A parallel spatial quantum search algorithm applied to the 3-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.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.

quant-pharXiv:2604.09980Apr 14, 20260 citations

Solving Highly Constrained Search Problems with Quantum Computers

Tad Hogg

A previously developed quantum search algorithm for solving 1-SAT problems in a single step is generalized to apply to a range of highly constrained k-SAT problems. We identify a bound on the number of clauses in satisfiability problems for which the generalized algorithm can find a solution in a constant number of steps as the number of variables increases. This performance contrasts with the linear growth in the number of steps required by the best classical algorithms, and the exponential number required by classical and quantum methods that ignore the problem structure. In some cases, the algorithm can also guarantee that insoluble problems in fact have no solutions, unlike previously proposed quantum search algorithms. 1. Introduction Quantum computers (Benioff, 1982; Bernstein & Vazirani, 1993; Deutsch, 1985, 1989; DiVincenzo, 1995; Feynman, 1986; Lloyd, 1993) offer a new approach to combinatorial search problems (Garey & Johnson, 1979) with quantum parallelism, i.e., the abilit...A previously developed quantum search algorithm for solving 1-SAT problems in a single step is generalized to apply to a range of highly constrained k-SAT problems. We identify a bound on the number of clauses in satisfiability problems for which the generalized algorithm can find a solution in a constant number of steps as the number of variables increases. This performance contrasts with the linear growth in the number of steps required by the best classical algorithms, and the exponential number required by classical and quantum methods that ignore the problem structure. In some cases, the algorithm can also guarantee that insoluble problems in fact have no solutions, unlike previously proposed quantum search algorithms. 1. Introduction Quantum computers (Benioff, 1982; Bernstein & Vazirani, 1993; Deutsch, 1985, 1989; DiVincenzo, 1995; Feynman, 1986; Lloyd, 1993) offer a new approach to combinatorial search problems (Garey & Johnson, 1979) with quantum parallelism, i.e., the abilit...

Jan 1, 19989 citations

Three “quantum” algorithms to solve 3-SAT

Alberto Leporati, Sara Felloni

Theoretical Computer ScienceDec 1, 200617 citations

Procedure of Solving 3-SAT Problem by Combining Quantum Search Algorithm and DPLL Algorithm

Runkai Zhang, Jing Chen, Huiling Zhao

Although some classical algorithms have been applied to solve the satisfiability problem, more effective methods are still explored because existing algorithms are constrained by inadequate computing capability of traditional computers. The parallelism of quantum computation makes quantum algorithms with promising potential to improve the computing ability, but existing quantum algorithms still require too large number of qubits to solve a simple problem effectively. In this paper, an optimized data structure was structured to solve Boolean satisfiability problem by utilizing Grover's algorithm, and then the corresponding formula was proposed to balance variables in consideration of complexity. With reasonable simplification, quantum circuits were built to decrease the number of qubits required in Grover's algorithm. The result of verification experiment further demonstrated that the proposed approach is simple, reliable and of a certain practical value.Although some classical algorithms have been applied to solve the satisfiability problem, more effective methods are still explored because existing algorithms are constrained by inadequate computing capability of traditional computers. The parallelism of quantum computation makes quantum algorithms with promising potential to improve the computing ability, but existing quantum algorithms still require too large number of qubits to solve a simple problem effectively. In this paper, an optimized data structure was structured to solve Boolean satisfiability problem by utilizing Grover's algorithm, and then the corresponding formula was proposed to balance variables in consideration of complexity. With reasonable simplification, quantum circuits were built to decrease the number of qubits required in Grover's algorithm. The result of verification experiment further demonstrated that the proposed approach is simple, reliable and of a certain practical value.

Computing Performance and Communication systemsDec 4, 20204 citations

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.