and an explicit algorithm for generating any prescribed interference pattern with an arbitrary precision is provided.Abstract:
Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. A common pattern underpinning quantum algorithms can be identified when quantum computation is viewed as multiparticle interference. We use this approach to review (and improve) some of the existing quantum algorithms and to show how they are related to different instances of quantum phase estimation. We provide an explicit algorithm for generating any prescribed interference pattern with an arbitrary precision.read more
Citations
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Quantum Computation and Quantum Information
TL;DR: This chapter discusses quantum information theory, public-key cryptography and the RSA cryptosystem, and the proof of Lieb's theorem.
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Quantum information and computation
TL;DR: In information processing, as in physics, the classical world view provides an incomplete approximation to an underlying quantum reality that can be harnessed to break codes, create unbreakable codes, and speed up otherwise intractable computations.
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Quantum algorithm for linear systems of equations.
TL;DR: This work exhibits a quantum algorithm for estimating x(-->)(dagger) Mx(-->) whose runtime is a polynomial of log(N) and kappa, and proves that any classical algorithm for this problem generically requires exponentially more time than this quantum algorithm.
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Measurement-based quantum computation on cluster states
TL;DR: This work gives a detailed account of the one-way quantum computer, a scheme of quantum computation that consists entirely of one-qubit measurements on a particular class of entangled states, the cluster states, and proves its universality.
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Quantum Amplitude Amplification and Estimation
TL;DR: In this article, the amplitude amplification algorithm was proposed to find a good solution after an expected number of applications of the algorithm and its inverse which is proportional to a factor proportional to 1/a.
References
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Journal ArticleDOI
Elementary gates for quantum computation.
Adriano Barenco,Charles H. Bennett,Richard Cleve,David P. DiVincenzo,Norman Margolus,Peter W. Shor,Tycho Sleator,John A. Smolin,Harald Weinfurter +8 more
TL;DR: U(2) gates are derived, which derive upper and lower bounds on the exact number of elementary gates required to build up a variety of two- and three-bit quantum gates, the asymptotic number required for n-bit Deutsch-Toffoli gates, and make some observations about the number of unitary operations on arbitrarily many bits.
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Quantum theory, the Church-Turing principle and the universal quantum computer
TL;DR: In this paper, it is argued that underlying the Church-Turing hypothesis there is an implicit physical assertion: every finitely realizable physical system can be perfectly simulated by a universal model computing machine operating by finite means.
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Rapid Solution of Problems by Quantum Computation
David Deutsch,Richard Jozsa +1 more
TL;DR: A class of problems is described which can be solved more efficiently by quantum computation than by any classical or stochastic method.
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Quantum Computation and Shor's Factoring Algorithm
Artur Ekert,Richard Jozsa +1 more
TL;DR: The authors give an exposition of Shor's algorithm together with an introduction to quantum computation and complexity theory, and discuss experiments that may contribute to its practical implementation.
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Conditional Quantum Dynamics and Logic Gates
TL;DR: A simple quantum logic gate, the quantum controlled-NOT, is described, and two possible physical realizations of the gate are discussed, one based on Ramsey atomic interferometry and the other on the selective driving of optical resonances of two subsystems undergoing a dipole-dipole interaction.