2018/06/30 by Mario S. Könz, Guglielmo Mazzola, Andrew J. Ochoa +2
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Computer science #Degeneracy (biology) #Engineering #Importance sampling #Mathematics #Monte Carlo method #Optics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Monte Carlo #Quantum annealing #Quantum computer #Quantum many-body systems #Quantum mechanics #Sampling (signal processing) #Statistical physics #Statistics #Theoretical and Computational Physics #Transverse plane #cond-mat.dis-nn #quant-ph
paper · pdf · doi:10.1103/physreva.100.030303
published as Phys. Rev. A 100, 030303 (2019) · 6 pages, 5 figures
openalex created_date 2018/06/21 · openalex publication_date 2019/09/20 · arxiv created 2019/09/21 · arxiv updated 2019/09/25 · openalex updated_date 2026/08/06
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.