Beyond Standard Quantum Annealing

G. Aeppli, T. F. Rosenbaum

Kazutaka Takahashi

We study a bifurcation mechanism of quantum annealing. Using spins with quantum number S=1, we construct a simple model to make a bifurcation. The qutrit can be composed by nesting two qubits. We numerically solve the Schroedinger equation to confirm that the bifurcation-based quantum annealing (BQA) works well and the ground state can be found efficiently. The result is compared with that by the standard quantum annealing (QA) using qubits. We find that the performance of the BQA is comparable to the standard QA, or gives better results in some cases.

Mario S. Könz, Guglielmo Mazzola, Andrew J. Ochoa +2 more

Recently, it was demonstrated both theoretically and experimentally on the D-Wave quantum annealer that transverse-field quantum annealing does not find all ground states with equal probability. In particular, it was proposed that more complex driver Hamiltonians beyond transverse fields might mitigate this shortcoming. Here, we investigate the mechanisms of (un)fair sampling in quantum annealing. While higher-order terms can improve the sampling for selected small problems, we present multiple counterexamples where driver Hamiltonians that go beyond transverse fields do not remove the sampling bias. Using perturbation theory we explain why this is the case. In addition, we present large-scale quantum Monte Carlo simulations for spin glasses with known degeneracy in two space dimensions and demonstrate that the fair-sampling performance of quadratic driver terms is comparable to standard transverse-field drivers. Our results suggest that quantum annealing machines are not well suited for sampling applications, unless postprocessing techniques to improve the sampling are applied.

Y. S. Yang, P. Tyson, A. B Murphy

The weighted Max-Cut problem is an NP-hard problem with application implications. It is investigated on a cubic lattice with 113 nodes and mixed-signed random edge weights. For a fixed upper bound on edge weights, it has been demonstrated that the computational difficulty increases as the lower bound on edge weights becomes more negative. The solution time for the problem using a novel error-mitigated quantum annealing approach is compared with standard D-Wave quantum annealing (QA) and BQM hybrid solvers, as well as various classical solvers. For the QPU-embeddable weighted Max-Cut instances with mixed-signed edge weights, it has been quantitatively demonstrated that the SEMO (spin-error mitigation for optimisation) error-mitigated quantum annealing achieved substantially shorter time-to solution than standard D-Wave QA, D-Wave BQM, simulated annealing and Tabu search baselines. The error-mitigated quantum annealing approach presented in this article potentially elevates the efficiency and application scope of quantum annealing and would be applicable in solving other discrete optimisation problems that can be formulated as QUBO or Ising instances. The promising solution time advantage would be particularly impactful for time-critical optimisation applications.

Sei Suzuki, Jun‐ichi Inoue, Bikas K. Chakrabarti