Solving Segment Display Problems Using Quantum Grover's Search Algorithm

TL;DR

This paper presents a novel quantum approach using Grover's algorithm and reversible circuits to solve Segment Display Problems, demonstrated through a matchstick problem example on a simulated quantum computer.

Contribution

Introduces a Boolean-based quantum methodology for SDPs, including quantum oracle construction with reversible circuits and application to a classical problem.

Findings

Successfully solved a matchstick SDP instance using quantum Grover's search

Demonstrated feasibility on a noisy simulated quantum computer

Proposed a new quantum oracle construction method for SDPs

Abstract

This paper introduces a new Boolean-based methodology for constructing Segment Display Problems (SDPs) in the quantum domain and solving them using Grover's quantum search algorithm. In the classical domain, the SDPs are typically solved using various techniques, such as human deduction, heuristic search, and methods for solving Boolean satisfiability (SAT) and constraint satisfaction problems (CSPs) that are based on different problem design models. In this paper, our newly introduced methodology proposes a quantum-based approach for solving such SDPs, by building their quantum oracle using binary reversible circuits and our previously proposed step-decreasing structures shaped operators (Stesso). To demonstrate the usability of this proposed method, we experimentally solve an SDP instance of the matchstick problem using Grover's algorithm with a noisy simulated quantum computer implemented in Qiskit.