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
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 201–289 of 289
Decoherence for phase-sensitive relaxation
Kilin, D. S., & Schreiber, M. (2000) · Journal of Luminescence · doi:10.1016/s0022-2313(00)00247-7 · Cited by 3
Signatures of non-Markovian relaxation in two-level atoms due to environmental perturbations
Vemuri, G., & Kemple, M. D. (2000) · The Journal of Chemical Physics · doi:10.1063/1.480837 · Cited by 3
Kuo, D. M.-T. (2025) · Nanoscale · doi:10.1039/d5nr02677f · Cited by 2
Dissipative evolution of a two-level system through a geometry-based classical mapping
Gil, D., Bargueño, P., & Miret-Artés, S. (2025) · New Journal of Physics · doi:10.1088/1367-2630/ae2989 · Cited by 2
Quantum security and theory of decoherence
Mironowicz, P. (2022) · New Journal of Physics · doi:10.1088/1367-2630/aca558 · Cited by 2
Quantum Computing :Circuits, Algorithms and Application
Nayak, M. P., Rathod, S., Surabhi, & Sukanya, S. (2024) · International Journal of Advanced Research in Science Communication and Technology · doi:10.48175/ijarsct-19321 · Cited by 2
Dubbers, D., & Stöckmann, H. ‐. (2013) · Graduate texts in physics · doi:10.1007/978-3-642-31060-7_15 · Cited by 2
Decoherence of encoded quantum registers
Borghoff, S., & Klesse, R. (2008) · Physical Review A · doi:10.1103/physreva.77.012306 · Cited by 2
Decoherence of two-level systems can be very different from Brownian particles
Hu, B. L. (2002) · Chaos Solitons & Fractals · doi:10.1016/s0960-0779(02)00299-0 · Cited by 3
A new approach to constructing CSS codes based on factor graphs
Huisong, W., Jun, W., Du, Q., & Zeng, G. (2007) · Information Sciences · doi:10.1016/j.ins.2007.10.027 · Cited by 2
Influence of non-resonant effects on the dynamics of quantum logic gates at room temperature
Berman, G. P., Bishop, A. R., Doolen, G. D., López, G. V., & Tsifrinovich, V. I. (2001) · Physica B Condensed Matter · doi:10.1016/s0921-4526(00)00555-x · Cited by 2
Studies in Quantum Chaos: From an almost exactly solvable model to Hypersensitive operators
Meenakshisundaram, N. (2009) · Cited by 2
Uniformly decaying subspaces for error-mitigated quantum computation
Suri, N., Saied, J., & Venturelli, D. (2024) · Physical Review A · doi:10.1103/physreva.110.042621 · Cited by 3
Conditional wave theory of environmental interactions with a quantum particle
van Geleuken, R., & Martin, A. V. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.033189 · Cited by 2
Scale decoherence in inhomogeneous potentialsPreprint
Meyer, D. (1998) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/9805039 · Cited by 5
A quantum code in decoherence-free and interaction-free subspaces
Zhang, Y., Zhou, Z.-W., Yu, B. H., & Guo, G. (2003) · Journal of Optics B Quantum and Semiclassical Optics · doi:10.1088/1464-4266/5/3/317 · Cited by 2
Zhang, Y., Luo, J. L., Li, X., Fu, L.-P., Jian-qing, Q., Zeng, X., & Ye, C. (1999) · Chinese Physics Letters · doi:10.1088/0256-307x/16/9/026 · Cited by 2
Decoherence of Two-Level Systems Can Be Very Different From Brownian ParticlesPreprint
Hu, B. L. (2002) · Cited by 2
Karacan, E., Chen, Y., & Mendl, C. B. (2025) · Quantum · doi:10.22331/q-2025-02-06-1624 · Cited by 4
A numerically exact, non-Markovian, non-Gaussian noise model for open quantum system dynamics
Lin, Z., & Cheng, Y. (2026) · The Journal of Chemical Physics · doi:10.1063/5.0331181 · Cited by 1
Analysis of the “Toolkit” Method for the Time-Dependent Schrödinger Equation
Baudouin, L., Salomon, J., & Turinici, G. (2010) · Journal of Scientific Computing · doi:10.1007/s10915-010-9450-6 · Cited by 1
Duce, A. D., & Bayvel, P. (2009) · IEEE Journal of Selected Topics in Quantum Electronics · doi:10.1109/jstqe.2009.2024326 · Cited by 1
Quantum repeaters based on CNOT gate under decoherence
Tong, Z.-Y., Liao, P., & Kuang, L. (2007) · 物理学前沿：英文版 · doi:10.1007/s11467-007-0061-0 · Cited by 1
Decoding Quantum Error Correction Codes With Local Variation
Hanks, M., Munro, W. J., & Nemoto, K. (2020) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2020.2967890 · Cited by 1
Sequentially Encodable Codeword Stabilized Codes
Sudevan, S., Das, S., Aswanth, T., & Kashyap, N. (2024) · doi:10.1109/isit-w61686.2024.10591769
Quantum Attacks on ECDLP-Based Cryptosystems
Yan, S. Y. (2013) · Springer eBooks · doi:10.1007/978-1-4419-7722-9_4 · Cited by 1
Distillability of two entanglement particles transmitted through a noisy channel
Yi, X. X., & Guo, G. (2000) · Physical Review A · doi:10.1103/physreva.62.062312 · Cited by 1
Classical and Quantum Computation
Yan, S. Y. (2015) · Springer eBooks · doi:10.1007/978-3-319-25823-2_2 · Cited by 1
On the fidelity of quantum gates under T1 and T2 relaxation
Chernyavskiy, A. Y. (2019) · International Conference on Micro- and Nano-Electronics (ICMNE) · doi:10.1117/12.2522383 · Cited by 1
Quantum Attacks on IFP-Based Cryptosystems
Yan, S. Y. (2013) · Springer eBooks · doi:10.1007/978-1-4419-7722-9_2 · Cited by 1
Quantum Network Optimization Based on the Use of Relaxing Qubits
Jiang, M., Zhang, Z., & Tarn, T. (2006) · Lecture notes in computer science · doi:10.1007/11816171_105 · Cited by 1
Quantum logic as a sum over classical logic gatesPreprint
Nachtergaele, B., & Periwal, V. (1996) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/9606018 · Cited by 1
A Framework for Quantum Search HeuristicsPreprint
Hogg, T. (1996) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/9611004 · Cited by 1
An intrinsic limitation on the size of quantum databasePreprint
Long, G. L., Li, Y., Zhang, W. L., & Tu, C. C. (1999) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/9910076 · Cited by 1
Collective quantum decoherence induced by qubit–electron interaction
Gao, Y., & Xiong, S. (2008) · Physics Letters A · doi:10.1016/j.physleta.2008.04.028 · Cited by 1
Benioff, P. A. (1997) · Physical review. B, Condensed matter · doi:10.1103/physrevb.55.9482 · Cited by 3
Estimating the efficiency of ensemble quantum computing
Krishnan, V. V. (2001) · Physics Letters A · doi:10.1016/s0375-9601(01)00696-x · Cited by 1
Spingineering : quantum control in the presence of relaxation
Recht, B. (2002) · Cited by 1
An approach to bridging atom optics and bulk spin quantum computation
Murali, K. V. R. M. (2003) · DSpace@MIT (Massachusetts Institute of Technology) · Cited by 1
Cosmic Quantum Optical Probing of Quantum Gravity Through a Gravitational LensPreprint
Oniga, T., Mansfield, E., & Wang, C. H.-T. (2017) · arXiv (Cornell University) · Cited by 1
Quantum Data Centres in the Presence of Noise data
Campbell, K. (2024) · Zenodo (CERN European Organization for Nuclear Research) · doi:10.5281/zenodo.13773228 · Cited by 1
Spin swap and exchange coupling in a quantum dot array
den Bouter, M. L. D. L. (2014) · Research Repository (Delft University of Technology)
Theory of angular-momentum relaxation: Quantum-dynamical semigroup approach
Artem’ev, A. Y. (2001) · Physical Review A · doi:10.1103/physreva.63.042103
Giraldi, F. (2015) · Journal of Mathematical Physics · doi:10.1063/1.4930558
Motional displacement and entanglement of a trapped ion
Zeng, H., Wang, Y., & Segawa, Y. (1999) · Journal of Physics B Atomic Molecular and Optical Physics · doi:10.1088/0953-4075/32/6/011
Zhou, Z., & Guo, G. C. (2000) · Physica A Statistical Mechanics and its Applications · doi:10.1016/s0378-4371(99)00399-4
Azuma, H. (2005) · Physical Review A · doi:10.1103/physreva.72.049902
Quantum interference visibility in an oscillating macroscopic mirror
Zhang, K. K., & Puri, A. (2012) · Journal of Applied Physics · doi:10.1063/1.4749399
Hypersensitivity to perturbation of some crucial operators relevant to quantum computation
Meenakshisundaram, N. (2015) · Physica Scripta · doi:10.1088/0031-8949/90/3/035102
Quantum gate arrays as coherent sums over classical logic gate arrays
Nachtergaele, B., & Periwal, V. (1997) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/30/24/027
Toward design principles for physically realizable algorithms for high-complexity computations
Miller, W. D. (1998) · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · doi:10.1117/12.312637
Macroscopic quantum states of a trapped ion
Zeng, H., & Tang, S. (2000) · Physical Review A · doi:10.1103/physreva.62.045402
A scheme for protecting one-qubit information against erasure error
Yang, C., Chu, S., & Han, S. (2002) · Journal of Optics B Quantum and Semiclassical Optics · doi:10.1088/1464-4266/4/5/305
Classic and Quantum Computation
Yan, S. Y. (2013) · Springer eBooks · doi:10.1007/978-1-4419-7722-9_1
Pseudoprimes, Poker and Remote Coin Tossing
Schroeder, M. R. (1997) · Springer series in information sciences · doi:10.1007/978-3-662-03430-9_19
When Abandoned Bits Bite Back - Reversibility and Quantum Computing
Fitzpatrick, P. (2002)
Architectures and Applications for Scalable Quantum Information Systems
Chuang, I. L. (2007) · Defense Technical Information Center (DTIC)
Self-citationAddressing large-scale qubit arrays for quantum computer
Barak, R. (2015) · Research Repository (Delft University of Technology)
Considerations for the extension of coherent optical processors into the quantum computing regime
Young, R. C. D., Birch, P. M., & Chatwin, C. R. (2016) · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · doi:10.1117/12.2220396
Quantum Algorithms for Integer Factorization
Yan, S. Y. (2015) · Springer eBooks · doi:10.1007/978-3-319-25823-2_3
Semiconductor-based Quantum Information
Paolo Zanardi, A., & Rossi, F. (1999) · Elsevier eBooks · doi:10.1016/b978-044450091-5/50018-x
Analysis of the Toolkit method for the time-dependant Schrödinger equationPreprint
Baudouin, L., Salomon, J., & Turinici, G. (2009) · arXiv (Cornell University) · doi:10.48550/arxiv.0907.2200
Frequency analysis of entanglement dynamics in coupled quantum oscillators
Shi, B., & Xu, C. (2019) · Conference proceedings/Conference proceedings - IEEE International Conference on Systems, Man, and Cybernetics · doi:10.1109/smc.2019.8914622
Entanglement and the Temperley-Lieb category
Brannan, M., & Collins, B. (2020) · Contemporary mathematics - American Mathematical Society · doi:10.1090/conm/747/15037
Quantum Algorithms in CyberneticsPreprint
Nikolov, P. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2103.05952 · Cited by 1
Truncated phase-based quantum arithmetic: Error propagation and resource reduction
White, G. A. L., Hill, C. D., & Hollenberg, L. C. L. (2023) · Physical Review A · doi:10.1103/physreva.108.052608
Lakatos on Crucial Experiments and the History of Interpretations of Quantum Mechanics
Szegedi, P. (2002) · Springer eBooks · doi:10.1007/978-94-017-0769-5_7
Circuit encapsulation for efficient quantum computing based on controlled many-body dynamicsPreprint
Ran, S.-J., Lu, Y., Zhou, P.-F., & Fei, S.-M. (2022) · Research Square · doi:10.21203/rs.3.rs-1523679/v1
(2010) · Springer eBooks · doi:10.1007/978-3-642-03296-7_5
Braunstein, S. L. (2003) · Wiley eBooks · doi:10.1002/3527600434.eap585
Yan, S. Y. (2018) · Springer eBooks · doi:10.1007/978-3-319-72536-9_3
(2012) · Royal Society of Chemistry eBooks · doi:10.1039/9781849733021-00316
Pseudoprimes, Poker and Remote Coin Tossing
(2006) · Springer series in information sciences · doi:10.1007/3-540-26598-8_19
Yan, S. Y. (2015) · Springer eBooks · doi:10.1007/978-3-319-25823-2_1
Preliminary Results of Applying Modified MSA Algorithm on Quantum Annealers (MAQ)
Lee, M. W. (2023) · The Journal of Computational Science Education · doi:10.22369/issn.2153-4136/14/1/5
Codeword Stabilized Codes From m -Uniform Graph States
Sudevan, S., Das, S., Aswanth, T., Patanker, N., & Kashyap, N. (2025) · IEEE Journal on Selected Areas in Information Theory · doi:10.1109/jsait.2025.3602744
Algebraic decoding for classes of quantum codes
Saouter, Y., & Burel, G. (2024) · IEEE International Mediterranean Conference on Communications and Networking (MeditCom) · doi:10.1109/meditcom61057.2024.10621269
Low-energy physics and finite-size effects in nonuniform parafermion chains
Fatmehsari, M. M. N., & Vaezi, M.-S. (2025) · Scientific Reports · doi:10.1038/s41598-025-94657-z
Realizing the Petz recovery map on an NMR quantum processor
Singh, G., Sahani, R. S., Jagadish, V., Lautenbacher, L., Bernardes, N. K., & Dorai, K. (2026) · Physical Review A · doi:10.1103/xd6k-swv7
Manipulating non-Abelian anyons of Kitaev quantum spin liquids with local magnetic fields
Wang, H., & Principi, A. (2025) · Physical review. B./Physical review. B · doi:10.1103/m2w7-54mp
Information-Theoretic Analysis of Weak Measurements and Their Reversal
Palma, L. D. Z., Maleki, Y., & Zubairy, M. S. (2026) · Fluctuation and Noise Letters · doi:10.1142/s0219477525400280
Quantum Computing : Fundamental Principles, Quantum Algorithms, and Emerging Applications
Koteswararao P, D. G. V., & Lohithsrinivas4, K. S. S. R. K. T. (2026) · International Journal of Advanced Research in Science Communication and Technology · doi:10.48175/ijarsct-32705
The disparate impact of noise on quantum learning algorithms
Angrisani, A. (2023) · theses.fr (ABES) · doi:10.70675/69f942ebz4417z4eceza746z1c9d436d09bb · Cited by 1
Gangopadhyay, S., Jagadish, V., & Srikanth, R. (2026) · Annals of Physics · doi:10.1016/j.aop.2026.170559
Trade-off Between Complexity and Energy in Quantum Phase Estimation
Anonymous, Guţǎ, M., & Adesso, G. (2026) · PRX Energy · doi:10.1103/zlhs-7m9m · Cited by 1
Model-based qubit noise spectroscopy
Anonymous, Watson, C. A., Murphy, A. J., Sweeney, T. M., & Quiroz, G. (2026) · Physical Review Applied · doi:10.1103/64bh-t137 · Cited by 2
Quantum Logic circuits for solid-state quantum information processing
Duce, A. D. (2010) · UCL Discovery (University College London)
Parametric Schroedinger Cat with No Decoherence
Branca, S., Martini, F. D., Giuseppc, G. D., & Mariani, F. (2002) · Springer eBooks · doi:10.1007/0-306-47097-7_50
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
