The DOI matches its Crossref record; 264 of the 266 references it cites were found in a registry or an index.
Quantum algorithms for algebraic problems
Open accessAbstract
Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for classical computers. Understanding what other computational problems can be solved significantly faster using quantum algorithms is one of the major challenges in the theory of quantum computation, and such algorithms motivate the formidable task of building a large-scale quantum computer. This article reviews the current state of quantum algorithms, focusing on algorithms with superpolynomial speedup over classical computation and, in particular, on problems with an algebraic flavor.
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
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
“However, an important technical point is that the sequences of operations (or quantum circuits, see Section 4.1.3) yielded from phase estimation are often too deep to be feasible on today's NISQ devices 51 .”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [51]
In the citing paper
“Furthermore, these early devices, also called 'pre-threshold' or NISQ 51 devices, cannot support quantum error correction schemes, which require additional overhead.”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [51]
Citations
Cites
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
Quantum computation and quantum information
Law, J. (2001) · ACM SIGSOFT Software Engineering Notes · doi:10.1145/505482.505499 · Cited by 20,450
New directions in cryptography
Diffie, W., & Hellman, M. (1976) · IEEE Transactions on Information Theory · doi:10.1109/tit.1976.1055638 · Cited by 14,713
A method for obtaining digital signatures and public-key cryptosystems
Rivest, R. L., Shamir, A., & Adleman, L. (1978) · Communications of the ACM · doi:10.1145/359340.359342 · Cited by 13,462
A method for obtaining digital signatures and public-key cryptosystems
Rivest, R. L., Shamir, A., & Adleman, L. (1983) · Communications of the ACM · doi:10.1145/357980.358017 · Cited by 13,012
Handbook of applied cryptography
(1997) · Choice Reviews Online · doi:10.5860/choice.34-4512 · Cited by 10,357
A fast quantum mechanical algorithm for database search
Grover, L. K. (1996) · Proceedings of the twenty-eighth annual ACM symposium on Theory of computing - STOC '96 · doi:10.1145/237814.237866 · Cited by 8,830
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
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
Simulating physics with computers
Feynman, R. P. (1982) · International Journal of Theoretical Physics · doi:10.1007/bf02650179 · Cited by 7,691
Research works printed but not linked: 69
- 10.4086/toc.2005.v001a004 · DOI
- Ajtai, M., 1996, ACM Symposium on Theory of Computing
- Ajtai, M., 1998, ACM Symposium on Theory of Computing
- Ajtai, M., 1997, ACM Symposium on Theory of Computing
- Ajtai, M., 2001, ACM Symposium on Theory of Computing
- Ambainis, A., 2007, IEEE Symposium on Foundations of Computer Science
- Ambainis, A., 2005, ACM-SIAM Symposium on Discrete Algorithms
- Ambainis, A., 2006, Symposium on Theoretical Aspects of Computer Science
- Babai, L., 1982, ACM Symposium on Theory of Computing
- Babai, L., 1983, IEEE Symposium on Foundations of Computer Science
- Babai, L., 1984, IEEE Symposium on Foundations of Computer Science
- Bacon, D., 2008, Quantum Inf. Comput., 8, 438
- Bacon, D., 2005, IEEE Symposium on Foundations of Computer Science
- Bacon, D., 2006, Chicago J. Theor. Comput. Sci., 2006, 2
- Beals, R., 1997, ACM Symposium on Theory of Computing
- Bernstein, E., 1993, ACM Symposium on Theory of Computing
- Boneh, D., 1995, Advances in Cryptology
- Buchmann, J. A., 1989, Advances in Cryptology
- Buhrman, H., 2006, ACM-SIAM Symposium on Discrete Algorithms
- Cheung, D., 2008, Proceedings of the Third Workshop on Theory of Quantum Computation, Communication, and Cryptography
- Cheung, K. K. H., 2001, Quantum Inf. Comput., 1, 26
- Childs, A. M., 2003, ACM Symposium on Theory of Computing
- Childs, A. M., 2007, IEEE Symposium on Foundations of Computer Science
- Childs, A. M., 2007, Quantum Inf. Comput., 7, 504
- Childs, A. M., 2007, ACM-SIAM Symposium on Discrete Algorithms
- Cleve, R., 2000, IEEE Symposium on Foundations of Computer Science
- Damgård, I. B., 1990, Advances in Cryptology
- Decker, T., 2009, Quantum Inf. Comput., 9, 215
- den Boer, B., 1990, Advances in Cryptology
- 10.4086/toc.2008.v004a008 · DOI
- Fenner, S. A., 2008, Proceedings of the Fifth Annual Conference on Theory and Applications of Models of Computation
- Filotti, I. S., 1980, ACM Symposium on Theory of Computing
- Flaxman, A. D., 2005, Symposium on Theoretical Aspects of Computer Science
- Friedl, K., 2003, ACM Symposium on Theory of Computing
- Gavinsky, D., 2004, Quantum Inf. Comput., 4, 229
- Hales, L., 2000, IEEE Symposium on Foundations of Computer Science
- Hallgren, S., 2005, ACM Symposium on Theory of Computing
- Hallgren, S., 2006, ACM Symposium on Theory of Computing
- Hayashi, M., 2008, Quantum Inf. Comput., 8, 345
- Impagliazzo, R., 1997, ACM Symposium on Theory of Computing
- Ivanyos, G., 2008, Quantum Inf. Comput., 8, 579
- Ivanyos, G., 2007, Symposium on Theoretical Aspects of Computer Science
- Ivanyos, G., 2008, Latin American Symposium on Theoretical Informatics
- Kawachi, A., 2005, Advances in Cryptology
- Kaye, P., 2005, Quantum Inf. Comput., 5, 474
- Lenstra, H. W., Jr., 2002, Not. Am. Math. Soc., 49, 182
- Lidl, R., 1997, Finite Fields
- Magniez, F., 2007, ACM Symposium on Theory of Computing
- Maslen, D. K., 1995, ACM-SIAM Symposium on Discrete Algorithms
- Miller, G., 1980, ACM Symposium on Theory of Computing
- Moore, C., 2007, ACM Symposium on Theory of Computing
- Mosca, M., 1999, Proceedings of the First NASA International Conference on Quantum Computing and Quantum Communication
- Okamoto, T., 2000, Advances in Cryptology
- Pérez-García, D., 2007, Quantum Inf. Comput., 7, 401
- Proos, J., 2003, Quantum Inf. Comput., 3, 317
- Püschel, M., 1999, International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
- Reichardt, B. W., 2004, ACM Symposium on Theory of Computing
- Reichardt, B. W., 2008, ACM Symposium on Theory of Computing
- Schmidt, A., 2005, ACM Symposium on Theory of Computing
- Shi, Y., 2003, Quantum Inf. Comput., 3, 84
- Shor, P. W., 1996, IEEE Symposium on Foundations of Computer Science
- Shor, P. W., 2008, Quantum Inf. Comput., 8, 681
- Spielman, D. A., 1996, ACM Symposium on Theory of Computing
- Szegedy, M., 2004, IEEE Symposium on Foundations of Computer Science
- van Dam, W., 2001, IEEE Symposium on Foundations of Computer Science
- Vollmer, U., 2000, Proceedings of the Fourth International Symposium on Algorithmic Number Theory
- Watrous, J., 2001, ACM Symposium on Theory of Computing
- Wocjan, P., 2008, Quantum Inf. Comput., 8, 147
- Yao, A. C.-C., 1993, IEEE Symposium on Foundations of Computer Science
Cited by
Sorted by citations
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
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
Quantum algorithms: an overview
Montanaro, A. (2016) · npj Quantum Information · doi:10.1038/npjqi.2015.23 · Cited by 1,071
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
Quantum walks: a comprehensive review
Venegas-Andraca, S. E. (2012) · Quantum Information Processing · doi:10.1007/s11128-012-0432-5 · Cited by 934
Quantum computing with defects
Weber, J. R., Koehl, W. F., Varley, J. B., Janotti, A., Buckley, B. B., de Walle, C. G. V., & Awschalom, D. D. (2010) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1003052107 · Cited by 816
Quantum random number generators
Herrero-Collantes, M., & García-Escartín, J. C. (2017) · Reviews of Modern Physics · doi:10.1103/revmodphys.89.015004 · Cited by 850
Burkard, G., Ladd, T. D., Pan, A., Nichol, J. M., & Petta, J. R. (2023) · Reviews of Modern Physics · doi:10.1103/revmodphys.95.025003 · Cited by 873
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
Quantum walks: a comprehensive reviewPreprint
Venegas-Andraca, S. E. (2012) · Cited by 533
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
Synthesis and optimization of reversible circuits—a survey
Saeedi, M., & Markov, I. L. (2013) · ACM Computing Surveys · doi:10.1145/2431211.2431220 · Cited by 294
Leone, L., Oliviero, S. F. E., & Hamma, A. (2022) · Physical Review Letters · doi:10.1103/physrevlett.128.050402 · Cited by 393
Hybrid Quantum-Classical Approach to Quantum Optimal Control
Li, J., Yang, X., Peng, X., & Sun, C.-P. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.150503 · Cited by 278
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 362
Maciejewski, F. B., Zimborás, Z., & Oszmaniec, M. (2020) · Quantum · doi:10.22331/q-2020-04-24-257 · Cited by 271
A novel quantum representation for log-polar images
Zhang, Y., Lü, K., Gao, Y., & Xu, K. (2013) · Quantum Information Processing · doi:10.1007/s11128-013-0587-8 · Cited by 204
Maciejewski, F., Zimborás, Z., & Oszmaniec, M. (2020) · Repository of the Academy's Library (Library of the Hungarian Academy of Sciences) · Cited by 184
Coherence depletion in the Grover quantum search algorithm
Shi, H., Liu, S., Wang, X.-H., Yang, W., Yang, Z.-Y., & Fan, H. (2017) · Physical Review A · doi:10.1103/physreva.95.032307 · Cited by 182
A novel image steganography technique based on quantum substitution boxes
El‐Latif, A. A. A., Abd-El-Atty, B., & Venegas-Andraca, S. E. (2019) · Optics & Laser Technology · doi:10.1016/j.optlastec.2019.03.005 · Cited by 181
Robust Encoding of a Qubit in a Molecule
Albert, V. V., Covey, J. P., & Preskill, J. P. (2020) · Physical Review X · doi:10.1103/physrevx.10.031050 · Cited by 172
Machine learning method for state preparation and gate synthesis on photonic quantum computers
Arrazola, J. M., Bromley, T. R., Izaac, J., Myers, C. R., Brádler, K., & Killoran, N. (2018) · Quantum Science and Technology · doi:10.1088/2058-9565/aaf59e · Cited by 153
Quantum Search Algorithms for Wireless Communications
Botsinis, P., Alanis, D., Babar, Z., Nguyen, H. V., Chandra, D., Ng, S. X., & Hanzo, L. (2019) · IEEE Communications Surveys & Tutorials · doi:10.1109/comst.2018.2882385 · Cited by 149
Experimental quantum fast hitting on hexagonal graphs
Tang, H., Di Franco, C., Shi, Z.-Y., He, T.-S., Feng, Z., Gao, J., Sun, K., Li, Z.-M., Jiao, Z.-Q., Wang, T.-Y., et al. (2018) · Nature Photonics · doi:10.1038/s41566-018-0282-5 · Cited by 113
Theory for Equivariant Quantum Neural Networks
Nguyen, Q. T., Schatzki, L., Braccia, P., Ragone, M., Coles, P. J., Sauvage, F., Larocca, M., & Cerezo, M. (2024) · PRX Quantum · doi:10.1103/prxquantum.5.020328 · Cited by 164
An Efficient Quantum Computing technique for cracking RSA using Shor’s Algorithm
Bhatia, V., & Ramkumar, K. R. (2020) · International Conference on Computing, Communication and Automation · doi:10.1109/iccca49541.2020.9250806 · Cited by 117
Giant anomalous Hall and Nernst effect in magnetic cubic Heusler compounds
Noky, J., Zhang, Y., Gooth, J., Felser, C., & Sun, Y. (2020) · npj Computational Materials · doi:10.1038/s41524-020-0342-5 · Cited by 103
Duong, T. Q., Nguyen, L. D., Narottama, B., Ansere, J. A., Huynh, D. V., & Shin, H. (2022) · IEEE Open Journal of the Communications Society · doi:10.1109/ojcoms.2022.3195219 · Cited by 110
Recent advances for quantum classifiers
Li, W., & Deng, D.-L. (2021) · Science China Physics Mechanics and Astronomy · doi:10.1007/s11433-021-1793-6 · Cited by 118
An encryption protocol for NEQR images based on one-particle quantum walks on a circle
Abd-El-Atty, B., El‐Latif, A. A. A., & Venegas-Andraca, S. E. (2019) · Quantum Information Processing · doi:10.1007/s11128-019-2386-3 · Cited by 101
High-Performance Computing with Quantum Processing Units
Britt, K. A., & Humble, T. S. (2017) · ACM Journal on Emerging Technologies in Computing Systems · doi:10.1145/3007651 · Cited by 112
Efficiently Computable Bounds for Magic State Distillation
Wang, X., Wilde, M. M., & Su, Y. (2020) · Physical Review Letters · doi:10.1103/physrevlett.124.090505 · Cited by 120
Quantum self-attention neural networks for text classification
Li, G., Zhao, X., & Wang, X. (2024) · Science China Information Sciences · doi:10.1007/s11432-023-3879-7 · Cited by 137
Quantum algorithm for nonhomogeneous linear partial differential equations
Arrazola, J. M., Kalajdzievski, T. Z., Weedbrook, C., & Lloyd, S. (2019) · Physical Review A · doi:10.1103/physreva.100.032306 · Cited by 98
Finding shortest lattice vectors faster using quantum search
Laarhoven, T., Mosca, M., & van de Pol, J. (2015) · Designs Codes and Cryptography · doi:10.1007/s10623-015-0067-5 · Cited by 97
Pal, S., Bhattacharya, M., Lee, S.-S., & Chakraborty, C. (2024) · Molecular Biotechnology · doi:10.1007/s12033-023-00765-4 · Cited by 103
Expressive power of parametrized quantum circuits
Du, Y., Hsieh, M.-H., Liu, T., & Tao, D. (2018) · UTS ePRESS (University of Technology Sydney) · Cited by 99
Attal, S., Petruccione, F., & Sinayskiy, I. (2012) · Physics Letters A · doi:10.1016/j.physleta.2012.03.040 · Cited by 73
Feo, L. D., Fouotsa, T. B., Kutas, P., Leroux, A., Merz, S.-P., Panny, L., & Wesolowski, B. (2023) · Lecture notes in computer science · doi:10.1007/978-3-031-31368-4_13 · Cited by 70
A quantum algorithm to solve nonlinear differential equations
Leyton, S. K., & Osborne, T. J. (2008) · arXiv · doi:10.48550/arxiv.0812.4423 · Cited by 65
Quantum computing with defects
Gordon, L., Weber, J. R., Varley, J. B., Janotti, A., Awschalom, D. D., & de Walle, C. G. V. (2013) · MRS Bulletin · doi:10.1557/mrs.2013.206 · Cited by 67
Generation of stable entanglement between two cavity mirrors by squeezed-reservoir engineering
Yang, C.-J., An, J., Yang, W., & Li, Y. (2015) · Physical Review A · doi:10.1103/physreva.92.062311 · Cited by 58
Chatrchyan, S., Khachatryan, V., Sirunyan, A. M., Tumasyan, A., Adam, W., Aguiló, E., Bergauer, T., Dragicevic, M., Erö, J., Fabjan, C. W., et al. (2013) · The European Physical Journal C · doi:10.1140/epjc/s10052-013-2404-z · Cited by 54
Primitive quantum gates for an SU(2) discrete subgroup: Binary tetrahedral
Gustafson, E., Lamm, H., Lovelace, F., & Musk, D. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.106.114501 · Cited by 71
Machine learning \& artificial intelligence in the quantum domainPreprint
Dunjko, V., & Briegel, H. J. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1709.02779 · Cited by 54
Davoudi, Z., Shaw, A. F., & Stryker, J. R. (2023) · Quantum · doi:10.22331/q-2023-12-20-1213 · Cited by 92
Primitive quantum gates for dihedral gauge theories
Alam, M. S., Hadfield, S., Lamm, H., & Li, A. C. Y. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.105.114501 · Cited by 49
Control by quantum dynamics on graphs
Godsil, C. D., & Simone Severini, B. (2010) · Physical Review A · doi:10.1103/physreva.81.052316 · Cited by 46
Brown, R., Tehei, M., Oktaria, S., Briggs, A., Stewart, C., Konstantinov, K., Rosenfeld, A. B., Corde, S., & Lerch, M. (2013) · Particle & Particle Systems Characterization · doi:10.1002/ppsc.201300276 · Cited by 45
Dissipative preparation of large W states in optical cavities
Sweke, R., Sinayskiy, I., & Petruccione, F. (2013) · Physical Review A · doi:10.1103/physreva.87.042323 · Cited by 43
Self-calibrating quantum state tomography
Brańczyk, A. M., Mahler, D. H., Rozema, L. A., Darabi, A., Steinberg, A. M., & James, D. F. V. (2012) · New Journal of Physics · doi:10.1088/1367-2630/14/8/085003 · Cited by 46
Programming quantum computers using design automation
Soeken, M., Häner, T., & Roetteler, M. (2018) · Design, Automation, and Test in Europe · doi:10.23919/date.2018.8341993 · Cited by 49
Validating quantum-classical programming models with tensor network simulations
McCaskey, A., Dumitrescu, E., Chen, M., Lyakh, D. I., & Humble, T. S. (2018) · PLoS ONE · doi:10.1371/journal.pone.0206704 · Cited by 45
Neural-network states for the classical simulation of quantum computingPreprint
Jónsson, B., Bauer, B., & Carleo, G. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1808.05232 · Cited by 81
A quantum annealing approach for boolean satisfiability problem
Su, J., Tu, T., & He, L. (2016) · ACM/IEEE Design Automation Conference (DAC) · doi:10.1145/2897937.2897973 · Cited by 39
Qunity: A Unified Language for Quantum and Classical Computing
Voichick, F., Li, L., Rand, R., & Hicks, M. (2023) · Proceedings of the ACM on Programming Languages · doi:10.1145/3571225 · Cited by 37
Provably Trainable Rotationally Equivariant Quantum Machine Learning
West, M. T., Heredge, J., Sevior, M. E., & Usman, M. (2024) · PRX Quantum · doi:10.1103/prxquantum.5.030320 · Cited by 50
Limitations of passive protection of quantum information
Pastawski, F., Kay, A., Schuch, N., & Cirac, J. I. (2010) · Quantum Information and Computation · doi:10.26421/qic10.7-8-3 · Cited by 42
Quantum algorithms for typical hard problems: a perspective of cryptanalysis
Suo, J., Wang, L., Yang, S., Zheng, W., & Zhang, J. (2020) · Quantum Information Processing · doi:10.1007/s11128-020-02673-x · Cited by 40
Mean Field Analysis of Quantum Annealing Correction
Matsuura, S., Nishimori, H., Albash, T., & Lidar, D. A. (2016) · Physical Review Letters · doi:10.1103/physrevlett.116.220501 · Cited by 38
Quantum computing for fusion energy science applications
Joseph, I., Shi, Y. C., Porter, M. D., Castelli, A. R., Geyko, V., Graziani, F. R., Libby, S. B., & DuBois, J. L. (2023) · Physics of Plasmas · doi:10.1063/5.0123765 · Cited by 42
Quantum Algorithms for Scientific Computing and Approximate OptimizationPreprint
Hadfield, S. (2018) · arXiv (Cornell University) · doi:10.7916/d8x650c9 · Cited by 76
A Comprehensive Survey on Quantum Machine Learning and Possible Applications
Umer, M. J., & Sharif, M. I. (2022) · International Journal of E-Health and Medical Communications · doi:10.4018/ijehmc.315730 · Cited by 41
General Linear Group Action on Tensors: A Candidate for Post-quantum Cryptography
Ji, Z., Qiao, Y., Song, F., & Yun, A. (2019) · Lecture notes in computer science · doi:10.1007/978-3-030-36030-6_11 · Cited by 45
Models of quantum computation and quantum programming languages
Miszczak, J. A. (2011) · Bulletin of the Polish Academy of Sciences Technical Sciences · doi:10.2478/v10175-011-0039-5 · Cited by 38
Quantum gates and architecture for the quantum simulation of the Fermi-Hubbard model
Dallaire-Demers, P.-L., & Wilhelm, F. (2016) · Physical Review A · doi:10.1103/physreva.94.062304 · Cited by 41
Mitigating Barren Plateaus of Variational Quantum Eigensolvers
Liu, X., Liu, G., Zhang, H.-K., Huang, J., & Wang, X. (2024) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2024.3383050 · Cited by 55
Experimental Realization of a One-Way Quantum Computer Algorithm Solving Simon’s Problem
Tame, M., Bell, B. A., Franco, C. D., Wadsworth, W. J., & Rarity, J. G. (2014) · Physical Review Letters · doi:10.1103/physrevlett.113.200501 · Cited by 35
A quantum-walk-inspired adiabatic algorithm for solving graph isomorphism problems
Tamascelli, D., & Zanetti, L. (2014) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/47/32/325302 · Cited by 37
Pretty good state transfer of entangled states through quantum spin chains
Sousa, R., & Omar, Y. (2014) · New Journal of Physics · doi:10.1088/1367-2630/16/12/123003 · Cited by 32
Quantum computation of discrete logarithms in semigroups
Childs, A. M., & Ivanyos, G. (2014) · Journal of Mathematical Cryptology · doi:10.1515/jmc-2013-0038 · Cited by 32
Self-citationGeneralized Deutsch-Jozsa problem and the optimal quantum algorithm
Qiu, D., & Zheng, S. (2018) · Physical Review A · doi:10.1103/physreva.97.062331 · Cited by 33
Entanglement of two rotating mirrors coupled to a single Laguerre-Gaussian cavity mode
Chen, Z., Peng, J., Fu, J., & Feng, X. (2019) · Optics Express · doi:10.1364/oe.27.029479 · Cited by 31
Quantum algorithm for solving hyperelliptic curve discrete logarithm problem
Huang, Y. T., Su, Z., Zhang, F., Ding, Y., & Cheng, R. (2020) · Quantum Information Processing · doi:10.1007/s11128-019-2562-5 · Cited by 33
Cheng, H.-J., Zhou, S.-J., Peng, J., Kundu, A., Li, H.-X., Jin, L., & Feng, X. (2020) · Journal of the Optical Society of America B · doi:10.1364/josab.405097 · Cited by 31
Quantum circuits for $${\mathbb {F}}_{2^{n}}$$ F 2 n -multiplication with subquadratic gate count
Kepley, S., & Steinwandt, R. (2015) · Quantum Information Processing · doi:10.1007/s11128-015-0993-1 · Cited by 32
Six-electron semiconductor double quantum dot qubits
Nielsen, E., Barnes, E., Kestner, J. P., & Sarma, S. D. (2013) · Physical Review B · doi:10.1103/physrevb.88.195131 · Cited by 29
Classical simulations of Abelian-group normalizer circuits with intermediate measurements
Bermejo-Vega, J., & den Nest, M. V. (2014) · Quantum Information and Computation · doi:10.26421/qic14.3-4-1 · Cited by 30
An Efficient Exact Quantum Algorithm for the Integer Square-free Decomposition Problem
Li, J., Peng, X., Du, J., & Suter, D. (2012) · Scientific Reports · doi:10.1038/srep00260 · Cited by 29
Quantum Computing for Cybersecurity
Alauthman, M., Almomani, A., Al–Qerem, A., Khaldy, M. A. A., Aldweesh, A. Y., Maqousi, A. Y. A., & Alkasassbeh, M. S. (2024) · Advances in information security, privacy, and ethics book series · doi:10.4018/979-8-3693-5330-1.ch004 · Cited by 28
A brief introduction to quantum algorithms
Zhang, S., & Li, L. (2022) · CCF Transactions on High Performance Computing · doi:10.1007/s42514-022-00090-3 · Cited by 31
Solving the Shortest Vector Problem in Lattices Faster Using Quantum Search
Laarhoven, T., Mosca, M., & van de Pol, J. (2013) · Lecture notes in computer science · doi:10.1007/978-3-642-38616-9_6 · Cited by 28
Efficient quantum algorithms for analyzing large sparse electrical networks
Wang, G. (2017) · Quantum Information and Computation · doi:10.26421/qic17.11-12-5 · Cited by 36
Quantum algorithm for obtaining the energy spectrum of a physical system
Wang, H., Ashhab, S., & Nori, F. (2012) · Physical Review A · doi:10.1103/physreva.85.062304 · Cited by 26
Primitive quantum gates for an S U ( 3 ) discrete subgroup: Σ ( 36 × 3 )
Gustafson, E., Ji, Y., Lamm, H., Murairi, E. M., Perez, S. O., & Zhu, S. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.110.034515 · Cited by 25
On the role of dealing with quantum coherence in amplitude amplification
Rastegin, A. E. (2018) · Quantum Information Processing · doi:10.1007/s11128-018-1946-2 · Cited by 25
Analysis of electromagnetic forces and causality in electron microscopy
Reyes–Coronado, A., Ortíz-Solano, C. G., Zabala, N., Rivacoba, A., & Esquivel-Sirvent, R. (2018) · Ultramicroscopy · doi:10.1016/j.ultramic.2018.06.006 · 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
Primitive quantum gates for an S U ( 2 ) discrete subgroup: Binary octahedral
Gustafson, E., Lamm, H., & Lovelace, F. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.109.054503 · Cited by 52
A quantum model for autonomous learning automata
Siomau, M. (2014) · Quantum Information Processing · doi:10.1007/s11128-013-0723-5 · Cited by 25
Quantum state transfer via Bloch oscillations
Tamascelli, D., Olivares, S., Rossotti, S., Osellame, R., & Paris, M. G. A. (2016) · Scientific Reports · doi:10.1038/srep26054 · Cited by 25
Quantum algorithms for highly non-linear Boolean functions
Rötteler, M. (2008) · Cited by 29
Gong, L.-H., He, X.-T., Tan, R.-C., & Zhou, Z. (2017) · International Journal of Theoretical Physics · doi:10.1007/s10773-017-3541-1 · Cited by 23
Algorithms for Quantum Computers
Smith, J., & Mosca, M. (2012) · Springer eBooks · doi:10.1007/978-3-540-92910-9_43 · Cited by 24
Factorization of numbers with Gauss sums: I. Mathematical background
Wölk, S., Merkel, W., Schleich, W. P., Averbukh, I. S., & Girard, B. (2011) · New Journal of Physics · doi:10.1088/1367-2630/13/10/103007 · Cited by 23
Cloud Computing: Security and Reliability Issues
Ahamed, F., Shahrestani, S. A., & Ginige, A. (2013) · Communications of the IBIMA · doi:10.5171/2013.655710 · Cited by 22
Kang, Y., Xiao, Y., Shi, Z., Wang, Y., Yang, J., Song, J., & Xia, Y. (2023) · New Journal of Physics · doi:10.1088/1367-2630/acc2de · Cited by 22
Can a quantum computer be applied for numerical weather prediction?
Фролов, А. В. (2017) · Russian Meteorology and Hydrology · doi:10.3103/s1068373917090011 · Cited by 22
Bloch–Landau–Zener dynamics induced by a synthetic field in a photonic quantum walk
D’Errico, A., Barboza, R., Tudor, R., Dauphin, A., Massignan, P., Marrucci, L., & Cardano, F. (2021) · APL Photonics · doi:10.1063/5.0037327 · Cited by 21
Mummaneni, B. C., Liu, J., Lefkidis, G., & Hübner, W. (2022) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.2c00172 · Cited by 23
Metadata
- Authors
- Childs, A. M., & van Dam, W.
- Affiliations
- University of Waterloo (CA)
- ORCID
- Childs, Andrew M.
- Venue
- Reviews of Modern Physics
- Publisher
- American Physical Society (APS)
- Published
- 2010-01-15
- Volume
- 82
- Issue
- 1
- Pages
- 1-52
- ISSN
- 0034-6861 (ISSN-L)
- 1539-0756
- OpenAlex
- W1972883454
- Cited by
- 344
- References
- 266
- Citations by year
- 2026: 14 · 2025: 20 · 2024: 23 · 2023: 53 · 2022: 23 · 2021: 13 · 2020: 18 · 2019: 16 · 2018: 19 · 2017: 17 · 2016: 15 · 2015: 16 · 2014: 24 · 2013: 24 · 2012: 22
- FWCI
- 23.31
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Reviews of Modern Physics (publishedVersion)
- arXiv (Cornell University) (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 › Computer Science › Computational Theory and Mathematics › Complexity and Algorithms in Graphs
- Keywords
- quantum algorithms, algebraic problems, integer factorization, Shor's algorithm, 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
