Algorithmic QUBO formulations for
            <i>k</i>
            -SAT and hamiltonian cycles

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

doi:10.1145/3520304.3533952

Cited by 8 publications

(2 citation statements)

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“…For applying QAOA to MAX-3SAT, the cost function in equation ( 2) is encoded in a cost Hamiltonian H ϕ . There are various formulations of this Hamiltonian [33,[36][37][38][39], with some focusing on reducing the number of operations required when implementing this cost function in the phase-separation operator. The formulations generally describe the cost Hamiltonian as a sum of clause operators…”

Section: Motivation and Research Questionsmentioning

confidence: 99%

Amplitude amplification-inspired QAOA: improving the success probability for solving 3SAT

Mandl,

Barzen,

Bechtold

et al. 2024

Quantum Sci. Technol.

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The Boolean satisfiability problem (SAT), in particular 3SAT with its bounded clause size, is a well-studied problem since a wide range of decision problems can be reduced to it. The Quantum Approximate Optimization Algorithm (QAOA) is a promising candidate for solving 3SAT for Noisy Intermediate-Scale Quantum devices in the near future due to its simple quantum ansatz. However, although QAOA generally exhibits a high approximation ratio, there are 3SAT problem instances where the algorithm's success probability when obtaining a satisfying variable assignment from the approximated solution drops sharply compared to the approximation ratio. To address this problem, in this paper, we present variants of the algorithm that are inspired by the amplitude amplification algorithm to improve the success probability for 3SAT. For this, (i) three amplitude amplification-inspired QAOA variants are introduced and implemented, (ii) the variants are experimentally compared with a standard QAOA implementation, and (iii) the impact on the success probability and ansatz complexity is analyzed. The experiment results show that an improvement in the success probability can be achieved with only a moderate increase in circuit complexity.

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Section: Motivation and Research Questionsmentioning

confidence: 99%

Amplitude amplification-inspired QAOA: improving the success probability for solving 3SAT

Mandl,

Barzen,

Bechtold

et al. 2024

Quantum Sci. Technol.

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“…In the recent past, a particular research effort was to transform NPhard optimization problems into instances of QUBO or Ising (e.g., see [15] for an overview). It is thus not surprising that the research community also studied satisfiability problems in the context of quantum computing (e.g., [16][17][18][19][20]).…”

Section: Introductionmentioning

confidence: 99%

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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