The DOI matches its Crossref record; 18 of the 18 references it cites were found in a registry or an index.
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.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“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]
In the citing paper
“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]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Bishop, O. (2007) · Routledge eBooks · doi:10.4324/9780080477527-64 · Cited by 25,031
Algorithms for quantum computation: discrete logarithms and factoring
Shor, P. W. (2002) · Proceedings 35th Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.1994.365700 · Cited by 8,713
Self-citationDynamics of the dissipative two-state system
Leggett, A. J., Chakravarty, S., Dorsey, A. T., Fisher, M. P. A., Garg, A., & Zwerger, W. (1987) · Reviews of Modern Physics · doi:10.1103/revmodphys.59.1 · Cited by 5,109
Quantum theory, the Church–Turing principle and the universal quantum computer
Deutsch, D. (1985) · Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences · doi:10.1098/rspa.1985.0070 · Cited by 4,597
Quantum Computations with Cold Trapped Ions
Cirac, J. I., & Zoller, P. (1995) · Physical Review Letters · doi:10.1103/physrevlett.74.4091 · Cited by 3,733
Decoherence and the Transition from Quantum to Classical
Zurek, W. H. (1991) · Physics Today · doi:10.1063/1.881293 · Cited by 2,632
Self-citationEnvironment-induced superselection rules
Zurek, W. H. (1982) · Physical Review D · doi:10.1103/physrevd.26.1862 · Cited by 1,415
Self-citationPointer basis of quantum apparatus: Into what mixture does the wave packet collapse?
Zurek, W. H. (1981) · Physical Review D · doi:10.1103/physrevd.24.1516 · Cited by 1,257
Self-citationTwo-bit gates are universal for quantum computation
DiVincenzo, D. P. (1995) · Physical Review A · doi:10.1103/physreva.51.1015 · Cited by 1,069
Lee, E. A., & Messerschmitt, D. G. (1988) · Springer eBooks · doi:10.1007/978-1-4684-0044-1 · Cited by 665
Flagged first, then by citations
Research works printed but not linked: 6
- GRAHAM R, CONCRETE MATH (1994).
- LANDAUER R, 4 P DREX S QUANT NON (1995).
- LENSTRA A, HDB THEORETICAL COMP A, 673 (1990).
- MONROE C, DEMONSTRATION UNIVER (1995).
- SHOR P.W., 35TH P ANN S F COMP 124, (1994).
- ZUREK W.H., FRONTIERS NONEQUILIB 151, (1986).
Cited by
Sorted by citations
Items 101–200 of 289
Decoherence in Grover’s quantum algorithm: Perturbative approach
Azuma, H. (2002) · Physical Review A · doi:10.1103/physreva.65.042311 · Cited by 27
Coherent control in a decoherence-free subspace of a collective multilevel system
Kiffner, M., Evers, J., & Keitel, C. H. (2007) · Physical Review A · doi:10.1103/physreva.75.032313 · Cited by 27
Dorai, K., Arvind, & Kumar, A. (2001) · Physical Review A · doi:10.1103/physreva.63.034101 · Cited by 27
Three-particle QKD protocol against a collective noise
Huang, W., Guo, F.-Z., Huang, Z., Wen, Q., & Zhu, F.-C. (2010) · Optics Communications · doi:10.1016/j.optcom.2010.08.073 · Cited by 25
Impact of time-correlated noise on zero-noise extrapolation
Schultz, K., LaRose, R., Mari, A., Quiroz, G., Shammah, N., Clader, B. D., & Zeng, W. J. (2022) · Physical Review A · doi:10.1103/physreva.106.052406 · Cited by 28
Quantum mechanics of lattice gas automata: boundary conditions and other inhomogeneities
MEYER, D. A. (1998) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/31/10/009 · Cited by 26
The effect of communication costs in solid-state quantum computing architectures
Copsey, D., Oskin, M., Metodiev, T., Chong, F. T., Chuang, I. L., & Kubiatowicz, J. D. (2003) · ACM Symposium on Parallelism in Algorithms and Architectures (SPAA) · doi:10.1145/777412.777424 · Cited by 23
Self-citationDecoherence slowing via feedback
Horoshko, D. B., & Kilin, S. Y. (1997) · Journal of Modern Optics · doi:10.1080/09500349708231866 · Cited by 23
A framework for structured quantum search
Hogg, T. (1998) · Physica D Nonlinear Phenomena · doi:10.1016/s0167-2789(98)00047-5 · Cited by 27
Avoiding quantum chaos in quantum computation
Berman, G. P., Borgonovi, F., Izrailev, F. M., & Tsifrinovich, V. I. (2001) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.65.015204 · Cited by 22
VACSEN : A V isualization A pproa c h for Noi s e Awaren e ss in Qua n tum Computing
Ruan, S., Wang, Y., Jiang, W., Mao, Y., & Guan, Q. (2022) · IEEE Transactions on Visualization and Computer Graphics · doi:10.1109/tvcg.2022.3209455 · Cited by 33
Gudder, S. (1999) · International Journal of Theoretical Physics · doi:10.1023/a:1026663432352 · Cited by 20
Muqeet, A., Ali, S., Yue, T., & Arcaini, P. (2024) · ACM Joint European Software Engineering Conference and Symposium on the Foundations of Software Engineering (ESEC/FSE) · doi:10.1145/3663529.3663830 · Cited by 20
The influence of entanglement and decoherence on the quantum Stackelberg duopoly game
Xia, Z., & Kuang, L. (2007) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/40/27/021 · Cited by 20
Nonlocal quantum macroscopic superposition in a high-thermal low-purity state
Brezinski, M. E., & Liu, B. (2008) · Physical Review A · doi:10.1103/physreva.78.063824 · Cited by 20
Low-rank density-matrix evolution for noisy quantum circuits
Chen, Y.-T., Farquhar, C., & Parrish, R. M. (2021) · npj Quantum Information · doi:10.1038/s41534-021-00392-4 · Cited by 24
Quantum entanglement and quantum computational algorithms
Arvind (2001) · Pramana · doi:10.1007/s12043-001-0130-9 · Cited by 20
Zhang, J., Peng, X., Rajendran, N., & Suter, D. (2007) · Physical Review A · doi:10.1103/physreva.75.042314 · Cited by 18
Spectral density classification for environment spectroscopy
Barr, J., Zicari, G., Ferraro, A., & Paternostro, M. (2024) · Machine Learning Science and Technology · doi:10.1088/2632-2153/ad2cf1 · Cited by 18
Investigation of excitons bound to fluorine donors in ZnSe
Pawlis, A., Sanaka, K., Götzinger, S., Yamamoto, Y., & Lischka, K. (2006) · Semiconductor Science and Technology · doi:10.1088/0268-1242/21/10/007 · Cited by 17
Quantum chaos in nanoelectromechanical systems
Gusso, A., da Luz, M. G. E., & Rego, L. G. C. (2006) · Physical Review B · doi:10.1103/physrevb.73.035436 · Cited by 17
Control of quantum dynamics: Concepts, procedures and future prospects
RABITZ, H. A., Turinici, G., & Brown, E. (2003) · Handbook of numerical analysis · doi:10.1016/s1570-8659(03)10016-6 · Cited by 15
Kirilyuk, A. P. (2002) · arXiv (Cornell University) · Cited by 18
Protecting privacy in the cyber era
Davis, J. C. (2000) · IEEE Technology and Society Magazine · doi:10.1109/44.846270 · Cited by 17
Teleportation via generalized measurements, and conclusive teleportationPreprint
Mor, T., & Horodecki, P. (1999) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/9906039 · Cited by 16
Extended techniques for feedback control of a single qubit
Yang, Y., Zhang, X. Y., Ma, J., & Yi, X. X. (2013) · Physical Review A · doi:10.1103/physreva.87.012333 · Cited by 15
Tunneling dynamics of Bose-Einstein condensates with Feshbach resonances
Hu, B., & Kuang, L. (2000) · Physical Review A · doi:10.1103/physreva.62.023610 · Cited by 15
Quantum ballistic evolution in quantum mechanics: Application to quantum computers
Benioff, P. A. (1996) · Physical Review A · doi:10.1103/physreva.54.1106 · Cited by 15
Controllability analysis of quantum systems immersed within an engineered environment
Grigoriu, A., RABITZ, H. A., & Turinici, G. (2013) · Journal of Mathematical Chemistry · doi:10.1007/s10910-013-0163-6 · Cited by 15
Tasaki, S., Tokuse, A., Paolo Facchi, A., & Pascazio, S. (2004) · International Journal of Quantum Chemistry · doi:10.1002/qua.10870 · Cited by 16
Factoring the unitary evolution operator and quantifying entanglement
Yi, X. X., & Sun, C. (1999) · Physics Letters A · doi:10.1016/s0375-9601(99)00609-x · Cited by 13
Quantum entanglement in the NMR implementation of the Deutsch-Jozsa algorithm
Arvind, Dorai, K., & Kumar, A. (2001) · Pramana · doi:10.1007/s12043-001-0095-8 · Cited by 25
Quantum entanglement in the NMR implementation of the Deutsch-Jozsa algorithm
Arvind, *., Dorai, K., & Kumar, A. (2001) · NOT FOUND REPOSITORY (Indian Institute of Science Bangalore) · Cited by 13
Comstock, M., Lozovoy, V. V., & Dantus, M. M. (2003) · The Journal of Chemical Physics · doi:10.1063/1.1603739 · Cited by 13
Alternative Computational Models: A Comparison of Biomolecular and Quantum Computation
Reif, J. H. (1998) · Lecture notes in computer science · doi:10.1007/978-3-540-49382-2_10 · Cited by 12
Bounds on decoherence and error
Schulman, L. S. (1998) · Physical Review A · doi:10.1103/physreva.57.840 · Cited by 12
New trends in quantum computing
Brassard, G. (1996) · Lecture notes in computer science · doi:10.1007/3-540-60922-9_1 · Cited by 14
Quantum information processing in localized modes of light within a photonic band-gap material
Vats, N., & Rudolph, T. (2001) · Journal of Modern Optics · doi:10.1080/09500340108231778 · Cited by 14
Dynamical imperfections in quantum computers
Paolo Facchi, A., Montangero, S., Rosario Fazio, B., & Pascazio, S. (2005) · Physical Review A · doi:10.1103/physreva.71.060306 · Cited by 12
Stabilization of quantum states in quantum-optical systems
Pellizzari, T., Beth, T., Grassl, M., & Müller‐Quade, J. (1996) · Physical Review A · doi:10.1103/physreva.54.2698 · Cited by 12
Polynomial Simulations of Decohered Quantum ComputersPreprint
Aharonov, D., & Ben-Or, M. (1996) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/9611029 · Cited by 20
Entanglement dynamics of coupled qubits and a semi-decoherence free subspace
Campagnano, G., Hamma, A., & Weiß, U. (2009) · Physics Letters A · doi:10.1016/j.physleta.2009.10.081 · Cited by 13
Conditions for independent decoherence
Duan, L.-M., & Guo, G. (1998) · Quantum and Semiclassical Optics Journal of the European Optical Society Part B · doi:10.1088/1355-5111/10/4/004 · Cited by 10
An expectation value expansion of Hermitian operators in a discrete Hilbert space
Asplund, R., Bjork, G. G., & Bourennane, M. (2001) · Journal of Optics B Quantum and Semiclassical Optics · doi:10.1088/1464-4266/3/3/314 · Cited by 11
Dynamical fidelity of a solid-state quantum computation
Berman, G. P., Borgonovi, F., Celardo, G. L., Izrailev, F. M., & Kamenev, D. I. (2002) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.66.056206 · Cited by 11
Universal-dephasing-noise injection via Schrödinger-wave autoregressive moving-average models
Murphy, A., Epstein, J., Quiroz, G., Schultz, K., Tewala, L., McElroy, K., Trout, C. J., Tien-Street, B., Hoffmann, J. A., Clader, B. D., et al. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.013081 · Cited by 11
Dynamics of a Control-Not gate for a quantum system of two weakly interacting spins
Berman, G. P., Campbell, D. K., Doolen, G. D., López, G. V., & Tsifrinovich, V. I. (1997) · Physica B Condensed Matter · doi:10.1016/s0921-4526(97)00434-1 · Cited by 10
Quantum error correction with spatially correlated decoherence
Duan, L.-M., & Guo, G. (1999) · Physical Review A · doi:10.1103/physreva.59.4058 · Cited by 10
Physics and the new computation
Vitanyi, P. M. B. (1995) · Lecture notes in computer science · doi:10.1007/3-540-60246-1_118 · Cited by 10
High fidelity quantum gates with ions in cryogenic microfabricated ion traps
Chuang, I. L., & Labaziewicz, J. (2008) · DSpace@MIT (Massachusetts Institute of Technology) · Cited by 10
Self-citationNonlinear Raman vibrational excitation of a trapped ion
Zeng, H., Wang, Y., & Segawa, Y. (1999) · Physical Review A · doi:10.1103/physreva.59.2174 · Cited by 10
Evolution of Quantum Machine Learning and an Attempt of Its Application for SDN Intrusion Detection
Shinde, A. R., & Bendale, S. P. (2023) · Studies in computational intelligence · doi:10.1007/978-981-19-9530-9_22 · Cited by 9
Zhang, Y., Xia, Y., Man, Z., & Guo, G. (2009) · Science in China. Series G, Physics, mechanics & astronomy/Science in China. Series G, Physics, Mechanics & Astronomy · doi:10.1007/s11433-009-0099-9 · Cited by 9
Quantum Decoherence for Multi-Photon Entangled States
Yan-Hua, S., Xia, Z., & Le-Man, K. (2005) · Chinese Physics Letters · doi:10.1088/0256-307x/22/8/003 · Cited by 9
Dynamical analysis of Grover’s search algorithm in arbitrarily high-dimensional search spaces
Jin, W. (2015) · Quantum Information Processing · doi:10.1007/s11128-015-1164-0 · Cited by 9
pez, G. V. L., Quezada, J. R. V., Berman, G. P., Doolen, G. D., & Tsifrinovich, V. I. (2003) · Journal of Optics B Quantum and Semiclassical Optics · doi:10.1088/1464-4266/5/2/311 · Cited by 6
Anomalous quantum chaotic behaviour in suspended electromechanical nanostructures
Rego, L. G. C., Gusso, A., & da Luz, M. G. E. (2005) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/38/39/l03 · Cited by 8
Scheme for reducing collective decoherence in quantum memory
Duan, L.-M., & Guo, G.-C. (1998) · Physics Letters A · doi:10.1016/s0375-9601(98)80119-9 · Cited by 9
Inhibiting decoherence via ancilla processes
Zeng, G., & Keitel, C. H. (2002) · Physical Review A · doi:10.1103/physreva.66.022306 · Cited by 8
Quantum Relational DatabasesPreprint
Cockshott, P. W. (1997) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/9712025 · Cited by 12
Introduction to Quantum Computers
Grimes, R. A. (2019) · Wiley eBooks · doi:10.1002/9781119618232.ch2 · Cited by 9
Quantum data centres: a simulation-based comparative noise analysis
Campbell, K., Lawey, A. Q., & Razavi, M. (2024) · Quantum Science and Technology · doi:10.1088/2058-9565/ad9cb8 · Cited by 7
Entanglement Dynamics Governed by Time-Dependent Quantum Generators
Czerwiński, A. (2022) · Axioms · doi:10.3390/axioms11110589 · Cited by 7
Gate imperfection in the quantum random-walk search algorithm
Li, Y., Ma, L., & Zhou, J. (2006) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/39/29/021 · Cited by 7
An efficient simulation of quantum error correction codes
Priya, R. P., & Baradeswaran, A. (2017) · Alexandria Engineering Journal · doi:10.1016/j.aej.2017.06.013 · Cited by 7
Yang, I.-S. (2018) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.97.066008 · Cited by 7
On the simulation of quantum turing machines
Carpentieri, M. (2003) · Theoretical Computer Science · doi:10.1016/s0304-3975(03)00054-9 · Cited by 7
QD-MSA : A quantum distributed tensor network framework for multimodal sentiment analysis
Li, Y., Li, Y., Qi, Z., Yang, H., Shang, R., & Jiao, L. (2025) · Information Fusion · doi:10.1016/j.inffus.2025.103404 · Cited by 7
Modular multiplication operator and quantized baker’s maps
Lakshminarayan, A. (2007) · Physical Review A · doi:10.1103/physreva.76.042330 · Cited by 6
Higher-order perturbation theory for decoherence in Grover’s algorithm
Azuma, H. (2005) · Physical Review A · doi:10.1103/physreva.72.042305 · Cited by 8
A Hamiltonian for quantum copying
Mozyrsky, D., Privman, V., & Hillery, M. (1997) · Physics Letters A · doi:10.1016/s0375-9601(96)00939-5 · Cited by 6
Speedup of iterated quantum search by parallel performancePreprint
Ozhigov, Y. (1999) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/9904039 · Cited by 7
Yan, S. Y. (2018) · Springer eBooks · doi:10.1007/978-3-319-72536-9_5 · Cited by 6
Quantum entanglement in an oscillating macroscopic mirror
Eslick, J. W., Pham, H. N., Radu, C., & Puri, A. (2006) · The European Physical Journal D · doi:10.1140/epjd/e2006-00060-0 · Cited by 5
Quantum Computational Number Theory
Yan, S. Y. (2012) · Wiley eBooks · doi:10.1002/9781118188606.ch10 · Cited by 5
Solving Random Satisfiability Problems with Quantum ComputersPreprint
Hogg, T. (2001) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0104048 · Cited by 5
Local Search Methods for Quantum ComputersPreprint
Hogg, T., & Yanik, M. F. (1998) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/9802043 · Cited by 5
Quantum Smart MatterPreprint
Hogg, T., & Chase, J. G. (1996) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/9611021 · Cited by 5
Quantum-jump effects in the motion of a Raman-driven trapped ion
Fidio, C. D., Wallentowitz, S., Kis, Z., & Vogel, W. (1999) · Physical Review A · doi:10.1103/physreva.60.r3393 · Cited by 5
Azuma, H. (2002) · Physical Review A · doi:10.1103/physreva.66.019903 · Cited by 6
Unconditional quantum magic advantage in shallow circuit computation
Zhang, X., Pan, Z., & Liu, G. (2024) · Nature Communications · doi:10.1038/s41467-024-54864-0 · Cited by 4
A systematic review of strategic approaches and applications in quantum computing
Sharma, N. V., & Saxena, V. (2025) · Optical and Quantum Electronics · doi:10.1007/s11082-025-08364-0 · Cited by 5
Laser-controlled state excitation and quantum computation
Zhang, D.-Y., & Zhan, M. (1999) · Acta Physica Sinica (Overseas Edition) · doi:10.1088/1004-423x/8/4/004 · Cited by 4
Strong decoherence in quantum systems undergoing collisions
Miller, M., & Olkiewicz, R. (2011) · Physics Letters A · doi:10.1016/j.physleta.2011.07.042 · Cited by 3
Bruns, D., Sperling, J., & Scheel, S. (2016) · Physical Review A · doi:10.1103/physreva.93.032132 · Cited by 4
Rajesh, A., Bandyopadhyay, M., & Jayannavar, A. M. (2017) · The European Physical Journal B · doi:10.1140/epjb/e2017-80292-3 · Cited by 4
A small error-correction code for protecting three-qubit quantum information
Yang, C., Chu, S., & Han, S. (2004) · Journal of Experimental and Theoretical Physics Letters · doi:10.1134/1.1753423 · Cited by 4
Comets, Information, and the Origin of Life
Sheldon, R. B. (2012) · Cellular origin and life in extreme habitats · doi:10.1007/978-94-007-2941-4_21 · Cited by 4
INTEGRABILITY, ENTROPY AND QUANTUM COMPUTATION
Krishnamurthy, E. V. (1999) · International Journal of Modern Physics C · doi:10.1142/s012918319900098x · Cited by 4
A Hamiltonian for Quantum CopyingPreprint
Mozyrsky, D., Privman, V., & Hillery, M. (1996) · Cited by 4
Joint Interoperability: Fog or Lens for Joint Vision 2010
Reddy, P. C. (1997) · Defense Technical Information Center (DTIC) · doi:10.21236/ada388057 · Cited by 4
Non‐Markovian Cost Function for Quantum Error Mitigation
Ahn, D., & Park, B. (2024) · Advanced Quantum Technologies · doi:10.1002/qute.202300138 · Cited by 4
Fidelity of the Kitaev honeycomb model under a quench
Roberts, W., Vogl, M. R., & Fiete, G. A. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.109.l220406 · Cited by 6
Atomic GHZ States Prepared in Two Directly Coupled Cavities with Virtual Excitations in One Step
Yang, R., Huang, Z., Guo, Y., Zhang, P., Zhong, C.-Y., & Zhang, T. (2011) · Communications in Theoretical Physics · doi:10.1088/0253-6102/56/4/10 · Cited by 3
Performance of 1D quantum cellular automata in the presence of error
McNally, D. M., & Clemens, J. (2016) · AIP Advances · doi:10.1063/1.4963300 · Cited by 3
Long-range order and quantum criticality in a dissipative spin chain
Butcher, M., Pixley, J. H., & Nevidomskyy, A. H. (2022) · Physical review. B./Physical review. B · doi:10.1103/physrevb.105.l180407 · Cited by 3
Quantum compiling with a variational instruction set for accurate and fast quantum computing
Lu, Y., Zhou, P.-F., Fei, S.-M., & Ran, S.-J. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.023096 · Cited by 5
Energy range for quantum coherence
Giraldi, F. (2015) · Physical Review A · doi:10.1103/physreva.91.062112 · Cited by 3
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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
