Comparing the hardness of MAX 2-SAT problem instances for quantum and classical algorithms

• URL: http://arxiv.org/abs/2206.06876v2
• Date: Fri, 21 Jul 2023 11:16:11 GMT
• Title: Comparing the hardness of MAX 2-SAT problem instances for quantum and classical algorithms
• Authors: Puya Mirkarimi, Adam Callison, Lewis Light, Nicholas Chancellor, Viv Kendon
• Abstract summary: An algorithm for a particular problem may find some instances of the problem easier and others harder to solve, even for a fixed input size. We numerically analyse the relative hardness of MAX 2-SAT problem instances for various continuous-time quantum algorithms and a comparable classical algorithm.
• Score: 1.0499611180329804
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: An algorithm for a particular problem may find some instances of the problem easier and others harder to solve, even for a fixed input size. We numerically analyse the relative hardness of MAX 2-SAT problem instances for various continuous-time quantum algorithms and a comparable classical algorithm. This has two motivations: to investigate whether small-sized problem instances, which are commonly used in numerical simulations of quantum algorithms for benchmarking purposes, are a good representation of larger instances in terms of their hardness to solve, and to determine the applicability of continuous-time quantum algorithms in a portfolio approach, where we take advantage of the variation in the hardness of instances between different algorithms by running them in parallel. We find that, while there are correlations in instance hardness between all of the algorithms considered, they appear weak enough that a portfolio approach would likely be desirable in practice. Our results also show a widening range of hardness of randomly generated instances as the problem size is increased, which demonstrates both the difference in the distribution of hardness at small sizes and the value of a portfolio approach that can reduce the number of extremely hard instances. We identify specific weaknesses of these quantum algorithms that can be overcome with a portfolio approach, such their inability to efficiently solve satisfiable instances (which is easy classically).

Related papers

• Sum-of-Squares inspired Quantum Metaheuristic for Polynomial Optimization with the Hadamard Test and Approximate Amplitude Constraints [76.53316706600717]
  Recently proposed quantum algorithm arXiv:2206.14999 is based on semidefinite programming (SDP) We generalize the SDP-inspired quantum algorithm to sum-of-squares. Our results show that our algorithm is suitable for large problems and approximate the best known classicals.
  arXiv  Detail & Related papers  (2024-08-14T19:04:13Z)
• Benchmarking Variational Quantum Algorithms for Combinatorial Optimization in Practice [0.0]
  Variational quantum algorithms and, in particular, variants of the varational quantum eigensolver have been proposed to address optimization (CO) problems. We numerically investigate what this scaling result means in practice for solving CO problems using Max-Cut as a benchmark.
  arXiv  Detail & Related papers  (2024-08-06T09:57:34Z)
• Variational Quantum Algorithms for the Allocation of Resources in a Cloud/Edge Architecture [1.072460284847973]
  We show that Variational Quantum Algorithms can be a viable alternative to classical algorithms in the near future. In particular, we compare the performances, in terms of success probability, of two algorithms, i.e., Quantum Approximate Optimization Algorithm (QAOA) and Variational Quantum Eigensolver (VQE) The simulation experiments, performed for a set of simple problems, %CM230124 that involve a Cloud and two Edge nodes, show that the VQE algorithm ensures better performances when it is equipped with appropriate circuit textitansatzes that are able to restrict the search space
  arXiv  Detail & Related papers  (2024-01-25T17:37:40Z)
• Quantum Algorithm for Maximum Biclique Problem [11.96554895748371]
  Identifying a biclique with the maximum number of edges bears considerable implications for numerous fields of application. We propose a ground-breaking algorithm qMBS with time complexity O*(2(n/2)), illustrating a quadratic speed-up in terms of complexity compared to the state-of-the-art. We detail two variants tailored for the maximum biclique problem and the maximum balanced biclique problem.
  arXiv  Detail & Related papers  (2023-09-08T04:43:05Z)
• Benchmarking Small-Scale Quantum Devices on Computing Graph Edit Distance [52.77024349608834]
  Graph Edit Distance (GED) measures the degree of (dis)similarity between two graphs in terms of the operations needed to make them identical. In this paper we present a comparative study of two quantum approaches to computing GED.
  arXiv  Detail & Related papers  (2021-11-19T12:35:26Z)
• Quadratic Unconstrained Binary Optimisation via Quantum-Inspired Annealing [58.720142291102135]
  We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. We benchmark our approach for large scale problem instances with tuneable hardness and planted solutions.
  arXiv  Detail & Related papers  (2021-08-18T09:26:17Z)
• Entropic barriers as a reason for hardness in both classical and quantum algorithms [2.062593640149623]
  We study both classical and quantum algorithms to solve a hard optimization problem, namely 3-XORSAT on 3-regular random graphs. By introducing a new quasi-greedy algorithm that is not allowed to jump over large energy barriers, we show that the problem hardness is mainly due to entropic barriers.
  arXiv  Detail & Related papers  (2021-01-30T07:58:24Z)
• Qualifying quantum approaches for hard industrial optimization problems. A case study in the field of smart-charging of electric vehicles [0.0]
  We present a case study for two industrial NP-Hard problems drawn from the strongly developing field of smart-charging of electric vehicles. Quantum algorithms exhibit the same approximation ratios than conventional approximation algorithms, or improve them. The next step will be to confirm them on larger instances, on actual devices, and for more complex versions of the problems addressed.
  arXiv  Detail & Related papers  (2020-12-29T17:10:31Z)
• The limits of min-max optimization algorithms: convergence to spurious non-critical sets [82.74514886461257]
  min-max optimization algorithms encounter problems far greater because of the existence of periodic cycles and similar phenomena. We show that there exist algorithms that do not attract any points of the problem. We illustrate such challenges in simple to almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost almost
  arXiv  Detail & Related papers  (2020-06-16T10:49:27Z)
• Beyond Worst-Case Analysis in Stochastic Approximation: Moment Estimation Improves Instance Complexity [58.70807593332932]
  We study oracle complexity of gradient based methods for approximation problems. We focus on instance-dependent complexity instead of worst case complexity. Our proposed algorithm and its analysis provide a theoretical justification for the success of moment estimation.
  arXiv  Detail & Related papers  (2020-06-08T09:25:47Z)
• Learning to Accelerate Heuristic Searching for Large-Scale Maximum Weighted b-Matching Problems in Online Advertising [51.97494906131859]
  Bipartite b-matching is fundamental in algorithm design, and has been widely applied into economic markets, labor markets, etc. Existing exact and approximate algorithms usually fail in such settings due to either requiring intolerable running time or too much computation resource. We propose textttNeuSearcher which leverages the knowledge learned from previously instances to solve new problem instances.
  arXiv  Detail & Related papers  (2020-05-09T02:48:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.