Solving Max-3SAT Using QUBO Approximation

• URL: http://arxiv.org/abs/2409.15891v1
• Date: Tue, 24 Sep 2024 09:02:34 GMT
• Title: Solving Max-3SAT Using QUBO Approximation
• Authors: Sebastian Zielinski, Jonas Nüßlein, Michael Kölle, Thomas Gabor, Claudia Linnhoff-Popien, Sebastian Feld,
• Abstract summary: We study whether systematically approximating QUBO representations of the MAX-3SAT problem can improve the solution quality when solved on contemporary quantum hardware. In an empirical evaluation, we demonstrate that using our QUBO approximations for solving MAX-3SAT problems on D-Wave's quantum annealer Advantage_System6.4 can yield better results than using state-of-the-art exact QUBO transformations.
• Score: 7.894094635723313
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: As contemporary quantum computers do not possess error correction, any calculation performed by these devices can be considered an involuntary approximation. To solve a problem on a quantum annealer, it has to be expressed as an instance of Quadratic Unconstrained Binary Optimization (QUBO). In this work, we thus study whether systematically approximating QUBO representations of the MAX-3SAT problem can improve the solution quality when solved on contemporary quantum hardware, compared to using exact, non-approximated QUBO representations. For a MAX-3SAT instance consisting of a 3SAT formula with n variables and m clauses, we propose a method of systematically creating approximate QUBO representations of dimension (n x n), which is significantly smaller than the QUBO matrices of any exact, non-approximated MAX-3SAT QUBO transformation. In an empirical evaluation, we demonstrate that using our QUBO approximations for solving MAX-3SAT problems on D-Wave's quantum annealer Advantage_System6.4 can yield better results than using state-of-the-art exact QUBO transformations. Furthermore, we demonstrate that using naive QUBO approximation methods, based on removing values from exact (n+m)x(n+m)-dimensional QUBO representations of MAX-3SAT instances is ineffective.

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)
• Using an Evolutionary Algorithm to Create (MAX)-3SAT QUBOs [8.364707571011266]
  We propose two methods of using evolutionary algorithms to automatically create QUBO representations of MAX-3SAT problems. We evaluate our created QUBOs on 500 and 1000-clause 3SAT formulae and find competitive performance to state-of-the-art baselines.
  arXiv  Detail & Related papers  (2024-05-15T11:41:13Z)
• Stochastic Optimization for Non-convex Problem with Inexact Hessian Matrix, Gradient, and Function [99.31457740916815]
  Trust-region (TR) and adaptive regularization using cubics have proven to have some very appealing theoretical properties. We show that TR and ARC methods can simultaneously provide inexact computations of the Hessian, gradient, and function values.
  arXiv  Detail & Related papers  (2023-10-18T10:29:58Z)
• A hybrid Quantum proposal to deal with 3-SAT problem [75.38606213726906]
  This paper presents and describes a hybrid quantum computing strategy for solving 3-SAT problems. The performance of this approximation has been tested over a set of representative scenarios when dealing with 3-SAT from the quantum computing perspective.
  arXiv  Detail & Related papers  (2023-06-07T12:19:22Z)
• Pattern QUBOs: Algorithmic construction of 3SAT-to-QUBO transformations [9.466991829376576]
  We will introduce the name Pattern QUBO for a concept that has been used implicitly in the construction of 3SAT-to-QUBO transformations before. We will show that approximate 3SAT-to-QUBO transformations can nevertheless be very effective in some cases.
  arXiv  Detail & Related papers  (2023-05-04T08:57:51Z)
• 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)
• Solving (Max) 3-SAT via Quadratic Unconstrained Binary Optimization [10.156623881772362]
  We introduce a novel approach to translate arbitrary 3-SAT instances to Quadratic Unconstrained Binary Optimization (QUBO) Our approach requires fewer couplings and fewer physical qubits than the current state-of-the-art, which results in higher solution quality.
  arXiv  Detail & Related papers  (2023-02-07T15:38:29Z)
• How to Approximate any Objective Function via Quadratic Unconstrained Binary Optimization [11.095381943951539]
  We present a toolkit of methods to transform almost arbitrary problems to Quadratic unconstrained binary optimization (QUBO) We showcase the usage of our approaches on two example problems (ratio cut and logistic regression)
  arXiv  Detail & Related papers  (2022-04-23T09:43:06Z)
• Adiabatic Quantum Computing for Multi Object Tracking [170.8716555363907]
  Multi-Object Tracking (MOT) is most often approached in the tracking-by-detection paradigm, where object detections are associated through time. As these optimization problems are often NP-hard, they can only be solved exactly for small instances on current hardware. We show that our approach is competitive compared with state-of-the-art optimization-based approaches, even when using of-the-shelf integer programming solvers.
  arXiv  Detail & Related papers  (2022-02-17T18:59:20Z)
• Transformer-based Machine Learning for Fast SAT Solvers and Logic Synthesis [63.53283025435107]
  CNF-based SAT and MaxSAT solvers are central to logic synthesis and verification systems. In this work, we propose a one-shot model derived from the Transformer architecture to solve the MaxSAT problem.
  arXiv  Detail & Related papers  (2021-07-15T04:47:35Z)
• Adiabatic Quantum Graph Matching with Permutation Matrix Constraints [75.88678895180189]
  Matching problems on 3D shapes and images are frequently formulated as quadratic assignment problems (QAPs) with permutation matrix constraints, which are NP-hard. We propose several reformulations of QAPs as unconstrained problems suitable for efficient execution on quantum hardware. The proposed algorithm has the potential to scale to higher dimensions on future quantum computing architectures.
  arXiv  Detail & Related papers  (2021-07-08T17:59:55Z)

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.