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Quantum Algorithm for Variant Maximum Satisfiability.

Abdirahman Alasow1, Peter Jin1, Marek Perkowski1

  • 1Department of Electrical & Computer Engineering, Portland State University, Portland, OR 97207, USA.

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Summary

We developed a new quantum algorithm for the maximum satisfiability (MAX-SAT) problem. This quantum counter approach efficiently determines how close a Boolean function is to being satisfiable, reducing qubit requirements.

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Grover search algorithmmaximum satisfiabilityquantum circuitquantum countersatisfiability

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Area of Science:

  • Quantum Computing
  • Computational Complexity Theory
  • Boolean Satisfiability Problems

Background:

  • The Satisfiability (SAT) problem is fundamental in computer science, determining if a Boolean function can be satisfied.
  • The Maximum Satisfiability (MAX-SAT) problem seeks to satisfy the maximum number of clauses in unsatisfiable Boolean functions.
  • Existing quantum algorithms for SAT and MAX-SAT often require significant qubit resources.

Purpose of the Study:

  • To propose a novel quantum algorithm for solving the MAX-SAT problem, particularly for POS (Product of ORs) SAT.
  • To provide a measure of how close an unsatisfiable Boolean function is to satisfaction.
  • To reduce the quantum resource requirements, specifically ancilla qubits, compared to traditional methods.

Main Methods:

  • Implementation of Grover's algorithm integrated with a novel 'quantum counter' block within the oracle circuit.
  • Design of a quantum circuit that adapts to various satisfiability expressions and related problems.
  • Utilizing the quantum counter and mirrors to reduce ancilla qubits from T to approximately log2(T)+1 for T terms.

Main Results:

  • The proposed quantum algorithm effectively addresses the MAX-SAT problem for POS SAT instances.
  • A significant reduction in the number of required ancilla qubits was achieved.
  • Analysis indicates a lower quantum cost for the novel oracle design compared to traditional approaches.

Conclusions:

  • The novel quantum algorithm offers an efficient method for MAX-SAT, providing insights into function satisfiability.
  • The developed circuit design demonstrates improved qubit efficiency and reduced quantum cost.
  • This approach is adaptable for various satisfiability-related computational problems.