Solving (Max) 3-SAT via Quadratic Unconstrained Binary Optimization

Nüßlein, Jonas; Zielinski, Sebastian; Gabor, Thomas; Linnhoff‐Popien, Claudia; Feld, Sebastian

doi:10.1007/978-3-031-36030-5_3

Cited by 3 publications

(1 citation statement)

References 14 publications

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“…The Nüßlein n+m formulation 20 has a lower number of nonzero couplings between QUBO/Ising variables. Nüßlein n+m uses four different clause literal negation patterns20 for Max-3SAT, where each pattern corresponds to the number of negated literals in the clauses. The formulation then consists of constructing (or updating) the Hamiltonian, clause by clause.…”

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confidence: 99%

3SAT on an all-to-all-connected CMOS Ising solver chip

Cılasun,

Zeng,

et al. 2024

Sci Rep

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This work solves 3SAT, a classical NP-complete problem, on a CMOS-based Ising hardware chip with all-to-all connectivity. The paper addresses practical issues in going from algorithms to hardware. It considers several degrees of freedom in mapping the 3SAT problem to the chip—using multiple Ising formulations for 3SAT; exploring multiple strategies for decomposing large problems into subproblems that can be accommodated on the Ising chip; and executing a sequence of these subproblems on CMOS hardware to obtain the solution to the larger problem. These are evaluated within a software framework, and the results are used to identify the most promising formulations and decomposition techniques. These best approaches are then mapped to the all-to-all hardware, and the performance of 3SAT is evaluated on the chip. Experimental data shows that the deployed decomposition and mapping strategies impact SAT solution quality: without our methods, the CMOS hardware cannot achieve 3SAT solutions on SATLIB benchmarks. Under the assumption of some hardware improvements, our chip-based 3SAT solver demonstrates a remarkable 250$$\times$$ × acceleration compared to Tabu search in dwave-hybrid on a CPU.

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confidence: 99%

3SAT on an all-to-all-connected CMOS Ising solver chip

Cılasun,

Zeng,

et al. 2024

Sci Rep

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SATQUBOLIB: A Python Framework for Creating and Benchmarking (Max-)3SAT QUBOs

Zielinski,

Benkard,

Nüßlein

et al. 2024

Communications in Computer and Information Science

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Pattern QUBOs: Algorithmic Construction of 3SAT-to-QUBO Transformations

Zielinski,

Nüßlein,

Stein

et al. 2023

Electronics

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One way of solving 3sat instances on a quantum computer is to transform the 3sat instances into instances of Quadratic Unconstrained Binary Optimizations (QUBOs), which can be used as an input for the QAOA algorithm on quantum gate systems or as an input for quantum annealers. This mapping is performed by a 3sat-to-QUBO transformation. Recently, it has been shown that the choice of the 3sat-to-QUBO transformation can significantly impact the solution quality of quantum annealing. It has been shown that the solution quality can vary up to an order of magnitude difference in the number of correct solutions received, depending solely on the 3sat-to-QUBO transformation. An open question is: what causes these differences in the solution quality when solving 3sat-instances with different 3sat-to-QUBO transformations? To be able to conduct meaningful studies that assess the reasons for the differences in the performance, a larger number of different 3sat-to-QUBO transformations would be needed. However, currently, there are only a few known 3sat-to-QUBO transformations, and all of them were created manually by experts, who used time and clever reasoning to create these transformations. In this paper, we will solve this problem by proposing an algorithmic method that is able to create thousands of new and different 3sat-to-QUBO transformations, and thus enables researchers to systematically study the reasons for the significant difference in the performance of different 3sat-to-QUBO transformations. Our algorithmic method is an exhaustive search procedure that exploits properties of 4×4 dimensional pattern QUBOs, a concept which has been used implicitly in the creation of 3sat-to-QUBO transformations before, but was never described explicitly. We will thus also formally and explicitly introduce the concept of pattern QUBOs in this paper.

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Solving (Max) 3-SAT via Quadratic Unconstrained Binary Optimization

Cited by 3 publications

References 14 publications

3SAT on an all-to-all-connected CMOS Ising solver chip

3SAT on an all-to-all-connected CMOS Ising solver chip

SATQUBOLIB: A Python Framework for Creating and Benchmarking (Max-)3SAT QUBOs

Pattern QUBOs: Algorithmic Construction of 3SAT-to-QUBO Transformations

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