Quantum Support Vector Machine for Big Data Classification
Open accessAbstract
Supervised machine learning is the classification of new data based on already classified training examples. In this work, we show that the support vector machine, an optimized binary classifier, can be implemented on a quantum computer, with complexity logarithmic in the size of the vectors and the number of training examples. In cases where classical sampling algorithms require polynomial time, an exponential speedup is obtained. At the core of this quantum big data algorithm is a nonsparse matrix exponentiation technique for efficiently performing a matrix inversion of the training data inner-product (kernel) matrix.
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
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?
Exponential speedup has been shown to be possible for quantum support vector machines.
“Exponential speedup has, for instance, shown to be possible for quantum support vector machines [110]”
From Neutral atom quantum computing hardware: performance and end-user perspective (2023) · cites this paper as [110]
By more sophisticated Trotter-Suzuki decompositions, the approximation error can be made to depend on progressively higher orders in τ.
“First, by more sophisticated Trotter-Suzuki decompositions 261 , the approximation error can be made to depend on progressively-higher orders in τ 196,260,261 .”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [261]
For an arbitrary vector |χ, the method serves as a tool for supervised learning and cluster assignment.
“If |χ is some other vector, then the method provides a method for supervised learning and cluster assignment 9,10,21,28 :”
From Quantum principal component analysis (2014) · cites this paper as [28]
The expressivity boost is not limited to neural networks and has been observed for support vector machines.
“Note that this expressivity boost is not limited to neural networks and has been observed, for instance, for support vector machines.[222,228,229]”
From Quantum Computing for Molecular Biology** (2023) · cites this paper as [222]
Quantum realizations of principal components analysis and support vector machine have been derived.
“The first advantage has been leveraged in deriving the quantum realization of the principal components analysis algorithm [221] and of a support vector machine.[222]”
From Quantum Computing for Molecular Biology** (2023) · cites this paper as [222]
Rebentrost et al. presented a quantum algorithm that can train a SVM with a polynomial kernel in O(log N), later extended to the radial basis function kernel.
“Rebentrost et al. [75] presented a quantum algorithm that can train a SVM with a polynomial kernel in O log N ð Þ, and this was later extended to the radial basis function (RBF) kernel [76].”
From The prospects of quantum computing in computational molecular biology (2021) · cites this paper as [75]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Cortes, C., & Vapnik, V. (1995) · Machine Learning · doi:10.1007/bf00994018 · Cited by 59,421 · see citing works
Boyd, S., & Vandenberghe, L. (2004) · doi:10.1017/cbo9780511804441 · Cited by 56,601 · see citing works
An Introduction to the Bootstrap
Efron, B., & Tibshirani, R. J. (1994) · doi:10.1201/9780429246593 · Cited by 40,500 · see citing works
Least Squares Support Vector Machine Classifiers
Suykens, J., & Vandewalle, J. (1999) · Neural Processing Letters · doi:10.1023/a:1018628609742 · Cited by 9,481 · see citing works
(2012) · Cited by 9,062 · see citing works
Information theory, inference, and learning algorithms
(2004) · Choice Reviews Online · doi:10.5860/choice.41-5949 · Cited by 6,535 · see citing works
Proceedings of the 25th international conference on Machine learning
Cohen, W. W., McCallum, A., & Roweis, S. T. (2008) · Cited by 5,691 · see citing works
ASH, R. B. (1966) · Cited by 3,910 · see citing works
An introduction to kernel-based learning algorithms
Müller, K. R., Mika, S., Rätsch, G., Tsuda, K., & Schölkopf, B. (2001) · IEEE Transactions on Neural Networks · doi:10.1109/72.914517 · Cited by 3,485 · see citing works
Quantum Algorithm for Linear Systems of Equations
Harrow, A. W., Hassidim, A., & Lloyd, S. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.150502 · Cited by 3,325 · see citing works
Self-citationPattern recognition and machine learning
(2007) · Choice Reviews Online · doi:10.5860/choice.44-5091 · Cited by 2,782 · see citing works
Matrix multiplication via arithmetic progressions
Coppersmith, D., & Winograd, S. (1990) · Journal of Symbolic Computation · doi:10.1016/s0747-7171(08)80013-2 · Cited by 2,248 · see citing works
Kernel methods in machine learning
Hofmann, T., Schölkopf, B., & Smola, A. J. (2008) · The Annals of Statistics · doi:10.1214/009053607000000677 · Cited by 1,758 · see citing works
Quantum principal component analysis
Lloyd, S., Mohseni, M., & Rebentrost, P. (2014) · Nature Physics · doi:10.1038/nphys3029 · Cited by 1,385 · see citing works
Self-citationProceedings Of The International Joint Conference On Neural Networks 2003
(2003) · International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn.2003.1223944 · Cited by 953 · see citing works
Giovannetti, V., Lloyd, S., & Maccone, L. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.160501 · Cited by 935 · see citing works
Self-citationInformation Theory, Inference, and Learning Algorithms
(2004) · IEEE Transactions on Information Theory · doi:10.1109/tit.2004.834752 · Cited by 866 · see citing works
Efficient Quantum Algorithms for Simulating Sparse Hamiltonians
Berry, D. W., Ahokas, G., Cleve, R., & Sanders, B. C. (2007) · Communications in Mathematical Physics · doi:10.1007/s00220-006-0150-x · Cited by 692 · see citing works
Book Review: Pattern Recognition and Machine Learning
Nasrabadi, N. M. (2007) · Journal of Electronic Imaging · doi:10.1117/1.2819119 · Cited by 636 · see citing works
Fast Monte Carlo Algorithms for Matrices II: Computing a Low-Rank Approximation to a Matrix
Drineas, P., Kannan, R., & Mahoney, M. W. (2006) · SIAM Journal on Computing · doi:10.1137/s0097539704442696 · Cited by 569 · see citing works
Randomized algorithms for the low-rank approximation of matrices
Liberty, E., Woolfe, F., Martinsson, P.-G., Rokhlin, V., & Tygert, M. (2007) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0709640104 · Cited by 559 · see citing works
Quantum Algorithm for Data Fitting
Wiebe, N., Braun, D., & Lloyd, S. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.050505 · Cited by 528 · see citing works
Self-citationOn the Relationship Between Continuous- and Discrete-Time Quantum Walk
Childs, A. M. (2010) · Communications in Mathematical Physics · doi:10.1007/s00220-009-0930-1 · Cited by 411 · see citing works
Introduction to Machine Learning (Adaptive Computation and Machine Learning)
Alpaydın, E. (2004) · The MIT Press eBooks · Cited by 291 · see citing works
Quantum Speedup for Active Learning Agents
Paparo, G. D., Dunjko, V., Makmal, A., Martin-Delgado, M. A., & Briegel, H. J. (2014) · Physical Review X · doi:10.1103/physrevx.4.031002 · Cited by 192 · see citing works
Quantum adiabatic machine learning
Pudenz, K. L., & Lidar, D. A. (2012) · Quantum Information Processing · doi:10.1007/s11128-012-0506-4 · Cited by 139 · see citing works
Quantum optimization for training support vector machines
Anguita, D., Ridella, S., Rivieccio, F., & Zunino, R. (2003) · Neural Networks · doi:10.1016/s0893-6080(03)00087-x · Cited by 120 · see citing works
Equivalences and Separations Between Quantum and Classical Learnability
Servedio, R. A., & Gortler, S. J. (2004) · SIAM Journal on Computing · doi:10.1137/s0097539704412910 · Cited by 118 · see citing works
Quantum learning and universal quantum matching machine
Sasaki, M., & Carlini, A. (2002) · Physical Review A · doi:10.1103/physreva.66.022303 · Cited by 103 · see citing works
Proceedings of the 29 th International Conference on Machine Learning, Edinburgh, Scotland, UK, 2012
Zhong, M., & Girolami, M. (2012) · Cited by 23 · see citing works
Flagged first, then by citations
Research works printed but not linked: 13
- [8]H. Neven, V. Denchev, G. Rose, and W. Macready, arXiv:quant-ph/0811.0416 (2008).
- [9]H. Neven, V. Denchev, G. Rose, and W. Macready, arXiv:0912.0779 (2009). · arXiv
- [10]K. Pudenz and D. Lidar, Quant. Inf. Proc. 12 , 2027 (2013).
- [11]V. S. Denchev, N. Ding, S. V. N. Vishwanathan, and H. Neven, arXiv:1205.1148 (2012). · arXiv
- [14]S. Lloyd, M. Mohseni, and P. Rebentrost, arXiv:1307.0411 (2013). · arXiv
- [18]S. Lloyd, M. Mohseni, and P. Rebentrost, arXiv:1307.0401 (2013). · arXiv
- [19]K.-R. M¨ uller, S. Mika, G. R¨ atsch, K. Tsuda, and B. Sch¨ olkopf, IEEE T. Neural Networ. 12 , 181 (2001).
- [23]S. Aaronson, arXiv:0910.4698 (2009). · arXiv
- [28]E. Liberty, F. Woolfe, P.-G. Martinsson, V. Rokhlin, and M. Tygert, Proc. Natl. Acad. Sci. USA 104 , 20167 (2007).
- [30]Z. Bar-Yossef, in Proc. 35th Annual ACM Symp. on Theory of Computing (2003).
- [31]N. Wiebe, A. Kapoor, and K. Svore, arXiv:1401.2142 (2014). · arXiv
- [32]G. D. Paparo, V. Dunjko, A. Makmal, M. A. Martin-Delgado, and H. J. Briegel, arXiv:1401.4997 (2014). · arXiv
- [33]C. Ding and X. He, in Proceedings of the 21st International Conference on Machine learning (2004).
Cited by
Sorted by citations
Biamonte, J., Wittek, P., Pancotti, N., Rebentrost, P., Wiebe, N., & Lloyd, S. (2017) · Nature · doi:10.1038/nature23474 · Cited by 4,779 · see citing works
Self-citationSupervised learning with quantum-enhanced feature spaces
Havlíček, V., Córcoles, A. D., Temme, K., Harrow, A. W., Kandala, A., Chow, J. M., & Gambetta, J. M. (2019) · Nature · doi:10.1038/s41586-019-0980-2 · Cited by 2,572 · see citing works
A quantum engineer's guide to superconducting qubits
Krantz, P., Kjærgaard, M., Yan, F., Orlando, T. P., Gustavsson, S., & Oliver, W. D. (2019) · Applied Physics Reviews · doi:10.1063/1.5089550 · Cited by 2,056 · see citing works
Quantum Machine Learning in Feature Hilbert Spaces
Schuld, M., & Killoran, N. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.040504 · Cited by 1,840 · see citing works
Big data in healthcare: management, analysis and future prospects
Dash, S., Shakyawar, S. K., Sharma, M., & Kaushik, S. (2019) · Journal of Big Data · doi:10.1186/s40537-019-0217-0 · Cited by 1,747 · see citing works
Mitarai, K., Negoro, M., Kitagawa, M., & Fujii, K. (2018) · Physical Review A · doi:10.1103/physreva.98.032309 · Cited by 1,639 · see citing works
Quantum Chemistry in the Age of Quantum Computing
Cao, Y., Romero, J., Olson, J. P., Degroote, M., Johnson, P. D., Kieferová, M., Kivlichan, I. D., Menke, T., Peropadre, B., Sawaya, N. P. D., et al. (2019) · Chemical Reviews · doi:10.1021/acs.chemrev.8b00803 · Cited by 1,560 · see citing works
Albash, T., & Lidar, D. A. (2018) · Reviews of Modern Physics · doi:10.1103/revmodphys.90.015002 · Cited by 1,546 · see citing works
Quantum principal component analysis
Lloyd, S., Mohseni, M., & Rebentrost, P. (2014) · Nature Physics · doi:10.1038/nphys3029 · Cited by 1,385 · see citing works
Self-citationAn introduction to quantum machine learning
Schuld, M., Sinayskiy, I., & Petruccione, F. (2015) · Contemporary Physics · doi:10.1080/00107514.2014.964942 · Cited by 1,381 · see citing works
Parameterized 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 1,324 · see citing works
Quantum Chemistry in the Age of Quantum Computing
Cao, Y., Romero, J., Olson, J., Degroote, M., Johnson, P., Kieferová, M., Kivlichan, I., Menke, T., Peropadre, B., Sawaya, N., et al. (n.d.) · OPUS - Open Publications of UTS Scholars (University of Technology Sydney) · Cited by 1,265 · see citing works
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 1,132 · see citing works
Circuit-centric quantum classifiers
Schuld, M., Bocharov, A., Svore, K. M., & Wiebe, N. (2020) · Physical Review A · doi:10.1103/physreva.101.032308 · Cited by 1,057 · see citing works
Quantum information processing with superconducting circuits: a review
Wendin, G. P. (2017) · Reports on Progress in Physics · doi:10.1088/1361-6633/aa7e1a · Cited by 970 · see citing works
Power of data in quantum machine learning
Huang, H.-Y., Broughton, M., Mohseni, M., Babbush, R., Boixo, S., Neven, H., & McClean, J. R. (2021) · Nature Communications · doi:10.1038/s41467-021-22539-9 · Cited by 896 · see citing works
Self-citationTsai, C.-W., Lai, C.-F., Chao, H.-C., & Vasilakos, A. V. (2015) · Journal of Big Data · doi:10.1186/s40537-015-0030-3 · Cited by 818 · see citing works
Effect of data encoding on the expressive power of variational quantum-machine-learning models
Schuld, M., Sweke, R., & Meyer, J. J. (2021) · Physical Review A · doi:10.1103/physreva.103.032430 · Cited by 739 · see citing works
Data re-uploading for a universal quantum classifier
Pérez-Salinas, A., Cervera-Lierta, A., Gil-Fuster, E., & Latorre, J. I. (2020) · Quantum · doi:10.22331/q-2020-02-06-226 · Cited by 713 · see citing works
Challenges and opportunities in quantum machine learning
Cerezo, M., Verdon, G., Huang, H.-Y., Cincio, Ł., & Coles, P. J. (2022) · Nature Computational Science · doi:10.1038/s43588-022-00311-3 · Cited by 735 · see citing works
Quantum computing for finance: Overview and prospects
Orús, R., Mugel, S., & Lizaso, E. (2019) · Reviews in Physics · doi:10.1016/j.revip.2019.100028 · Cited by 714 · see citing works
Classification with Quantum Neural Networks on Near Term Processors
Farhi, E., & Neven, H. (2020) · doi:10.37686/qrl.v1i2.80 · Cited by 909 · see citing works
Quantum Machine Learning for 6G Communication Networks: State-of-the-Art and Vision for the Future
Nawaz, S. J., Sharma, S. K., Wyne, S., Patwary, M. N., & Asaduzzaman, M. (2019) · IEEE Access · doi:10.1109/access.2019.2909490 · Cited by 658 · see citing works
A Survey on quantum computing technology
Gyongyosi, L., & Imre, S. (2019) · Computer Science Review · doi:10.1016/j.cosrev.2018.11.002 · Cited by 646 · see citing works
A rigorous and robust quantum speed-up in supervised machine learning
Liu, Y., Arunachalam, S., & Temme, K. (2021) · Nature Physics · doi:10.1038/s41567-021-01287-z · Cited by 649 · see citing works
Aaronson, S. (2015) · Nature Physics · doi:10.1038/nphys3272 · Cited by 567 · see citing works
Hybrid Quantum-Classical Algorithms and Quantum Error Mitigation
Endo, S., Cai, Z., Benjamin, S. C., & Yuan, X. (2021) · Journal of the Physical Society of Japan · doi:10.7566/jpsj.90.032001 · Cited by 566 · see citing works
Amin, M. H., Andriyash, E., Rolfe, J., Kulchytskyy, B., & Melko, R. (2018) · Physical Review X · doi:10.1103/physrevx.8.021050 · Cited by 520 · see citing works
Quantum machine learning: a classical perspective
Ciliberto, C., Herbster, M., Ialongo, A. D., Pontil, M., Rocchetto, A., Severini, S., & Wossnig, L. (2018) · Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences · doi:10.1098/rspa.2017.0551 · Cited by 518 · see citing works
Quantum-Enhanced Machine Learning
Dunjko, V., Taylor, J. M., & Briegel, H. J. (2016) · Physical Review Letters · doi:10.1103/physrevlett.117.130501 · Cited by 460 · see citing works
An introduction to quantum machine learningPreprint
Schuld, M., Sinayskiy, I., & Petruccione, F. (2014) · Cited by 435 · see citing works
Continuous-variable quantum neural networks
Killoran, N., Bromley, T. R., Arrazola, J. M., Schuld, M., Quesada, N., & Lloyd, S. (2019) · Physical Review Research · doi:10.1103/physrevresearch.1.033063 · Cited by 418 · see citing works
Self-citationSuperconducting quantum computing: a review
Huang, H.-L., Wu, D., Fan, D., & Zhu, X. (2020) · Science China Information Sciences · doi:10.1007/s11432-020-2881-9 · Cited by 389 · see citing works
Quantum convolutional neural network for classical data classification
Hur, T., Kim, L., & Park, D. K. (2022) · Quantum Machine Intelligence · doi:10.1007/s42484-021-00061-x · Cited by 390 · see citing works
Continuous-variable quantum neural networks
Killoran, N., Bromley, T. R., Arrazola, J. M., Schuld, M., Quesada, N., & Lloyd, S. (2018) · DSpace@MIT (Massachusetts Institute of Technology) · Cited by 358 · see citing works
Self-citationPotential of quantum computing for drug discovery
Cao, Y., Romero, J., & Aspuru-Guzik, A. (2018) · IBM Journal of Research and Development · doi:10.1147/jrd.2018.2888987 · Cited by 357 · see citing works
Deep learning in drug discovery: opportunities, challenges and future prospects
Lavecchia, A. (2019) · Drug Discovery Today · doi:10.1016/j.drudis.2019.07.006 · Cited by 353 · see citing works
Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning
Fujii, K., & Nakajima, K. (2017) · Physical Review Applied · doi:10.1103/physrevapplied.8.024030 · Cited by 337 · see citing works
Hierarchical quantum classifiers
Grant, E., Benedetti, M., Cao, S., Hallam, A., Lockhart, J., Stojevic, V., Green, A. G., & Simone Severini, B. (2018) · npj Quantum Information · doi:10.1038/s41534-018-0116-9 · Cited by 364 · see citing works
Expressive power of parametrized quantum circuits
Du, Y., Hsieh, M.-H., Liu, T., & Tao, D. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.033125 · Cited by 318 · see citing works
Experimental Quantum Generative Adversarial Networks for Image Generation
Huang, H.-L., Du, Y., Gong, M., Zhao, Y., Wu, Y., Wang, C., Li, S., Liang, F., Lin, J., Xu, Y., et al. (2021) · Physical Review Applied · doi:10.1103/physrevapplied.16.024051 · Cited by 314 · see citing works
Hierarchical quantum classifiers
Grant, E., Benedetti, M., Cao, S., Hallam, A., Lockhart, J., Stojevic, V, Green, A. G., & Simone Severini, B. (2018) · UCL Discovery (University College London) · Cited by 296 · see citing works
Herman, D., Googin, C., Liu, X., Sun, Y., Galda, A., Safro, I., Pistoia, M., & Alexeev, Y. (2023) · Nature Reviews Physics · doi:10.1038/s42254-023-00603-1 · Cited by 310 · see citing works
Hybrid quantum-classical convolutional neural networks
Liu, J., Lim, K. H., Wood, K. L., Huang, W., Guo, C., & Huang, H.-L. (2021) · Science China Physics, Mechanics & Astronomy · doi:10.1007/s11433-021-1734-3 · Cited by 289 · see citing works
Implementing a distance-based classifier with a quantum interference circuit
Schuld, M., Fingerhuth, M., & Petruccione, F. (2017) · EPL (Europhysics Letters) · doi:10.1209/0295-5075/119/60002 · Cited by 285 · see citing works
Learning the quantum algorithm for state overlap
Cincio, L., Subaşı, Y., Sornborger, A. T., & Coles, P. J. (2018) · New Journal of Physics · doi:10.1088/1367-2630/aae94a · Cited by 282 · see citing works
Prediction by linear regression on a quantum computer
Schuld, M., Sinayskiy, I., & Petruccione, F. (2016) · Physical Review A · doi:10.1103/physreva.94.022342 · Cited by 277 · see citing works
Quantum generalisation of feedforward neural networks
Wan, K. H., Dahlsten, O., Kristjánsson, H., Gardner, R., & Kim, M. S. (2017) · npj Quantum Information · doi:10.1038/s41534-017-0032-4 · Cited by 276 · see citing works
Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers
Perdomo-Ortiz, A., Benedetti, M., Realpe-Gómez, J., & Biswas, R. (2018) · Quantum Science and Technology · doi:10.1088/2058-9565/aab859 · Cited by 274 · see citing works
Simulating Large Quantum Circuits on a Small Quantum Computer
Peng, T., Harrow, A. W., Ozols, M., & Wu, X. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.150504 · Cited by 264 · see citing works
Experimental fault-tolerant universal quantum gates with solid-state spins under ambient conditions
Rong, X., Geng, J., Shi, F., Liu, Y., Xu, K., Ma, W., Kong, F., Jiang, Z. L., Wu, Y., & Du, J. (2015) · Nature Communications · doi:10.1038/ncomms9748 · Cited by 256 · see citing works
Experimental Realization of Quantum Artificial Intelligence
Zhaokai, L., Xiaomei, L., Nanyang, X., & jiangfeng, D. (2014) · arXiv · doi:10.48550/arxiv.1410.1054 · Cited by 261 · see citing works
Experimental Realization of a Quantum Support Vector Machine
Li, Z., Liu, X., Xu, N., & Du, J. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.140504 · Cited by 260 · see citing works
A Survey of Important Issues in Quantum Computing and Communications
Yang, Z., Zolanvari, M., & Jain, R. K. (2023) · IEEE Communications Surveys & Tutorials · doi:10.1109/comst.2023.3254481 · Cited by 262 · see citing works
Information-Theoretic Bounds on Quantum Advantage in Machine Learning
Huang, H.-Y., Kueng, R., & Preskill, J. P. (2021) · Physical Review Letters · doi:10.1103/physrevlett.126.190505 · Cited by 258 · see citing works
Quantum Algorithm Implementations for Beginners
Jayakumar, A., Adedoyin, A. A., Ambrosiano, J. J., Anisimov, P. M., Casper, W., Chennupati, G., Coffrin, C., Djidjev, H. N., Gunter, D., Karra, S., et al. (2022) · ACM Transactions on Quantum Computing · doi:10.1145/3517340 · Cited by 299 · see citing works
Distributed secure quantum machine learning
Sheng, Y.-B., & Zhou, L. (2017) · Science Bulletin · doi:10.1016/j.scib.2017.06.007 · Cited by 245 · see citing works
Zhang, Z., & Zhuang, Q. (2020) · Quantum Science and Technology · doi:10.1088/2058-9565/abd4c3 · Cited by 246 · see citing works
Quantum Models as Kernel Methods
Schuld, M., & Petruccione, F. (2021) · Quantum science and technology · doi:10.1007/978-3-030-83098-4_6 · Cited by 242 · see citing works
Quantum algorithms for topological and geometric analysis of data
Lloyd, S., Garnerone, S., & Zanardi, P. (2016) · Nature Communications · doi:10.1038/ncomms10138 · Cited by 241 · see citing works
Self-citationAutomated Search for new Quantum Experiments
Krenn, M., Malik, M., Fickler, R., Łapkiewicz, R., & Zeilinger, A. (2016) · Physical Review Letters · doi:10.1103/physrevlett.116.090405 · Cited by 234 · see citing works
Variational Quantum Simulation of General Processes
Endo, S., Sun, J., Li, Y., Benjamin, S. C., & Yuan, X. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.010501 · Cited by 237 · see citing works
The prospects of quantum computing in computational molecular biology
Outeiral, C., Strahm, M., Shi, J., Morris, G. M., Benjamin, S. C., & Deane, C. M. (2021) · WIREs Computational Molecular Science · doi:10.1002/wcms.1481 · Cited by 232 · see citing works
Cichocki, A. S., Phan, A.-H., Zhao, Q., Lee, N., Oseledets, I. V., Sugiyama, M., & Mandic, D. P. (2017) · Foundations and Trends® in Machine Learning · doi:10.1561/2200000067 · Cited by 227 · see citing works
Quantum Linear System Algorithm for Dense Matrices
Wossnig, L., Zhao, Z., & Prakash, A. (2018) · Physical Review Letters · doi:10.1103/physrevlett.120.050502 · Cited by 224 · see citing works
A quantum deep convolutional neural network for image recognition
Li, Y., Zhou, R.-G., Xu, R., Luo, J., & Hu, W. (2020) · Quantum Science and Technology · doi:10.1088/2058-9565/ab9f93 · Cited by 225 · see citing works
Benedetti, M., Realpe-Gómez, J., Biswas, R., & Perdomo-Ortiz, A. (2016) · Physical Review A · doi:10.1103/physreva.94.022308 · Cited by 215 · see citing works
Is Quantum Advantage the Right Goal for Quantum Machine Learning?
Schuld, M., & Killoran, N. (2022) · PRX Quantum · doi:10.1103/prxquantum.3.030101 · Cited by 227 · see citing works
Machine Learning: Quantum vs Classical
Khan, T. M., & Robles‐Kelly, A. (2020) · IEEE Access · doi:10.1109/access.2020.3041719 · Cited by 217 · see citing works
Solving a Higgs optimization problem with quantum annealing for machine learning
Mott, A., Job, J., Vlimant, J.-R., Lidar, D. A., & Spiropulu, M. (2017) · Nature · doi:10.1038/nature24047 · Cited by 202 · see citing works
Varatharajan, R., Manogaran, G., & Kumar, P. M. (2017) · Multimedia Tools and Applications · doi:10.1007/s11042-017-5318-1 · Cited by 208 · see citing works
RetractedQuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits
Wang, H., Ding, Y., Gu, J., Lin, Y., Pan, D. Z., Chong, F. T., & Han, S. (2022) · IEEE International Symposium on High-Performance Computer Architecture (HPCA) · doi:10.1109/hpca53966.2022.00057 · Cited by 215 · see citing works
Quantum Machine Learning: A Review and Case Studies
Zeguendry, A., Jarir, Z., & Quafafou, M. (2023) · Entropy · doi:10.3390/e25020287 · Cited by 221 · see citing works
Quantum arithmetic with the quantum Fourier transform
Ruiz, L., & García-Escartín, J. C. (2017) · Quantum Information Processing · doi:10.1007/s11128-017-1603-1 · Cited by 206 · see citing works
Li, R. Y., Di Felice, R., Rohs, R., & Lidar, D. A. (2018) · npj Quantum Information · doi:10.1038/s41534-018-0060-8 · Cited by 202 · see citing works
Quantum Image Processing and Its Application to Edge Detection: Theory and Experiment
Yao, X., Wang, H., Liao, Z., Chen, M.-C., Pan, J., Li, J., Zhang, K., Lin, X., Wang, ., Luo, Z., et al. (2017) · Physical Review X · doi:10.1103/physrevx.7.031041 · Cited by 191 · see citing works
Quantum classifier with tailored quantum kernel
Blank, C., Park, D. K., Rhee, J. K., & Petruccione, F. (2020) · npj Quantum Information · doi:10.1038/s41534-020-0272-6 · Cited by 191 · see citing works
0.5 petabyte simulation of a 45-qubit quantum circuit
Häner, T., & Steiger, D. S. (2017) · International Conference for High Performance Computing, Networking, Storage and Analysis (SC) · doi:10.1145/3126908.3126947 · Cited by 184 · see citing works
Quantum-inspired support vector machine
Ding, C., Bao, T.-Y., & Huang, H.-L. (2022) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2021.3084467 · Cited by 186 · see citing works
Solving nonlinear differential equations with differentiable quantum circuits
Kyriienko, O., Paine, A. E., & Elfving, V. E. (2021) · Physical Review A · doi:10.1103/physreva.103.052416 · Cited by 185 · see citing works
Quantum Hopfield neural network
Rebentrost, P., Bromley, T. R., Weedbrook, C., & Lloyd, S. (2018) · Physical Review A · doi:10.1103/physreva.98.042308 · Cited by 176 · see citing works
Self-citationQuantum gradient descent for linear systems and least squares
Kerenidis, I., & Prakash, A. (2020) · Physical Review A · doi:10.1103/physreva.101.022316 · Cited by 177 · see citing works
Support vector machines on the D-Wave quantum annealer
Willsch, D., Willsch, M., Raedt, H. A. D., & Michielsen, K. F. L. (2019) · Computer Physics Communications · doi:10.1016/j.cpc.2019.107006 · Cited by 177 · see citing works
Quantum Machine Learning Algorithms for Drug Discovery Applications
Batra, K., Zorn, K. M., Foil, D. H., Minerali, E., Gawriljuk, V. O., Lane, T. R., & Ekins, S. (2021) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.1c00166 · Cited by 176 · see citing works
NISQ computing: where are we and where do we go?
Lau, J. W. Z., Lim, K. H., Shrotriya, H., & Kwek, L. C. (2022) · AAPPS bulletin · doi:10.1007/s43673-022-00058-z · Cited by 176 · see citing works
Supervised quantum machine learning models are kernel methods
Schuld, M. (2021) · arXiv · doi:10.48550/arxiv.2101.11020 · Cited by 173 · see citing works
A software methodology for compiling quantum programs
Häner, T., Steiger, D. S., Svore, K. M., & Troyer, M. (2018) · Quantum Science and Technology · doi:10.1088/2058-9565/aaa5cc · Cited by 171 · see citing works
Variational algorithms for linear algebra
Xu, X., Sun, J., Endo, S., Li, Y., Benjamin, S. C., & Yuan, X. (2021) · 中国科学通报：英文版 · doi:10.1016/j.scib.2021.06.023 · Cited by 170 · see citing works
Tomography and generative training with quantum Boltzmann machines
Kieferová, M., & Wiebe, N. (2017) · Physical Review A · doi:10.1103/physreva.96.062327 · Cited by 170 · see citing works
Quantum generative adversarial network for generating discrete distribution
Situ, H., He, Z., Wang, Y., Li, L., & Zheng, S. (2020) · Information Sciences · doi:10.1016/j.ins.2020.05.127 · Cited by 175 · see citing works
On Circuit-Based Hybrid Quantum Neural Networks for Remote Sensing Imagery Classification
Sebastianelli, A., Zaidenberg, D. A., Spiller, D., Le Saux, B., & Ullo, S. (2022) · IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing · doi:10.1109/jstars.2021.3134785 · Cited by 162 · see citing works
Quantum machine learning for electronic structure calculations
Xia, R., & Kais, S. (2018) · Nature Communications · doi:10.1038/s41467-018-06598-z · Cited by 157 · see citing works
Zhou, N.-R., Zhang, T.-F., Xie, X.-W., & Wu, J.-Y. (2023) · Signal Processing Image Communication · doi:10.1016/j.image.2022.116891 · Cited by 161 · see citing works
Experimental Machine Learning of Quantum States
Gao, J., Qiao, L., Jiao, Z., Ma, Y., Hu, C.-Q., Ren, R.-J., Yang, A.-L., Tang, H. L., Yung, M., & Jin, X. (2018) · Physical Review Letters · doi:10.1103/physrevlett.120.240501 · Cited by 151 · see citing works
Machine learning in the quantum realm: The state-of-the-art, challenges, and future vision
Houssein, E. H., Abohashima, Z., Elhoseny, M., & Mohamed, W. M. (2022) · Expert Systems with Applications · doi:10.1016/j.eswa.2022.116512 · Cited by 157 · see citing works
The Born supremacy: quantum advantage and training of an Ising Born machine
Coyle, B., Mills, D., Danos, V., & Kashefi, E. (2020) · npj Quantum Information · doi:10.1038/s41534-020-00288-9 · Cited by 155 · see citing works
Quantum-Assisted Learning of Hardware-Embedded Probabilistic Graphical Models
Benedetti, M., Realpe-Gómez, J., Biswas, R., & Perdomo‐Ortiz, A. (2017) · Physical Review X · doi:10.1103/physrevx.7.041052 · Cited by 155 · see citing works
Image classification based on quantum K-Nearest-Neighbor algorithm
Dang, Y., Jiang, N., Hu, H., Ji, Z., & Zhang, W. (2018) · Quantum Information Processing · doi:10.1007/s11128-018-2004-9 · Cited by 160 · see citing works
The strong gravitational lens finding challenge
Metcalf, R. B., Meneghetti, M., Avestruz, C., Bellagamba, F., Bom, C. R., Bertin, E., Cabanac, R., Courbin, F., Davies, A., Decencière, E., et al. (2019) · Astronomy & Astrophysics · doi:10.1051/0004-6361/201832797 · Cited by 152 · see citing works
Guest Column: A Survey of Quantum Learning Theory
Arunachalam, S., & de Wolf, R. (2017) · ACM SIGACT News · doi:10.1145/3106700.3106710 · Cited by 152 · see citing works
- Authors
- Rebentrost, P., Mohseni, M., & Lloyd, S.
- Affiliations
- Massachusetts Institute of Technology (US)
- Google (United States) (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2014-09-25
- Volume
- 113
- Issue
- 13
- Pages
- 130503-130503
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2103956991
- Cited by
- 1,951
- References
- 30
- Citations by year
- 2026: 229 · 2025: 306 · 2024: 274 · 2023: 277 · 2022: 205 · 2021: 208 · 2020: 151 · 2019: 105 · 2018: 77 · 2017: 54 · 2016: 45 · 2015: 13 · 2014: 7
- FWCI
- 39.50
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- DSpace@MIT (Massachusetts Institute of Technology) (submittedVersion, cc-by-nc)
- arXiv (Cornell University)
- Funders
- Defense Advanced Research Projects Agency (DARPA)
- National Science Foundation (NSF)
- Eni
- Air Force Office of Scientific Research (AFOSR)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- quantum support vector machine, quantum machine learning, big data classification, binary classification, quantum advantage, matrix inversion, kernel matrix, quantum computing
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
