A Quantum Search Approach to Magic Square Constraint Problems with Classical Benchmarking
This work addresses combinatorial constraint satisfaction problems for researchers in quantum computing, but it is incremental as it applies known quantum methods to a specific domain with limited experimental scale.
The paper tackled the problem of solving combinatorial constraint satisfaction problems, specifically generating magic squares, by reformulating it as a quantum search problem using Grover's algorithm, and validated the correctness of the approach with a theoretical quadratic query advantage over classical search.
This paper presents a quantum search approach to combinatorial constraint satisfaction problems, demonstrated through the generation of magic squares. We reformulate magic square construction as a quantum search problem in which a reversible, constraint-sensitive oracle marks valid configurations for amplitude amplification via Grover's algorithm. Classical pre-processing using the Siamese construction and partial constraint checks generates a compact candidate domain before quantum encoding. Rather than integrating classical and quantum solvers in an iterative loop, this work uses the classical component for structured initialisation and the quantum component for search, and benchmarks the quantum approach against classical brute-force enumeration and backtracking. Our Qiskit implementation demonstrates the design of multi-register modular arithmetic circuits, oracle logic, and diffusion operators. Experiments are conducted on small grid instances, as larger grids are intractable on classical statevector simulators due to exponential memory growth. The results validate the correctness of the proposed quantum search pipeline and confirm the theoretical quadratic query advantage over classical search.