Generation of Fixed Margin Binary Matrices Using Quantum Annealing

Fixed margin binary matrices are used across various scientific fields. However, generating such matrices remains a complicated computational task using classical algorithms since the best algorithm performs in exponential time. In this paper, we model this problem using a Quadratic Unconstrained Binary Optimization (QUBO). Furthermore, we use D-Wave's Quantum Annealing computer and their simulator to generate these matrices. Results obtained through the simulator attest to the capacity of our solution to effectively generate fixed margin binary matrices up to size <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$9\times 9$</tex> (constraint based on qubits availability). Results obtained from the quantum computer significantly suffer from noise compared to the simulator-based ones; however, we still get exact results with less effectiveness. Our solution and results are publicly available at https://github.com/Niten-luxld-wave-qubo-solver.