Papers
Topics
Authors
Recent
Search
2000 character limit reached

Quantum Complexity vs Classical Complexity: A Survey

Published 16 Dec 2023 in cs.CC and quant-ph | (2312.14075v5)

Abstract: Scientists have demonstrated that quantum computing has presented novel approaches to address computational challenges, each varying in complexity. Adapting problem-solving strategies is crucial to harness the full potential of quantum computing. Nonetheless, there are defined boundaries to the capabilities of quantum computing. This paper concentrates on aggregating prior research efforts dedicated to solving intricate classical computational problems through quantum computing. The objective is to systematically compile an exhaustive inventory of these solutions and categorize a collection of demanding open problems that await further exploration. Through statistical analysis, we help the researchers with their further investigations.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (258)
  1. Aaronson, S. Ten semi-grand challenges for quantum computing theory, 2005.
  2. Aaronson, S. Pdqp/qpoly= all. arXiv preprint arXiv:1805.08577 (2018).
  3. The need for structure in quantum speedups. Theory of Computing 10, 1 (2014), 133–166.
  4. Forrelation: A problem that optimally separates quantum from classical computing. In Proceedings of the forty-seventh annual ACM symposium on Theory of computing (2015), pp. 307–316.
  5. The computational complexity of linear optics, 2010.
  6. Certified randomness from quantum supremacy. arXiv preprint arXiv:2303.01625 (2023).
  7. Nonlinear quantum mechanics implies polynomial-time solution for np-complete and# p problems. Physical Review Letters 81, 18 (1998), 3992.
  8. Fast quantum algorithms for numerical integrals and stochastic processes. arXiv preprint quant-ph/9908083 (1999).
  9. Guest column: the quantum pcp conjecture. Acm sigact news 44, 2 (2013), 47–79.
  10. Interactive proofs for quantum computations. arXiv preprint arXiv:1704.04487 (2017).
  11. Quantum random walks. Physical Review A 48, 2 (1993), 1687.
  12. Hybrid classical-quantum optimization techniques for solving mixed-integer programming problems in production scheduling. IEEE Transactions on Quantum Engineering 3 (2022), 1–16.
  13. Near-Optimal Quantum Algorithms for String Problems. Proceedings of the 2022 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 2022, pp. 2791–2832.
  14. Non-interactive classical verification of quantum computation. In Theory of Cryptography Conference (2020), Springer, pp. 153–180.
  15. Quantum computing and the hunt for hidden symmetry. Bull. EATCS 93 (2007), 53–75.
  16. Alber, G. Entanglement and the linearity of quantum mechanics, 1999.
  17. Quantum Speedups for Exponential-Time Dynamic Programming Algorithms. Proceedings of the 2019 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 2019, pp. 1783–1793.
  18. Nlts hamiltonians from good quantum codes. In Proceedings of the 55th Annual ACM Symposium on Theory of Computing (2023), pp. 1090–1096.
  19. A unified framework of quantum walk search. arXiv preprint arXiv:1912.04233 (2019).
  20. Quantum depth in the random oracle model. In Proceedings of the 55th Annual ACM Symposium on Theory of Computing (2023), pp. 1111–1124.
  21. Quantum computing techniques for multi-knapsack problems. arXiv preprint arXiv:2301.05750 (2023).
  22. k-forrelation optimally separates quantum and classical query complexity. In Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing (2021), pp. 1303–1316.
  23. Bartusek, J. Secure quantum computation with classical communication. In Theory of Cryptography Conference (2021), Springer, pp. 1–30.
  24. Candidate obfuscation of null quantum circuits and witness encryption for qma. IACR Cryptol. ePrint Arch. 2021 (2021), 421.
  25. The quantum approximate optimization algorithm at high depth for maxcut on large-girth regular graphs and the sherrington-kirkpatrick model. arXiv preprint arXiv:2110.14206 (2021).
  26. Beaver, D. Correlated pseudorandomness and the complexity of private computations. In Proceedings of the twenty-eighth annual ACM symposium on Theory of computing (1996), pp. 479–488.
  27. Improved generic algorithms for hard knapsacks. In Annual International Conference on the Theory and Applications of Cryptographic Techniques (2011), Springer, pp. 364–385.
  28. Improved generic algorithms for hard knapsacks. In Advances in Cryptology – EUROCRYPT 2011 (Berlin, Heidelberg, 2011), K. G. Paterson, Ed., Springer Berlin Heidelberg, pp. 364–385.
  29. Quantum Speedup Based on Classical Decision Trees. Quantum 4 (Mar. 2020), 241.
  30. Quantum speedup based on classical decision trees. Quantum 4 (2020), 241.
  31. Time-and query-optimal quantum algorithms based on decision trees. ACM Transactions on Quantum Computing 3, 4 (2022), 1–31.
  32. Belovs, A. Learning-graph-based quantum algorithm for k-distinctness. In 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science (2012), IEEE, pp. 207–216.
  33. Ben-Or, M. Lower bounds for algebraic computation trees. In Proceedings of the Fifteenth Annual ACM Symposium on Theory of Computing (New York, NY, USA, 1983), STOC ’83, Association for Computing Machinery, p. 80–86.
  34. Measurement-driven quantum computing: Performance of a 3-sat solver. arXiv preprint arXiv:1711.02687 (2017).
  35. Integer programming techniques for minor-embedding in quantum annealers. In Integration of Constraint Programming, Artificial Intelligence, and Operations Research: 17th International Conference, CPAIOR 2020, Vienna, Austria, September 21–24, 2020, Proceedings 17 (2020), Springer, pp. 112–129.
  36. Quantum algorithms for the subset-sum problem. In Post-Quantum Cryptography: 5th International Workshop, PQCrypto 2013, Limoges, France, June 4-7, 2013. Proceedings 5 (2013), Springer, pp. 16–33.
  37. Quantum algorithms for the subset-sum problem. Cryptology ePrint Archive, Paper 2013/199, 2013. https://eprint.iacr.org/2013/199.
  38. An approach for improving complexity of longest common subsequence problems using queue and divide-and-conquer method. In 2019 1st international conference on advances in science, engineering and robotics technology (ICASERT) (2019), IEEE, pp. 1–5.
  39. Solving sat (and maxsat) with a quantum annealer: Foundations, encodings, and preliminary results. Information and computation 275 (2020), 104609.
  40. Solving subset sum problems using quantum inspired optimization algorithms with applications in auditing and financial data analysis. In 2022 21st IEEE International Conference on Machine Learning and Applications (ICMLA) (2022), IEEE, pp. 903–908.
  41. Optimizing the depth of variational quantum algorithms is strongly qcma-hard to approximate, 2023.
  42. Bjorklund, A. Determinant sums for undirected hamiltonicity. SIAM Journal on Computing 43, 1 (2014), 280–299.
  43. Quantum mycielski graphs. arXiv preprint arXiv:2306.09994 (2023).
  44. Improved classical and quantum algorithms for subset-sum. In Advances in Cryptology–ASIACRYPT 2020: 26th International Conference on the Theory and Application of Cryptology and Information Security, Daejeon, South Korea, December 7–11, 2020, Proceedings, Part II 26 (2020), Springer, pp. 633–666.
  45. Approximating edit distance in truly subquadratic time: Quantum and mapreduce. Journal of the ACM (JACM) 68, 3 (2021), 1–41.
  46. Decoding linear codes with high error rate and its impact for lpn security. In International Conference on Post-Quantum Cryptography (2018), Springer, pp. 25–46.
  47. Predicting parameters for the quantum approximate optimization algorithm for max-cut from the infinite-size limit. arXiv preprint arXiv:2110.10685 (2021).
  48. A cryptographic test of quantumness and certifiable randomness from a single quantum device. In 59th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2018, Paris, France, October 7-9, 2018 (2018), 320–331.
  49. Models of quantum complexity growth. PRX Quantum 2, 3 (2021), 030316.
  50. An optimal quantum algorithm to approximate the mean and its application for approximating the median of a set of points over an arbitrary distance. arXiv preprint arXiv:1106.4267 (2011).
  51. Quantum amplitude amplification and estimation. Contemporary Mathematics 305 (2002), 53–74.
  52. Quantum counting. In Automata, Languages and Programming: 25th International Colloquium, ICALP’98 Aalborg, Denmark, July 13–17, 1998 Proceedings 25 (1998), Springer, pp. 820–831.
  53. Bravyi, S. Efficient algorithm for a quantum analogue of 2-sat. Contemporary Mathematics 536 (2011), 33–48.
  54. Obstacles to variational quantum optimization from symmetry protection. Physical review letters 125, 26 (2020), 260505.
  55. Hybrid quantum-classical algorithms for approximate graph coloring. Quantum 6 (2022), 678.
  56. Second law of quantum complexity. Phys. Rev. D 97 (Apr 2018), 086015.
  57. Factoring integers with the number field sieve. In The development of the number field sieve (1993), Springer, pp. 50–94.
  58. A practical heuristic for finding graph minors. arXiv preprint arXiv:1406.2741 (2014).
  59. On the quantum chromatic number of a graph. arXiv preprint quant-ph/0608016 (2006).
  60. An adiabatic quantum algorithm and its application to dna motif model discovery. Information Sciences 296 (2015), 275–281.
  61. Lattice sieving via quantum random walks. In Advances in Cryptology–ASIACRYPT 2021: 27th International Conference on the Theory and Application of Cryptology and Information Security, Singapore, December 6–10, 2021, Proceedings, Part IV 27 (2021), Springer, pp. 63–91.
  62. On hybrid quantum and classical computing algorithms for mixed-integer programming. arXiv preprint arXiv:2010.07852 (2020).
  63. Quantum speedup and mathematical solutions of implementing bio-molecular solutions for the independent set problem on ibm quantum computers. IEEE Transactions on NanoBioscience 20, 3 (2021), 354–376.
  64. Quantum algorithms and mathematical formulations of biomolecular solutions of the vertex cover problem in the finite-dimensional hilbert space. IEEE transactions on nanobioscience 14, 1 (2014), 121–128.
  65. Quantum algorithms and mathematical representation of bio-molecular solutions for the hitting-set problem on a quantum computer. In 2010 International Conference on Computational Aspects of Social Networks (2010), IEEE, pp. 721–724.
  66. Quantum speedup for the maximum cut problem. arXiv preprint arXiv:2305.16644 (2023).
  67. Faster approximate pattern matching: A unified approach. In 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS) (2020), pp. 978–989.
  68. Quantum cooperative search algorithm for 3-sat. Journal of Computer and System Sciences 73, 1 (2007), 123–136.
  69. Classical verification of quantum computations with efficient verifier. In Theory of Cryptography Conference (2020), Springer, pp. 181–206.
  70. Childs, A. M. Universal computation by quantum walk. Physical review letters 102, 18 (2009), 180501.
  71. Finding cliques by quantum adiabatic evolution. arXiv preprint quant-ph/0012104 (2000).
  72. Constant-round blind classical verification of quantum sampling. In Annual International Conference on the Theory and Applications of Cryptographic Techniques (2022), Springer, pp. 707–736.
  73. The classical complexity of boson sampling. In Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms (2018), SIAM, pp. 146–155.
  74. Graph partitioning into hamiltonian subgraphs on a quantum annealer. arXiv preprint arXiv:2104.09503 (2021).
  75. Qfactory: classically-instructed remote secret qubits preparation. In Advances in Cryptology–ASIACRYPT 2019: 25th International Conference on the Theory and Application of Cryptology and Information Security, Kobe, Japan, December 8–12, 2019, Proceedings, Part I 25 (2019), Springer, pp. 615–645.
  76. Commander, C. W. Maximum cut problem, MAX-CUTMaximum Cut Problem, MAX-CUT. Springer US, Boston, MA, 2009, pp. 1991–1999.
  77. The quantum alternating operator ansatz on maximum k-vertex cover. In 2020 IEEE International Conference on Quantum Computing and Engineering (QCE) (2020), IEEE, pp. 83–92.
  78. A sublinear-time quantum algorithm for approximating partition functions. In Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) (2023), SIAM, pp. 1245–1264.
  79. Near-optimal quantum algorithms for multivariate mean estimation. In Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing (2022), pp. 33–43.
  80. Crooks, G. E. Performance of the quantum approximate optimization algorithm on the maximum cut problem. arXiv preprint arXiv:1811.08419 (2018).
  81. A qubo formulation of minimum multicut problem instances in trees for d-wave quantum annealers. Scientific reports 9, 1 (2019), 17216.
  82. Solving hamiltonian cycle problem using quantum ℤ2subscriptℤ2\mathbb{Z}_{2}blackboard_Z start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT lattice gauge theory. arXiv preprint arXiv:2202.08817 (2022).
  83. Random oracles in a quantum world. CoRR (2010).
  84. Mind the gap: Achieving a super-grover quantum speedup by jumping to the end. In Proceedings of the 55th Annual ACM Symposium on Theory of Computing (2023), pp. 1131–1144.
  85. Quantum invariants for the graph isomorphism problem. arXiv preprint arXiv:2209.14914 (2022).
  86. Improved low-memory subset sum and lpn algorithms via multiple collisions. In IMA International Conference on Cryptography and Coding (2019), Springer, pp. 178–199.
  87. Dill, K. A. Theory for the folding and stability of globular proteins. Biochemistry 24, 6 (1985), 1501–1509.
  88. Doern, S. Quantum complexity bounds for independent set problems, 2007.
  89. Doern, S. Quantum complexity of graph and algebraic problems, Feb 2008.
  90. Dörn, S. Quantum algorithms for graph traversals and related problems. In Proceedings of CIE (2007), vol. 7, pp. 123–131.
  91. Dörn, S. Quantum algorithms for matching problems. Theory Comput. Syst. 45, 3 (2009), 613–628.
  92. A novel algebraic geometry compiling framework for adiabatic quantum computations. arXiv preprint arXiv:1810.01440 (2018).
  93. Dugić, M. A note on the ohya-masuda quantum algorithm. Open Systems & Information Dynamics 9, 2 (may 2002), 115–123.
  94. A quantum algorithm for finding the minimum. arXiv preprint quant-ph/9607014 (1996).
  95. Dziemba, F. A. Adiabatic quantum computation, 2016.
  96. Quantum optimization of maximum independent set using rydberg atom arrays. Science 376, 6598 (2022), 1209–1215.
  97. Quantum linear algorithm for edit distance using the word qram model. arXiv preprint arXiv:2112.13005 (2021).
  98. Decodable quantum ldpc codes beyond the square root distance barrier using high dimensional expanders. In 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS) (2020).
  99. The quantum approximate optimization algorithm needs to see the whole graph: A typical case. arXiv preprint arXiv:2004.09002 (2020).
  100. The quantum approximate optimization algorithm needs to see the whole graph: Worst case examples. arXiv preprint arXiv:2005.08747 (2020).
  101. The quantum approximate optimization algorithm and the sherrington-kirkpatrick model at infinite size. Quantum 6 (2022), 759.
  102. Fleischner, H. Eulerian graphs and related topics. Elsevier, 1990.
  103. Fowler, A. G. Minimum weight perfect matching of fault-tolerant topological quantum error correction in average o⁢(1)𝑜1o(1)italic_o ( 1 ) parallel time. arXiv preprint arXiv:1307.1740 (2013).
  104. Computational self-testing of multi-qubit states and measurements. arXiv preprint arXiv:2201.13430 (2022), 6.
  105. Fujimura, T. Quantum algorithm for knapsack problem. Global Journal of Pure and Applied Mathematics 6, 3 (2010), 263–267.
  106. Gabow, H. N. Data structures for weighted matching and nearest common ancestors with linking. In Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms (1990), pp. 434–443.
  107. Gabow, H. N. The weighted matching approach to maximum cardinality matching. Fundamenta Informaticae 154, 1-4 (2017), 109–130.
  108. Graph isomorphism and adiabatic quantum computing. Physical Review A 89, 2 (feb 2014).
  109. A knn quantum cuckoo search algorithm applied to the multidimensional knapsack problem. Applied Soft Computing 102 (2021), 107077.
  110. Garey, M. R. Computers and intractability: A guide to the theory of np-completeness, freeman. Fundamental (1997).
  111. Computers and intractability: A guide to the theory of np-completeness, 1979.
  112. A hybrid algorithm framework for small quantum computers with application to finding hamiltonian cycles. Journal of Mathematical Physics 61, 1 (jan 2020), 012201.
  113. Hardness of approximation for quantum problems. In Automata, Languages, and Programming: 39th International Colloquium, ICALP 2012, Warwick, UK, July 9-13, 2012, Proceedings, Part I 39 (2012), Springer, pp. 387–398.
  114. Gheorghica, R.-I. The gr2 algorithm for subgraph isomorphism. a study from parallelism to quantum computing. In 2021 International Conference on Software, Telecommunications and Computer Networks (SoftCOM) (2021), pp. 1–6.
  115. Gheorghica, R.-I. The gr3 algorithm for parallel quantum searching of subgraph isomorphism. In 2021 International Conference on Software, Telecommunications and Computer Networks (SoftCOM) (2021), IEEE, pp. 1–6.
  116. Verification of quantum computation: An overview of existing approaches. Theory of computing systems 63 (2019), 715–808.
  117. Quantum cryptography with classical communication: parallel remote state preparation for copy-protection, verification, and more. arXiv preprint arXiv:2201.13445 (2022).
  118. Computationally-secure and composable remote state preparation. In 2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS) (2019), IEEE, pp. 1024–1033.
  119. Gindikin, S. G. Algebraic logic. Springer Science & Business Media, 1985.
  120. Quantum 3-sat is qma _1-complete. SIAM Journal on Computing 45, 3 (2016), 1080–1128.
  121. The quantum and classical complexity of translationally invariant tiling and hamiltonian problems. In 2009 50th Annual IEEE Symposium on Foundations of Computer Science (2009), IEEE, pp. 95–104.
  122. Quantum algorithms for the-xor problem. In International Conference on the Theory and Application of Cryptology and Information Security (2018), Springer, pp. 527–559.
  123. Introduction to Quantum Mechanics, 3 ed. Cambridge University Press, 2018.
  124. The graph isomorphism problem. Communications of the ACM 63, 11 (2020), 128–134.
  125. Grover, L. K. A fast quantum mechanical algorithm for database search. In Proceedings of the twenty-eighth annual ACM symposium on Theory of computing (1996), pp. 212–219.
  126. Qaoa for max-cut requires hundreds of qubits for quantum speed-up. Scientific reports 9, 1 (2019), 6903.
  127. Gurvits, L. Classical complexity and quantum entanglement. Journal of Computer and System Sciences 69, 3 (2004), 448–484. Special Issue on STOC 2003.
  128. A hybrid quantum particle swarm optimization for the multidimensional knapsack problem. Engineering Applications of Artificial Intelligence 55 (2016), 1–13.
  129. Identifying the minor set cover of dense connected bipartite graphs via random matching edge sets. Quantum Information Processing 16, 4 (2017), 94.
  130. Hamoudi, Y. Quantum algorithms for the Monte Carlo method. PhD thesis, Université Paris Cité, 2021.
  131. Hamoudi, Y. Quantum Sub-Gaussian Mean Estimator. In 29th Annual European Symposium on Algorithms (ESA 2021) (Dagstuhl, Germany, 2021), P. Mutzel, R. Pagh, and G. Herman, Eds., vol. 204 of Leibniz International Proceedings in Informatics (LIPIcs), Schloss Dagstuhl – Leibniz-Zentrum für Informatik, pp. 50:1–50:17.
  132. Faster k-sat algorithms using biased-ppsz. In Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing (New York, NY, USA, 2019), STOC 2019, Association for Computing Machinery, p. 578–589.
  133. Scalable and exponential quantum error mitigation of bqp computations using verification. arXiv preprint arXiv:2306.04351 (2023).
  134. Haverly, A. R. A comparison of quantum algorithms for the maximum clique problem. Rochester Institute of Technology, 2021.
  135. Heinrich, S. Quantum summation with an application to integration. Journal of Complexity 18, 1 (2002), 1–50.
  136. Heinrich, S. On the power of quantum algorithms for vector valued mean computation. Monte Carlo Methods and Applications (2004).
  137. On a problem in quantum summation. Journal of Complexity 19, 1 (2003), 1–18.
  138. A dynamic programming approach to sequencing problems. Journal of the Society for Industrial and Applied Mathematics 10, 1 (1962), 196–210.
  139. Subset sum quantumly in 1.17^ n. In 13th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2018) (2018), Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik.
  140. The power of few qubits and collisions–subset sum below grover’s bound. In International Conference on Post-Quantum Cryptography (2020), Springer, pp. 445–460.
  141. Quantum complexity for discrete logarithms and related problems. arXiv preprint arXiv:2307.03065 (2023).
  142. Explicit lower bounds against Ω (n)-rounds of sum-of-squares. In 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS) (2022), IEEE, pp. 662–673.
  143. Performance models for split-execution computing systems. In 2016 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW) (may 2016), IEEE.
  144. Computing graph edit distance on quantum devices. Quantum Machine Intelligence 4, 2 (aug 2022).
  145. Multidimensional quantum walks, with application to k𝑘kitalic_k-distinctness. arXiv preprint arXiv:2208.13492 (2022).
  146. Quantum programming of the satisfiability problem with rydberg atom graphs, 2023.
  147. The power of unentangled quantum proofs with non-negative amplitudes. In Proceedings of the 55th Annual ACM Symposium on Theory of Computing (New York, NY, USA, 2023), STOC 2023, Association for Computing Machinery, p. 1629–1642.
  148. Jiang, J.-R. Quantum circuit based on grover algorithm to solve hamiltonian cycle problem. In 2022 IEEE 4th Eurasia Conference on IOT, Communication and Engineering (ECICE) (2022), IEEE, pp. 364–367.
  149. Quantum speed-ups for string synchronizing sets, longest common substring, and k-mismatch matching. In Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) (2023), SIAM, pp. 5090–5121.
  150. Quantum annealing with manufactured spins. Nature 473, 7346 (May 2011), 194–198.
  151. Jozsa, R. An introduction to measurement based quantum computation. NATO Science Series, III: Computer and Systems Sciences. Quantum Information Processing-From Theory to Experiment 199 (2006), 137–158.
  152. The quantum and classical streaming complexity of quantum and classical max-cut. In 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS) (2022), IEEE, pp. 498–506.
  153. Scalable Architecture for Adiabatic Quantum Computing of Np-Hard Problems. Springer US, Boston, MA, 2004, pp. 229–236.
  154. An optimal space lower bound for approximating max-cut. In Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing (2019), pp. 277–288.
  155. Simulating chemistry using quantum computers. Annual review of physical chemistry 62 (2011), 185–207.
  156. String synchronizing sets: Sublinear-time bwt construction and optimal lce data structure. In Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing (New York, NY, USA, 2019), STOC 2019, Association for Computing Machinery, p. 756–767.
  157. Dynamic suffix array with polylogarithmic queries and updates. In Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing (New York, NY, USA, 2022), STOC 2022, Association for Computing Machinery, p. 1657–1670.
  158. Kempe, J. Quantum random walks: an introductory overview. Contemporary Physics 44, 4 (2003), 307–327.
  159. Asymptotically faster quantum distributed algorithms for approximate steiner trees and directed minimum spanning trees. arXiv preprint arXiv:2304.02825 (2023).
  160. Quantum algorithm for dynamic programming approach for dags and applications. Lobachevskii Journal of Mathematics 44, 2 (2023), 699–712.
  161. Kieu, T. D. The travelling salesman problem and adiabatic quantum computation: an algorithm. Quantum Information Processing 18, 3 (2019), 90.
  162. Rydberg quantum wires for maximum independent set problems. Nature Physics 18, 7 (2022), 755–759.
  163. A query-efficient quantum algorithm for maximum matching on general graphs. In Algorithms and Data Structures: 17th International Symposium, WADS 2021, Virtual Event, August 9–11, 2021, Proceedings 17 (2021), Springer, pp. 543–555.
  164. Kitaev, A. Y. Fault-tolerant quantum computation by anyons. Annals of physics 303, 1 (2003), 2–30.
  165. Algorithm design. Pearson Education India, 2006.
  166. Mean estimation when you have the source code; or, quantum monte carlo methods. In Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) (2023), SIAM, pp. 1186–1215.
  167. Kretschmer, W. Quantum Pseudorandomness and Classical Complexity. In 16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021) (Dagstuhl, Germany, 2021), M.-H. Hsieh, Ed., vol. 197 of Leibniz International Proceedings in Informatics (LIPIcs), Schloss Dagstuhl – Leibniz-Zentrum für Informatik, pp. 2:1–2:20.
  168. Laarhoven, T. Search problems in cryptography: from fingerprinting to lattice sieving. Ph.D. Thesis, Eindhoven University of Technology (2016).
  169. Solving low-density subset sum problems. Journal of the ACM (JACM) 32, 1 (1985), 229–246.
  170. Diversity-preserving quantum particle swarm optimization for the multidimensional knapsack problem. Expert Systems with Applications 149 (2020), 113310.
  171. Incremental string comparison. SIAM Journal on Computing 27, 2 (1998), 557–582.
  172. Quantum Meets Fine-Grained Complexity: Sublinear Time Quantum Algorithms for String Problems. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022) (Dagstuhl, Germany, 2022), M. Braverman, Ed., vol. 215 of Leibniz International Proceedings in Informatics (LIPIcs), Schloss Dagstuhl – Leibniz-Zentrum für Informatik, pp. 97:1–97:23.
  173. Quantum meets fine-grained complexity: Sublinear time quantum algorithms for string problems. Algorithmica 85, 5 (2023), 1251–1286.
  174. Verifying bqp computations on noisy devices with minimal overhead. PRX Quantum 2, 4 (2021), 040302.
  175. Three “quantum” algorithms to solve 3-sat. Theoretical Computer Science 372, 2-3 (2007), 218–241.
  176. Quantum tanner codes. In 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS) (2022), IEEE, pp. 872–883.
  177. Decoding quantum tanner codes. IEEE Transactions on Information Theory (2023).
  178. Efficient decoding up to a constant fraction of the code length for asymptotically good quantum codes. In Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) (2023), SIAM, pp. 1216–1244.
  179. Qubit mapping based on subgraph isomorphism and filtered depth-limited search. IEEE Transactions on Computers 70, 11 (2020), 1777–1788.
  180. Upper bounds on quantum query complexity inspired by the elitzur–vaidman bomb tester. Theory of Computing 12, 18 (2016), 1–35.
  181. Universal quantum computation using the discrete-time quantum walk. Physical Review A 81, 4 (2010), 042330.
  182. Approximation of the nearest classical-classical state to a quantum state. arXiv preprint arXiv:2301.09316 (2023).
  183. Mean estimation and regression under heavy-tailed distributions: A survey. Foundations of Computational Mathematics 19, 5 (2019), 1145–1190.
  184. Lyubashevsky, V. The parity problem in the presence of noise, decoding random linear codes, and the subset sum problem. In Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques: 8th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2005 and 9th International Workshop on Randomization and Computation, RANDOM 2005, Berkeley, CA, USA, August 22-24, 2005. Proceedings (2005), Springer, pp. 378–389.
  185. Search via quantum walk. In Proceedings of the thirty-ninth annual ACM symposium on Theory of computing (2007), pp. 575–584.
  186. Mahadev, U. Classical verification of quantum computations. In 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS) (2018), IEEE, pp. 259–267.
  187. Solving the hamiltonian cycle problem using a quantum computer. In Proceedings of the Australasian Computer Science Week Multiconference (2019), pp. 1–9.
  188. Manyem, P. Maximum independent set (stable set) problem: Computational testing with binary search and convex programming using a bin packing approach, 2023.
  189. A quantum algorithm for the sub-graph isomorphism problem. ACM Transactions on Quantum Computing 4, 2 (2023), 1–34.
  190. A quantum walk-assisted approximate algorithm for bounded np optimisation problems. Quantum Information Processing 18 (2019), 1–18.
  191. Mathews, G. B. On the partition of numbers. Proceedings of the London Mathematical Society 1, 1 (1896), 486–490.
  192. Benchmarking d-wave quantum annealers: Spectral gap scaling of maximum cardinality matching problems. In International Conference on Computational Science (2022), Springer, pp. 150–163.
  193. An o (v— v— c— e—) algoithm for finding maximum matching in general graphs. In 21st Annual Symposium on Foundations of Computer Science (sfcs 1980) (1980), IEEE, pp. 17–27.
  194. Quantum speedup for the minimum steiner tree problem. In International Computing and Combinatorics Conference (2020), Springer, pp. 234–245.
  195. Mohr, A. Quantum computing in complexity theory and theory of computation. Carbondale, IL 1 (2014).
  196. The subgraph isomorphism problem for port graphs and quantum circuits. arXiv preprint arXiv:2302.06717 (2023).
  197. Montanaro, A. Aceleración cuántica de los métodos de monte carlo. Actas de la Royal Society of London A: Mathematical, Physical and Engineering Sciences 471, 10.1098 (2015).
  198. Montanaro, A. Quantum walk speedup of backtracking algorithms. arXiv preprint arXiv:1509.02374 (2015).
  199. Quantum speedup of the traveling-salesman problem for bounded-degree graphs. Physical Review A 95, 3 (2017), 032323.
  200. Optimal merging in quantum k k-xor and k-sum algorithms. In Advances in Cryptology–EUROCRYPT 2020: 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Zagreb, Croatia, May 10–14, 2020, Proceedings, Part II 30 (2020), Springer, pp. 311–340.
  201. Non-abelian anyons and topological quantum computation. Reviews of Modern Physics 80, 3 (2008), 1083.
  202. Solving (max) 3-sat via quadratic unconstrained binary optimization. arXiv preprint arXiv:2302.03536 (2023).
  203. Np problem in quantum algorithm, 1998.
  204. Quantum computing, np-complete problems and chaotic dynamics, 1999.
  205. Nisq circuit compilation is the travelling salesman problem on a torus. Quantum Science and Technology 6, 2 (2021), 025016.
  206. Asymptotically good quantum and locally testable classical ldpc codes. In Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing (2022), pp. 375–388.
  207. Solving large minimum vertex cover problems on a quantum annealer. In Proceedings of the 16th ACM International Conference on Computing Frontiers (2019), pp. 76–84.
  208. Quantum optimization for maximum independent set using rydberg atom arrays, 2018.
  209. Ramanujan, M. On approximate compressions for connected minor-hitting sets. In 29th Annual European Symposium on Algorithms (ESA 2021) (2021), Schloss Dagstuhl-Leibniz-Zentrum für Informatik.
  210. A one-way quantum computer. Physical review letters 86, 22 (2001), 5188.
  211. Measurement-based quantum computation on cluster states. Physical review A 68, 2 (2003), 022312.
  212. Raz, R. Quantum information and the pcp theorem. In 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS’05) (2005), IEEE, pp. 459–468.
  213. Classical command of quantum systems. Nature 496, 7446 (2013), 456–460.
  214. The subspace flatness conjecture and faster integer programming. arXiv preprint arXiv:2303.14605 (2023).
  215. Robson, J. M. Finding a maximum independent set in time o (2n/4). Tech. rep., Technical Report 1251-01, LaBRI, Université Bordeaux I, 2001.
  216. Quantum divide and conquer for combinatorial optimization and distributed computing. arXiv preprint arXiv:2107.07532 10 (2021).
  217. Unconstrained binary models of the travelling salesman problem variants for quantum optimization. Quantum Information Processing 21, 2 (2022), 67.
  218. Schoning, T. A probabilistic algorithm for k-sat and constraint satisfaction problems. In 40th Annual Symposium on Foundations of Computer Science (Cat. No. 99CB37039) (1999), IEEE, pp. 410–414.
  219. Nilpotent adjacency matrices, random graphs and quantum random variables. Journal of Physics A: Mathematical and Theoretical 41, 15 (2008), 155205.
  220. A t=o⁢(2n/2)𝑡𝑜superscript2𝑛2t=o(2^{n/2})italic_t = italic_o ( 2 start_POSTSUPERSCRIPT italic_n / 2 end_POSTSUPERSCRIPT ), s=o⁢(2n/4)𝑠𝑜superscript2𝑛4s=o(2^{n/4})italic_s = italic_o ( 2 start_POSTSUPERSCRIPT italic_n / 4 end_POSTSUPERSCRIPT ) algorithm for certain np-complete problems. SIAM Journal on Computing 10, 3 (1981), 456–464.
  221. A t=o(2^n/2), s=o(2^n/4) algorithm for certain np-complete problems. SIAM journal on Computing 10, 3 (1981), 456–464.
  222. Solving optimization problems with rydberg analog quantum computers: Realistic requirements for quantum advantage using noisy simulation and classical benchmarks. Physical Review A 102, 5 (nov 2020).
  223. Shor, P. W. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM review 41, 2 (1999), 303–332.
  224. Qubit allocation as a combination of subgraph isomorphism and token swapping. Proceedings of the ACM on Programming Languages 3, OOPSLA (2019), 1–29.
  225. Efficient quantum algorithm for solving travelling salesman problem: An ibm quantum experience. arXiv preprint arXiv:1805.10928 (2018).
  226. Staples, G. S. A new adjacency matrix for finite graphs. Advances in Applied Clifford Algebras 18, 3-4 (2008), 979–991.
  227. Staples, G. S. Hamiltonian cycle enumeration via fermion-zeon convolution. International Journal of Theoretical Physics 56, 12 (2017), 3923–3934.
  228. Adaptive simulated annealing: A near-optimal connection between sampling and counting. Journal of the ACM (JACM) 56, 3 (2009), 1–36.
  229. Hyqsat: A hybrid approach for 3-sat problems by integrating quantum annealer with cdcl. In 2023 IEEE International Symposium on High-Performance Computer Architecture (HPCA) (2023), pp. 731–744.
  230. Terhal, B. Quantum algorithms and quantum entanglement. PhD thesis, University of Amsterdam, 1999.
  231. Faster quantum concentration via grover’s search. International Journal of Parallel, Emergent and Distributed Systems (2023), 1–16.
  232. Quantum optimization heuristics with an application to knapsack problems. In 2021 IEEE International Conference on Quantum Computing and Engineering (QCE) (2021), IEEE, pp. 160–170.
  233. Quantum hybrid algorithm for solving sat problem. Engineering Applications of Artificial Intelligence 121 (2023), 106058.
  234. On the design and characterization of set packing problem on quantum annealers. In IEEE EUROCON 2023 International Conference on Smart Technologies (2023), pp. 1–7.
  235. Revisiting old combinatorial beasts in the quantum age: quantum annealing versus maximal matching. In Computational Science–ICCS 2020: 20th International Conference, Amsterdam, The Netherlands, June 3–5, 2020, Proceedings, Part VI 20 (2020), Springer, pp. 473–487.
  236. Classical zero-knowledge arguments for quantum computations. Quantum 4 (2020), 266.
  237. Applying the quantum approximate optimization algorithm to the tail-assignment problem. Physical Review Applied 14, 3 (2020), 034009.
  238. Wang, G. Classically-boosted quantum optimization algorithm. arXiv preprint arXiv:2203.13936 (2022).
  239. Quantum speedup for solving the minimum vertex cover problem based on grover search algorithm. Quantum Information Processing 22, 7 (2023), 271.
  240. Warren, R. H. Adapting the traveling salesman problem to an adiabatic quantum computer. Quantum information processing 12 (2013), 1781–1785.
  241. Witter, R. T. A Query-Efficient Quantum Algorithm for Maximum Matching. PhD thesis, Middlebury, 2022.
  242. Wolsey, L. A. Mixed integer programming. Wiley Encyclopedia of Computer Science and Engineering (2007), 1–10.
  243. Fast quantum algorithm for protein structure prediction in hydrophobic-hydrophilic model. Journal of Parallel and Distributed Computing 164 (2022), 178–190.
  244. A review on algorithms for maximum clique problems. European Journal of Operational Research 242, 3 (2015), 693–709.
  245. Exact algorithms for maximum independent set. Information and Computation 255 (2017), 126–146.
  246. A scalable photonic computer solving the subset sum problem. Science Advances 6, 5 (2020), eaay5853.
  247. Yablonsky, S. V. Introduction to discrete mathematics. (No Title) (1989).
  248. Verifiable quantum advantage without structure. In 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS) (2022), IEEE, pp. 69–74.
  249. First results solving arbitrarily structured maximum independent set problems using quantum annealing. In 2018 IEEE Congress on Evolutionary Computation (CEC) (2018), pp. 1–6.
  250. Younes, A. A bounded-error quantum polynomial-time algorithm for two graph bisection problems. Quantum Information Processing 14 (2015), 3161–3177.
  251. Solution of sat problems with the adaptive-bias quantum approximate optimization algorithm. Physical Review Research 5, 2 (2023), 023147.
  252. Zhang, J. Succinct blind quantum computation using a random oracle. In Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing (2021), pp. 1370–1383.
  253. Zhang, J. Classical verification of quantum computations in linear time. In 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS) (2022), IEEE, pp. 46–57.
  254. Procedure of solving 3-sat problem by combining quantum search algorithm and dpll algorithm. Computing 4 (2020), 14–24.
  255. Applying the quantum approximate optimization algorithm to the minimum vertex cover problem. Applied Soft Computing 118 (2022), 108554.
  256. Analyzing the barren plateau phenomenon in training quantum neural networks with the ZX-calculus. Quantum 5 (jun 2021), 466.
  257. Zhegalkin, I. I. On a technique of evaluation of propositions in symbolic logic. Matematisheskii Sbornik 34, 1 (1927), 9–27.
  258. Quantum algorithm and experimental demonstration for the subset sum problem. Science China Information Sciences 65 (2022), 1–14.

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Generate Now

Tweets

Sign up for free to view the 4 tweets with 99 likes about this paper.

Sign Up for Free