理论物理通讯：英文版

A Parallel Quantum Algorithm for the Satisfiability Problem

Liu, WenZhang, Zhang, Jingfu, Long, Gui-Lu

Published Jan 1, 2008• 1 citation

Abstract

在这篇论文我们在场为可满足性问题的一个古典平行的量算法。我们利用了发展在的量算法的古典并行[长的 G.L 和 L. 小， Phys。加快。一 69 (2004 ) 052303 ] ，以便另外的加速能被使用古典并行获得。量算法首先用数算法，然后由使用量寻找算法的量估计答案的数字，明确的答案被发现。

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理论物理通讯：英文版

A Parallel Quantum Algorithm for the Satisfiability Problem

Liu, WenZhang, Zhang, Jingfu, Long, Gui-Lu

Published Jan 1, 2008• 1 citation

OpenAlex

Abstract

Related papers

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DNA computation could in principle solve the satisfiability (SAT) problem due to the operations in parallel on extremely large numbers of strands. We demonstrate some quantum gates corresponding to the DNA ones, based on which an implementation of DNA algorithm for SAT problem is available by quantum mechanical way. Since quantum computation owns the favorable feature of operations in parallel on 2 $^{n}$ states by using only n qubits, instead of 2 $^{n}$ strands in DNA computation, computational complexity is much reduced in treating the SAT problem quantum mechanically. We take a three-clause SAT problem with two variables as an example, and carry out a NMR experiment for solving a one-variable SAT problem.DNA computation could in principle solve the satisfiability (SAT) problem due to the operations in parallel on extremely large numbers of strands. We demonstrate some quantum gates corresponding to the DNA ones, based on which an implementation of DNA algorithm for SAT problem is available by quantum mechanical way. Since quantum computation owns the favorable feature of operations in parallel on 2$^{n}$ states by using only n qubits, instead of 2$^{n}$ strands in DNA computation, computational complexity is much reduced in treating the SAT problem quantum mechanically. We take a three-clause SAT problem with two variables as an example, and carry out a NMR experiment for solving a one-variable SAT problem.

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Denshi Jouhou Tsuushin Gakkai Tsuushin Sosaieti magajin/B-plus/Denshi Jouhou Tsuushin Gakkai Tsuushin Sosaeti magajinJan 1, 20200 citations

^{n}

states by using only n qubits, instead of 2

^{n}

strands in DNA computation, computational complexity is much reduced in treating the SAT problem quantum mechanically. We take a three-clause SAT problem with two variables as an example, and carry out a NMR experiment for solving a one-variable SAT problem.

Boolean satisfiability (SAT) problem is of fundamental importance in computer science and many application domains. For Grover's algorithm, solving the SAT problem requires

\mathcal{O}(\sqrt{2^n})

queries--where n denotes the number of logic variables in the problem. However, Grover's algorithm suffers from the Souffle problem: specifically, when the number of solutions is unknown, terminating the algorithm too early or too late leads to a significant reduction in the probability of obtaining a solution. In this paper, we propose a parallel fixed-point (PFP) search algorithm to solve the SAT problem. By exploiting entanglement, each clause in the conjunctive normal form (CNF) formula can be processed independently, leading to a significant reduction in circuit depth. We also discuss how to perform the algorithm in distributed manner. These make the PFPS algorithm particularly suitable for the noisy intermediate-scale quantum (NISQ) era.