Quantum Computers, Factoring, and Decoherence

It is known that quantum computers can dramatically speed up the task of finding factors of large numbers, a problem of practical significance for cryptographic applications. Factors of an L-digit number can be found in $\sim$L$^2$ time [compared to ∼exp(L$^{1/3}$) time] by a quantum computer, which...

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Published inScience (American Association for the Advancement of Science) Vol. 270; no. 5242; pp. 1633 - 1635
Main Authors Chuang, I. L., Laflamme, R., Shor, P. W., Zurek, W. H.
Format Journal Article
LanguageEnglish
Published Washington, DC American Society for the Advancement of Science 08.12.1995
American Association for the Advancement of Science
The American Association for the Advancement of Science
Subjects
Algorithms
Applied sciences
Computers
Computers, microcomputers
Cryptography
Electronics
Environment
Exact sciences and technology
Hardware
Information, signal and communications theory
Mathematics
Molecular computing
Numbers
Personality
Probability distributions
Quantum computers
Quantum decoherence
Quantum electronics
Quantum theory
Scientific Concepts
Signal and communications theory
Telecommunications and information theory
Fourier transformation
Coherence
Wave function
Computer
Quantum effect
Probability distribution
Cryptography
Algorithm
Factorization
Prime number
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Summary:It is known that quantum computers can dramatically speed up the task of finding factors of large numbers, a problem of practical significance for cryptographic applications. Factors of an L-digit number can be found in $\sim$L$^2$ time [compared to ∼exp(L$^{1/3}$) time] by a quantum computer, which simultaneously follows all paths corresponding to distinct classical inputs, obtaining the solution from the coherent quantum interference of the alternatives. Here it is shown how the decoherence process degrades the interference pattern that emerges from the quantum factoring algorithm. For a quantum computer performing logical operations, an exponential decay of quantum coherence is inevitable. However, even in the presence of exponential decoherence, quantum computation can be useful as long as a sufficiently low decoherence rate can be achieved to allow meaningful results to be extracted from the calculation.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0036-8075
1095-9203
DOI:10.1126/science.270.5242.1633