Verification of Quantum Optimizers
F. Baccari, Christian Gogolin, Péter Wittek, Antonio Acín · arXiv (Cornell University) · 2018
Methods for finding ground states of classical spin models are of great importance in optimization and are gaining additional relevance now for verifying the results quantum optimizers. We combine the state-of-the-art branch and bound method for solving such optimization problems via converging upper- and lower-bounds with ideas from polynomial optimization and semidefinite programming (SDP). The resulting chordal branch and bound (CBB) algorithm can exploit the locality and resulting sparsity in relevant Ising spin models in a systematic way. This yields certified solutions for many of the problems that are being used to benchmark quantum annealing devices more efficiently and for larger system sizes. We are able to verify the output of a D-Wave 2000Q device for the largest triangular lattice that can be embedded in the hardware and provide exact ground states for cases in which the quantum annealer returns a configuration with almost minimal energy but markedly different spin pattern. The method always yields provable polynomial time upper and lower bounds on the ground state energy. We benchmark our method against further planar and non-planar graphs and show that these bounds often converge after a small number of steps, even though the NP-hardness of general Ising models implies that exponentially many steps are required in the worst case. This new tool is a flexible and scalable solution for the verification and benchmarking of the next generation of quantum optimization devices.