A Resource Efficient Ising Model‐Based Quantum Sudoku Solver

ABSTRACT Background Quantum algorithms exploit superposition and parallelism to address complex combinatorial problems, many of which fall into the non‐polynomial (NP) class. Sudoku, a widely known logic‐based puzzle, is proven to be NP‐complete and thus presents a suitable testbed for exploring quantum optimization approaches. The Ising model—originally introduced for NP‐hard Ising spin glass problems—provides a natural mathematical framework for expressing constraints in a form amenable to quantum computation. Objective This work aims to develop a quantum Sudoku solver inspired by the Ising model that minimizes the number of logical qubits required, making it suitable for today's resource‐limited quantum hardware. The broader goal is to demonstrate a modeling strategy that may generalize to other NP optimization problems. Methods The solver construction begins by translating Sudoku constraints into mathematical expressions represented through couplings of atomic spins. These constraints are formulated into observable operators using Pauli operators, enabling the calculation of expectation values over candidate quantum states. Individual quantum algorithmic components are then integrated into a global optimization pipeline. The performance and correctness of this solver are evaluated through the Quantum Approximate Optimization Algorithm (QAOA) combined with the COBYLA classical optimizer within the IBM Qiskit SDK. A code example illustrates the implementation of multiple puzzle constraints and the verification of the resulting quantum circuits. Results The modeling approach successfully encodes Sudoku rules into an Ising Hamiltonian with reduced qubit requirements. Preliminary evaluations using QAOA and COBYLA demonstrate that the solver can identify puzzle‐consistent solutions while maintaining low resource consumption. The quantum circuit construction matches theoretical expectations, and the code snippet confirms successful constraint enforcement within the Qiskit environment. Conclusions The proposed quantum Sudoku solver highlights the potential of Ising‐based formulations to address NP optimization problems on near‐term quantum devices. By reducing logical qubit usage without sacrificing algorithmic integrity, this strategy may support broader applications in constrained optimization. The implementation serves as both a proof of concept and a practical guide for extending Ising‐inspired quantum modeling to other NP‐hard domains.