Solving Segment Display Problems Using Quantum Grover's Search Algorithm

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.