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Quantum Computers, Factoring, and Decoherence
Open accessAbstract
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 ∼ 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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“After the results were first published, it was shown by Gottesman[32] that fault tolerant procedures for the universal set of gates introduced by Shor can be constructed for any stabilizer code, using basically the same technique as presented by Shor for the CSS codes, a result which was generalized to qupits[33].”
From Fault-Tolerant Quantum Computation with Constant Error Rate (2008) · cites this paper as [33]
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“Noise, decoherence, and manufacturing problems make constructing large-scale quantum computers difficult 9-13 .”
From Experimental realization of a quantum algorithm (1998) · cites this paper as [10]
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Cites
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Cited by
Sorted by citations
Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
Shor, P. W. (1997) · SIAM Journal on Computing · doi:10.1137/s0097539795293172 · Cited by 8,472
Self-citationQuantum computation with quantum dots
Loss, D., & DiVincenzo, D. P. (1998) · Physical Review A · doi:10.1103/physreva.57.120 · Cited by 6,840
Elementary gates for quantum computation
Barenco, A., Bennett, C. H., Cleve, R., DiVincenzo, D. P., Margolus, N., Shor, P., Sleator, T., Smolin, J. A., & Weinfurter, H. (1995) · Physical Review A · doi:10.1103/physreva.52.3457 · Cited by 4,311
Self-citationPolynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
Shor, P. W. (1999) · SIAM Review · doi:10.1137/s0036144598347011 · Cited by 3,904
Self-citationLloyd, S. (1996) · Science · doi:10.1126/science.273.5278.1073 · Cited by 3,088
Metadata
- Authors
- Chuang, I. L., Laflamme, R., Shor, P. W., & Zurek, W. H.
- Affiliations
- Stanford University (US)
- Los Alamos National Laboratory (US)
- AT&T (United States) (US)
- Venue
- Science
- Published
- 1995-12-08
- Volume
- 270
- Issue
- 5242
- Pages
- 1633-1635
- ISSN
- 0036-8075 (ISSN-L)
- 1095-9203
- OpenAlex
- W2107050628
- Cited by
- 289
- References
- 18
- Citations by year
- 2026: 7 · 2025: 8 · 2024: 11 · 2023: 5 · 2022: 10 · 2021: 4 · 2020: 4 · 2019: 3 · 2018: 5 · 2017: 3 · 2016: 3 · 2015: 8 · 2014: 1 · 2013: 8 · 2012: 4
- FWCI
- 37.21
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Science (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- quantum computing hardware, quantum factoring, decoherence, Shor's algorithm, quantum interference, quantum coherence, cryptographic security, decoherence rate
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