Sampling electronic structure quadratic unconstrained binary optimization problems (QUBOs) with Ocean and Mukai solvers

The most advanced D-Wave Advantage quantum annealer has 5000+ qubits, however, every qubit is connected to a small number of neighbors. As such, implementation of a fully-connected graph results in an order of magnitude reduction in qubit count. To compensate for the reduced number of qubits, one has to rely on special heuristic software such as qbsolv, the purpose of which is to decompose a large quadratic unconstrained binary optimization (QUBO) problem into smaller pieces that fit onto a quantum annealer. In this work, we compare the performance of the open-source qbsolv which is a part of the D-Wave Ocean tools and a new Mukai QUBO solver from Quantum Computing Inc. (QCI). The comparison is done for solving the electronic structure problem and is implemented in a classical mode (Tabu search techniques). The Quantum Annealer Eigensolver is used to map the electronic structure eigenvalue-eigenvector equation to a QUBO problem, solvable on a D-Wave annealer. We find that the Mukai QUBO solver outperforms the Ocean qbsolv with one to two orders of magnitude more accurate energies for all calculations done in the present work, both the ground and excited state calculations. This work stimulates the further development of software to assist in the utilization of modern quantum annealers.