A Quantum-Inspired Classical Solver for Boolean k-Satisfiability Problems

• URL: http://arxiv.org/abs/2109.10291v1
• Date: Tue, 21 Sep 2021 16:10:52 GMT
• Title: A Quantum-Inspired Classical Solver for Boolean k-Satisfiability Problems
• Authors: S. Andrew Lanham and Brian R. La Cour
• Abstract summary: We describe an algorithmic approach to the k-satisfiability (k-SAT) problem that is inspired by the amplification amplification algorithm. We then discuss meaningfully leveraging this setting in a classical digital or analog computing setting to identify the strengths and limitations of AmplifySAT.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper we detail a classical algorithmic approach to the k-satisfiability (k-SAT) problem that is inspired by the quantum amplitude amplification algorithm. This work falls under the emerging field of quantum-inspired classical algorithms. To propose our modification, we adopt an existing problem model for k-SAT known as Universal SAT (UniSAT), which casts the Boolean satisfiability problem as a non-convex global optimization over a real-valued space. The quantum-inspired modification to UniSAT is to apply a conditioning operation to the objective function that has the effect of "amplifying" the function value at points corresponding to optimal solutions. We describe the algorithm for achieving this amplification, termed "AmplifySAT," which follows a familiar two-step process of applying an oracle-like operation followed by a reflection about the average. We then discuss opportunities for meaningfully leveraging this processing in a classical digital or analog computing setting, attempting to identify the strengths and limitations of AmplifySAT in the context of existing non-convex optimization strategies like simulated annealing and gradient descent.

Related papers

• Iterative quantum optimization of spin glass problems with rapidly oscillating transverse fields [0.0]
  We introduce a new iterative quantum algorithm, called Iterative Symphonic Tunneling for Satisfiability problems (IST-SAT) IST-SAT solves quantum spin glass optimization problems using high-frequency oscillating transverse fields.
  arXiv  Detail & Related papers  (2024-08-13T02:09:30Z)
• Compressed sensing enhanced by quantum approximate optimization algorithm [0.0]
  We present a framework to deal with a range of large scale compressive sensing problems using a quantum subroutine. Our results explore a promising path of applying quantum computers in the compressive sensing field.
  arXiv  Detail & Related papers  (2024-03-26T05:26:51Z)
• Quantum Approximate Optimisation for Not-All-Equal SAT [9.427635404752936]
  We apply variational quantum algorithm QAOA to a variant of satisfiability problem (SAT): Not-All-Equal SAT. We show that while the runtime of both solvers scales exponentially with the problem size, the scaling for QAOA is smaller for large enough circuit depths.
  arXiv  Detail & Related papers  (2024-01-05T15:11:24Z)
• Challenges of variational quantum optimization with measurement shot noise [0.0]
  We study the scaling of the quantum resources to reach a fixed success probability as the problem size increases. Our results suggest that hybrid quantum-classical algorithms should possibly avoid a brute force classical outer loop.
  arXiv  Detail & Related papers  (2023-07-31T18:01:15Z)
• An Optimization-based Deep Equilibrium Model for Hyperspectral Image Deconvolution with Convergence Guarantees [71.57324258813675]
  We propose a novel methodology for addressing the hyperspectral image deconvolution problem. A new optimization problem is formulated, leveraging a learnable regularizer in the form of a neural network. The derived iterative solver is then expressed as a fixed-point calculation problem within the Deep Equilibrium framework.
  arXiv  Detail & Related papers  (2023-06-10T08:25:16Z)
• Amplitude amplification-inspired QAOA: Improving the success probability for solving 3SAT [55.78588835407174]
  The amplitude amplification algorithm can be applied to unstructured search for satisfying variable assignments. The Quantum Approximate Optimization Algorithm (QAOA) is a promising candidate for solving 3SAT for Noisy Intermediate-Scale Quantum devices. We introduce amplitude amplification-inspired variants of QAOA to improve the success probability for 3SAT.
  arXiv  Detail & Related papers  (2023-03-02T11:52:39Z)
• Exploring the Algorithm-Dependent Generalization of AUPRC Optimization with List Stability [107.65337427333064]
  optimization of the Area Under the Precision-Recall Curve (AUPRC) is a crucial problem for machine learning. In this work, we present the first trial in the single-dependent generalization of AUPRC optimization. Experiments on three image retrieval datasets on speak to the effectiveness and soundness of our framework.
  arXiv  Detail & Related papers  (2022-09-27T09:06:37Z)
• 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)
• Quantum constraint learning for quantum approximate optimization algorithm [0.0]
  This paper introduces a quantum machine learning approach to learn the mixer Hamiltonian required to hard constrain the search subspace. One can directly plug the learnt unitary into the QAOA framework using an adaptable ansatz. We also develop an intuitive metric that uses Wasserstein distance to assess the performance of general approximate optimization algorithms with/without constraints.
  arXiv  Detail & Related papers  (2021-05-14T11:31:14Z)
• Adaptive pruning-based optimization of parameterized quantum circuits [62.997667081978825]
  Variisy hybrid quantum-classical algorithms are powerful tools to maximize the use of Noisy Intermediate Scale Quantum devices. We propose a strategy for such ansatze used in variational quantum algorithms, which we call "Efficient Circuit Training" (PECT) Instead of optimizing all of the ansatz parameters at once, PECT launches a sequence of variational algorithms.
  arXiv  Detail & Related papers  (2020-10-01T18:14:11Z)
• Convergence of adaptive algorithms for weakly convex constrained optimization [59.36386973876765]
  We prove the $mathcaltilde O(t-1/4)$ rate of convergence for the norm of the gradient of Moreau envelope. Our analysis works with mini-batch size of $1$, constant first and second order moment parameters, and possibly smooth optimization domains.
  arXiv  Detail & Related papers  (2020-06-11T17:43:19Z)

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.