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 in | Science (American Association for the Advancement of Science) Vol. 270; no. 5242; pp. 1633 - 1635 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
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 | |
Online Access | Get full text |
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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. |
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Bibliography: | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
ISSN: | 0036-8075 1095-9203 |
DOI: | 10.1126/science.270.5242.1633 |