Journal ArticleDOI
Quantum Mechanical Computers
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TLDR
The physical limitations due to quantum mechanics on the functioning of computers are analyzed in this paper, where the physical limitations of quantum mechanics are discussed and the physical limits of quantum computing are analyzed.Abstract:
The physical limitations, due to quantum mechanics, on the functioning of computers are analyzed.read more
Citations
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Proceedings ArticleDOI
Algorithms for quantum computation: discrete logarithms and factoring
TL;DR: Las Vegas algorithms for finding discrete logarithms and factoring integers on a quantum computer that take a number of steps which is polynomial in the input size, e.g., the number of digits of the integer to be factored are given.
Journal ArticleDOI
Non-Abelian Anyons and Topological Quantum Computation
TL;DR: In this article, the authors describe the mathematical underpinnings of topological quantum computation and the physics of the subject are addressed, using the ''ensuremath{
u}=5∕2$ fractional quantum Hall state as the archetype of a non-Abelian topological state enabling fault-tolerant quantum computation.
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.
Journal ArticleDOI
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
TL;DR: In this paper, the authors considered factoring integers and finding discrete logarithms, two problems that are generally thought to be hard on classical computers and that have been used as the basis of several proposed cryptosystems.
Journal ArticleDOI
Universal Quantum Simulators
TL;DR: Feynman's 1982 conjecture, that quantum computers can be programmed to simulate any local quantum system, is shown to be correct.
References
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Journal ArticleDOI
Logical reversibility of computation
TL;DR: This result makes plausible the existence of thermodynamically reversible computers which could perform useful computations at useful speed while dissipating considerably less than kT of energy per logical step.
Journal ArticleDOI
The thermodynamics of computation—a review
TL;DR: In this paper, the authors consider the problem of rendering a computation logically reversible (e.g., creation and annihilation of a history file) in a Brownian computer, and show that it is not the making of a measurement that prevents the demon from breaking the second law but rather the logically irreversible act of erasing the record of one measurement to make room for the next.
Journal ArticleDOI
Bicontinuous extensions of invertible combinatorial functions
TL;DR: The solution of the problem of constructing a diffeomorphic componentwise extension for an arbitrary invertible combinatorial function constitutes a proof of the physical realizability of general computing mechanisms based on reversible primitives.
Journal ArticleDOI
On a simple combinatorial structure sufficient for syblying nontrivial self-reproduction
TL;DR: It can be shown that even in a world governed by this system M nontrivial self-reproduction can be established, thus illuminating what simple combinatorial structures allow for the handling of such logical somewhat difficult phenomenas as self-organization, self- reproduction, etc.