title: Exponentially Biased Ground-State Sampling of Quantum Annealing Machines with Transverse-Field Driving Hamiltonians.
abstract: We study the performance of the D-Wave 2X quantum annealing machine on systems with well-controlled ground-state degeneracy. While obtaining the ground state of a spin-glass benchmark instance represents a difficult task, the gold standard for any optimization algorithm or machine is to sample all solutions that minimize the Hamiltonian with more or less equal probability. Our results show that while naive transverse-field quantum annealing on the D-Wave 2X device can find the ground-state energy of the problems, it is not well suited in identifying all degenerate ground-state configurations associated with a particular instance. Even worse, some states are exponentially suppressed, in agreement with previous studies on toy model problems [New J. Phys. 11, 073021 (2009)NJOPFM1367-263010.1088/1367-2630/11/7/073021]. These results suggest that more complex driving Hamiltonians are needed in future quantum annealing machines to ensure a fair sampling of the ground-state manifold.
authors.affiliation: Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, Massachusetts 02138, USA.|NASA Ames Research Center Quantum Artificial Intelligence Laboratory (QuAIL), Mail Stop 269-1, Moffett Field, California 94035, USA.|Stinger Ghaffarian Technologies Inc., 7701 Greenbelt Road, Suite 400, Greenbelt, Maryland 20770, USA.
authors.forename: Salvatore
authors.initials: S
authors.lastname: Mandrà
authors.affiliation: Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA.
authors.forename: Zheng
authors.initials: Z
authors.lastname: Zhu
authors.affiliation: Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA.|Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA.
authors.forename: Helmut G
authors.initials: HG
authors.lastname: Katzgraber