The DOI matches its Crossref record; 83 of the 84 references it cites were found in a registry or an index.
The quest for a Quantum Neural Network
Open accessOverview
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?
The cited source says what the claim attributes to it.
In the citing paper
“has produced noteworthy advances in quantum random walks, 38,39 quantum control, 40 open quantum systems, 41 and pioneering work on quantum neural networks, 42 quantum machine learning, 43 and quantum processes in the brain.44”
From Toward a quantum future for South Africa (2021) · cites this paper as [42]
In the citing paper
“A key challenge to overcome is the clash between the nonlinear, dissipative dynamics of neural network computing and the linear, reversible dynamics of quantum computing.24”
From Quantum generalisation of feedforward neural networks (2017) · cites this paper as [24]
In the citing paper
“We make the individual neurons reversible and then naturally generalise them to being quantum reversible (unitary).This resolves the classical-quantum clash mentioned above from ref. 24.”
From Quantum generalisation of feedforward neural networks (2017) · cites this paper as [24]
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
An Introduction to the Bootstrap
Efron, B., & Tibshirani, R. J. (1994) · doi:10.1201/9780429246593 · Cited by 40,500
Quantum Computation and Quantum Information
Nielsen, M. A., Chuang, I., & Grover, L. K. (2002) · American Journal of Physics · doi:10.1119/1.1463744 · Cited by 21,895
Neural networks and physical systems with emergent collective computational abilities.
Hopfield, J. J. (1982) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.79.8.2554 · Cited by 19,270
A logical calculus of the ideas immanent in nervous activity
McCulloch, W. S., & Pitts, W. (1943) · The Bulletin of Mathematical Biophysics · doi:10.1007/bf02478259 · Cited by 18,566
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
Quantum Computation and Quantum Information: 10th Anniversary Edition
Nielsen, M. A., & Chuang, I. L. (2012) · doi:10.1017/cbo9780511976667 · Cited by 8,436
Hopfield, J. J. (1984) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.81.10.3088 · Cited by 6,918
Theory of open quantum systems
Xu, R., & Yan, Y. (2002) · The Journal of Chemical Physics · doi:10.1063/1.1474579 · Cited by 6,622
Introduction to the theory of neural computation
Hertz, J., Krogh, A., & Palmer, R. G. (1994) · Neural Networks · doi:10.1016/0893-6080(94)90014-0 · Cited by 6,410
The Theory of Open Quantum Systems
Breuer, H.-P., & Petruccione, F. (2007) · doi:10.1093/acprof:oso/9780199213900.001.0001 · Cited by 5,938
Self-citationError Detecting and Error Correcting Codes
Hamming, R. W. (1950) · Bell System Technical Journal · doi:10.1002/j.1538-7305.1950.tb00463.x · Cited by 5,377
Polynomial-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
ERROR DETECTING AND ERROR CORRECTING CODES
Chauhan, N., Yadav, P., & Kumari, P. (2014) · Cited by 3,270
Computing with Neural Circuits: A Model
Hopfield, J. J., & Tank, D. W. (1986) · Science · doi:10.1126/science.3755256 · Cited by 2,118
Quantum computation and quantum information
Paul, T. (2007) · Mathematical Structures in Computer Science · doi:10.1017/s0960129507006317 · Cited by 2,009
Introduction to the Theory of Neural Computation
Hertz, J., Krogh, A., & Palmer, R. G. (2018) · CRC Press eBooks · doi:10.1201/9780429499661 · Cited by 1,812
Weak pairwise correlations imply strongly correlated network states in a neural population
Schneidman, E., Berry, M. J., Segev, R., & Bialek, W. (2006) · Nature · doi:10.1038/nature04701 · Cited by 1,745
Abbott, L. F., & Regehr, W. G. (2004) · Nature · doi:10.1038/nature03010 · Cited by 1,684
Quantum computation and quantum-state engineering driven by dissipation
Verstraete, F., Wolf, M. M., & Ignacio Cirac, J. (2009) · Nature Physics · doi:10.1038/nphys1342 · Cited by 1,570
Quantum random walks: An introductory overview
Kempe, J. (2003) · Contemporary Physics · doi:10.1080/00107151031000110776 · Cited by 1,413
Girardot, J.-J. (2013) · HAL (Le Centre pour la Communication Scientifique Directe) · Cited by 1,404
Spin-glass models of neural networks
Amit, D. J., Gutfreund, H., & Sompolinsky, H. (1985) · Physical Review A · doi:10.1103/physreva.32.1007 · Cited by 1,201
Measurement-based quantum computation
Briegel, H. J., Browne, D. E., Dür, W., Raussendorf, R., & Van den Nest, M. (2009) · Nature Physics · doi:10.1038/nphys1157 · Cited by 1,090
Quantum random walks - an introductory overview
Kempe, J., & Einstein, A. (2003) · Cited by 1,035
Elements of Artificial Neural Networks
Mehrotra, K. G., Mohan, C. K., & Ranka, S. (1996) · The MIT Press eBooks · doi:10.7551/mitpress/2687.001.0001 · Cited by 921
Dynamical principles in neuroscience
Rabinovich, M. I., Varona, P., Selverston, A. I., & Abarbanel, H. D. I. (2006) · Reviews of Modern Physics · doi:10.1103/revmodphys.78.1213 · Cited by 839
(1996) · Cited by 824
Rojas, R. (1996) · doi:10.1007/978-3-642-61068-4 · Cited by 810
Importance of quantum decoherence in brain processes
Tegmark, M. (2000) · Physical Review E · doi:10.1103/physreve.61.4194 · Cited by 776
Quantum algorithms for supervised and unsupervised machine learning
Lloyd, S., Mohseni, M., & Rebentrost, P. (2013) · arXiv · doi:10.48550/arxiv.1307.0411 · Cited by 542
Quantum Computation by Adiabatic Evolution
Farhi, E., Goldstone, J., Gutmann, S., & Sipser, M. (2000) · arXiv · doi:10.48550/arxiv.quant-ph/0001106 · Cited by 536
Quantum computation in brain microtubules? The Penrose–Hameroff ‘Orch OR‘ model of consciousness
Hameroff, S. R. (1998) · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rsta.1998.0254 · Cited by 376
Physics of life: The dawn of quantum biology
Ball, P. (2011) · Nature · doi:10.1038/474272a · Cited by 307
Ventura, D. A. (2000) · Information Sciences · doi:10.1016/s0020-0255(99)00101-2 · Cited by 292
The Physical Implementation of Quantum Computation
Divincenzo, D. P. (2000) · Wiley eBooks · doi:10.1002/3527603182.ch1 · Cited by 288
Quantum algorithms for nearest-neighbor methods for supervised and unsupervised learning
Wiebe, N., Kapoor, A., & Svore, K. M. (2015) · Quantum Information and Computation · doi:10.26421/qic15.3-4-7 · Cited by 242
Kak, S. C. (1995) · Advances in imaging and electron physics · doi:10.1016/s1076-5670(08)70147-2 · Cited by 233
Quantum speed-up for unsupervised learning
Aı̈meur, E., Brassard, G., & Gambs, S. (2012) · Machine Learning · doi:10.1007/s10994-012-5316-5 · Cited by 218
Gupta, S., & Zia, R. K. P. (2001) · Journal of Computer and System Sciences · doi:10.1006/jcss.2001.1769 · Cited by 201
Quantum neural networks (QNNs): inherently fuzzy feedforward neural networks
Purushothaman, G., & Karayiannis, N. B. (1997) · IEEE Transactions on Neural Networks · doi:10.1109/72.572106 · Cited by 163
Quantum neural networks (QNNs): inherently fuzzy feedforward neural networks
Purushothaman, G., & Karayiannis, N. B. (2002) · IEEE International Conference on Neural Networks/IEEE ... International Conference on Neural Networks · doi:10.1109/icnn.1996.549049 · Cited by 152
Ezhov, A. A., & Ventura, D. (2000) · Studies in Fuzziness and Soft Computing · doi:10.1007/978-3-7908-1856-7_11 · Cited by 147
Probabilistic Quantum Memories
Trugenberger, C. A. (2001) · Physical Review Letters · doi:10.1103/physrevlett.87.067901 · Cited by 139
Efficient scheme for initializing a quantum register with an arbitrary superposed state
Long, G., & Sun, Y. (2001) · Physical Review A · doi:10.1103/physreva.64.014303 · Cited by 135
Trugenberger, C. A. (2002) · Quantum Information Processing · doi:10.1023/a:1024022632303 · Cited by 122
Simulations of quantum neural networks
Behrman, E., Nash, L. R., Steck, J. E., Chandrashekar, V. G., & Skinner, S. R. (2000) · Information Sciences · doi:10.1016/s0020-0255(00)00056-6 · Cited by 121
Altaisky, M. V. (2001) · arXiv · doi:10.48550/arxiv.quant-ph/0107012 · Cited by 101
Duality Quantum Computing and Duality Quantum Information Processing
Long, G. L. (2010) · International Journal of Theoretical Physics · doi:10.1007/s10773-010-0603-z · Cited by 96
Purves, D., Augustine, G. J., Fitzpatrick, D., Hall, W. C., LaMantia, A., McNamara, J. O., & Williams, S. (2004) · Cited by 92
Dissipation and spontaneous symmetry breaking in brain dynamics
Freeman, W. J., & Vitiello, G. (2008) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/41/30/304042 · Cited by 91
Neural networks with quantum architecture and quantum learning
Panella, M., & Martinelli, G. (2009) · International Journal of Circuit Theory and Applications · doi:10.1002/cta.619 · Cited by 79
Attal, S., Petruccione, F., & Sinayskiy, I. (2012) · Physics Letters A · doi:10.1016/j.physleta.2012.03.040 · Cited by 73
Self-citationFuture Directions for Intelligent Systems and Information Sciences
(2000) · Studies in fuzziness and soft computing · doi:10.1007/978-3-7908-1856-7 · Cited by 62
Zak, M. A., & Williams, C. P. (1998) · International Journal of Theoretical Physics · doi:10.1023/a:1026656110699 · Cited by 58
Spin-glass models of a neural network
van Hemmen, J. L. (1986) · Physical Review A · doi:10.1103/physreva.34.3435 · Cited by 50
Quantum Nearest-Neighbor Algorithms for Machine LearningPreprint
Wiebe, N., Kapoor, A., & Svore, K. M. (2014) · arXiv (Cornell University) · Cited by 50
Quantum pattern recognition with liquid-state nuclear magnetic resonance
Neigovzen, R., Neves, J. L., Sollacher, R., & Glaser, S. J. (2009) · Physical Review A · doi:10.1103/physreva.79.042321 · Cited by 49
Quantum walks on graphs representing the firing patterns of a quantum neural network
Schuld, M., Sinayskiy, I., & Petruccione, F. (2014) · Physical Review A · doi:10.1103/physreva.89.032333 · Cited by 49
Self-citationClassical and superposed learning for quantum weightless neural networks
da Silva, A. J., de Oliveira, W. R., & Ludermir, T. B. (2011) · Neurocomputing · doi:10.1016/j.neucom.2011.03.055 · Cited by 48
Efficiency of open quantum walk implementation of dissipative quantum computing algorithms
Sinayskiy, I., & Petruccione, F. (2012) · Quantum Information Processing · doi:10.1007/s11128-012-0426-3 · Cited by 46
Self-citationQuantum Effects in Neural Networks
Nishimori, H., & Nonomura, Y. (1996) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.65.3780 · Cited by 41
Quantum neural network in speech recognition
Li, F., Zhao, S., & Zheng, B. (2003) · doi:10.1109/icosp.2002.1180022 · Cited by 37
Quantum Associative Neural Network with Nonlinear Search Algorithm
Zhou, R., Wang, H., Wu, Q. H., & Shi, Y. (2011) · International Journal of Theoretical Physics · doi:10.1007/s10773-011-0950-4 · Cited by 37
A Quantum Neural Network Computes EntanglementPreprint
Behrman, E., Chandrashekar, V., Wang, Z., Belur, C. K., Steck, J. E., & Skinner, S. R. (2002) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0202131 · Cited by 36
Quantum Logical Neural Networks
de Oliveira, W. R., da Silva, A. J., Ludermir, T. B., Leonel, A., Galindo, W. R., & Pereira, J. C. C. (2008) · Brazilian Symposium on Neural Networks (SBRN) · doi:10.1109/sbrn.2008.9 · Cited by 34
A QUANTUM NEURAL NETWORK MODEL
Andrecut, M., & Ali, M. (2002) · International Journal of Modern Physics C · doi:10.1142/s0129183102002948 · Cited by 26
A quantum model for autonomous learning automata
Siomau, M. (2014) · Quantum Information Processing · doi:10.1007/s11128-013-0723-5 · Cited by 25
Open quantum random walks: Bistability on pure states and ballistically induced diffusion
Bauer, M., Bernard, D., & Tilloy, A. (2013) · Physical Review A · doi:10.1103/physreva.88.062340 · Cited by 24
Neurodynamics and attractors in quantum associative memories
Rigatos, G. G., & Tzafestaş, S. G. (2007) · Integrated Computer-Aided Engineering · doi:10.3233/ica-2007-14303 · Cited by 23
A spatial quantum neural computer
Behrman, E., Steck, J. E., & Skinner, S. R. (2003) · International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn.1999.831067 · Cited by 20
Autonomous Quantum Perceptron Neural NetworkPreprint
Sagheer, A., & Zidan, M. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1312.4149 · Cited by 18
A study of quantum neural networks
Fei, L., & Baoyu, Z. (2003) · International Conference on Neural Networks and Signal Processing · doi:10.1109/icnnsp.2003.1279330 · Cited by 16
Andrecut, M., & Ali, M. (2003) · International Journal of Modern Physics B · doi:10.1142/s0217979203018284 · Cited by 12
A quantum neural network computes its own relative phase
Behrman, E., & Steck, J. E. (2013) · IEEE Symposium on Swarm Intelligence (SIS) · doi:10.1109/sis.2013.6615168 · Cited by 9
Superposition Based Learning Algorithm
da Silva, A. J., Ludermir, T. B., & de Oliveira, W. R. (2010) · Brazilian Symposium on Neural Networks (SBRN) · doi:10.1109/sbrn.2010.9 · Cited by 9
Communication via quantum neural networks
Sagheer, A., & METWALLY, N. (2010) · World Congress on Nature and Biologically Inspired Computing (NaBIC) · doi:10.1109/nabic.2010.5716339 · Cited by 8
Quantum Algorithms for Nearest-Neighbor Methods for Supervised and Unsupervised LearningPreprint
Wiebe, N., Kapoor, A., & Svore, K. M. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1401.2142 · Cited by 8
Quantum Cybernetics and Complex Quantum Systems Science: A Quantum Connectionist Exploration
Gonçalves, C. P. (2015) · NeuroQuantology · doi:10.14704/nq.2015.13.1.804 · Cited by 7
Quantum Recurrent Networks for Simulating Stochastic Processes
Zak, M. A., & Williams, C. P. (1999) · Lecture notes in computer science · doi:10.1007/3-540-49208-9_5 · Cited by 5
Communication via Quantum Neural NetworkPreprint
Segher, A. A., & METWALLY, N. (2009) · arXiv (Cornell University) · doi:10.48550/arxiv.0912.2512 · Cited by 1
A quantum neural network computes its own relative phasePreprint
Behrman, E., & Steck, J. E. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1301.2808
The Physical Implementation of Quantum Computation
DiVincenzo, D. P. (2000) · Fortschritte der Physik · doi:10.1002/1521-3978(200009)48:9/11
Research works printed but not linked: 4
- Tóth, G., Lent, C.S., Tougaw, P.D., Brazhnik, Y., Weng, W., Porod, W., Liu, R.-W., Huang, Y.-F.: Quantum cellular neural networks (preprint). cond-mat/0005038 (2000) · arXiv
- Peruš, M.: Neural networks as a basis for quantum associative networks. Neural Netw. World 10(6), 1001–1013 (2000)
- Faber, J., Giraldi, G.A.: Quantum models for artificial neural networks. Electronically available: http://arquivosweb.lncc.br/pdfs/QNN-Review.pdf (2002)
- Siomau, M.: Quantum perceptron (preprint). arXiv:1210.6626 (2012) · arXiv
Cited by
Sorted by citations
Noisy intermediate-scale quantum algorithms
Bharti, K., Cervera-Lierta, A., Kyaw, T. H., Haug, T., Alperin-Lea, S., Anand, A., Degroote, M., Heimonen, H., Kottmann, J. S., Menke, T., et al. (2022) · Reviews of Modern Physics · doi:10.1103/revmodphys.94.015004 · Cited by 2,231
An introduction to quantum machine learning
Schuld, M., Sinayskiy, I., & Petruccione, F. (2015) · Contemporary Physics · doi:10.1080/00107514.2014.964942 · Cited by 1,381
Self-citationParameterized quantum circuits as machine learning models
Benedetti, M., Lloyd, E., Sack, S., & Fiorentini, M. (2019) · Quantum Science and Technology · doi:10.1088/2058-9565/ab4eb5 · Cited by 1,528
Machine learning & artificial intelligence in the quantum domain: a review of recent progress
Dunjko, V., & Briegel, H. J. (2018) · Reports on Progress in Physics · doi:10.1088/1361-6633/aab406 · Cited by 1,241
The power of quantum neural networks
Abbas, A., Sutter, D., Zoufal, C., Lucchi, A., Figalli, A., & Woerner, S. (2021) · Nature Computational Science · doi:10.1038/s43588-021-00084-1 · Cited by 1,082
Metadata
- Authors
- Schuld, M., Sinayskiy, I., & Petruccione, F.
- Affiliations
- University of KwaZulu-Natal (ZA)
- National Institute for Theoretical Physics (ZA)
- Corresponding author
- Schuld, Maria
- Venue
- Quantum Information Processing
- Published
- 2014-08-26
- Volume
- 13
- Issue
- 11
- Pages
- 2567-2586
- ISSN
- 1570-0755 (ISSN-L)
- 1573-1332
- OpenAlex
- W1990514347
- Cited by
- 671
- References
- 84
- Citations by year
- 2026: 83 · 2025: 131 · 2024: 72 · 2023: 80 · 2022: 51 · 2021: 83 · 2020: 49 · 2019: 41 · 2018: 38 · 2017: 17 · 2016: 15 · 2015: 6 · 2014: 5
- FWCI
- 14.29
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Quantum Information Processing (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Keywords
- quantum neural networks, Hopfield neural network, associative memory, quantum computing, artificial neural networks, nonlinear dynamics, unitary dynamics
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
