TY - JOUR
T1 - Dynamics of reverse annealing for the fully connected p -spin model
AU - Yamashiro, Yu
AU - Ohkuwa, Masaki
AU - Nishimori, Hidetoshi
AU - Lidar, Daniel A.
N1 - Funding Information:
This research is based upon work supported by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via the U.S. Army Research Office through Contract No. W911NF-17-C-0050. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the ODNI, IARPA, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. D.L. is additionally partially supported by a DOE/HEP QuantISED program grant and the Quantum Machine Learning and Quantum Computation Frameworks for HEP (QMLQCF) through Award No. DE-SC0019227. The work of H.N. is also supported partially by the JSPS through KAKENHI Grant No. 26287086.
Publisher Copyright:
© 2019 American Physical Society.
PY - 2019/11/18
Y1 - 2019/11/18
N2 - Reverse annealing is a relatively new variant of quantum annealing in which one starts from a classical state and increases and then decreases the amplitude of the transverse field, in the hope of finding a better classical state than the initial state for a given optimization problem. We numerically study the unitary quantum dynamics of reverse annealing for the mean-field-type p-spin model and show that the results are consistent with the predictions of equilibrium statistical mechanics. In particular, we corroborate the equilibrium analysis prediction that reverse annealing provides an exponential speedup over conventional quantum annealing in terms of solving the p-spin model. This lends support to the expectation that equilibrium analyses are effective at revealing essential aspects of the dynamics of quantum annealing. We also compare the results of quantum dynamics with the corresponding classical dynamics to reveal their similarities and differences. We distinguish between two reverse annealing protocols we call adiabatic and iterated reverse annealing. We further show that iterated reverse annealing, as has been realized in the D-Wave device, is ineffective in the case of the p-spin model but note that a recently introduced protocol ("h-gain"), which implements adiabatic reverse annealing, may lead to improved performance.
AB - Reverse annealing is a relatively new variant of quantum annealing in which one starts from a classical state and increases and then decreases the amplitude of the transverse field, in the hope of finding a better classical state than the initial state for a given optimization problem. We numerically study the unitary quantum dynamics of reverse annealing for the mean-field-type p-spin model and show that the results are consistent with the predictions of equilibrium statistical mechanics. In particular, we corroborate the equilibrium analysis prediction that reverse annealing provides an exponential speedup over conventional quantum annealing in terms of solving the p-spin model. This lends support to the expectation that equilibrium analyses are effective at revealing essential aspects of the dynamics of quantum annealing. We also compare the results of quantum dynamics with the corresponding classical dynamics to reveal their similarities and differences. We distinguish between two reverse annealing protocols we call adiabatic and iterated reverse annealing. We further show that iterated reverse annealing, as has been realized in the D-Wave device, is ineffective in the case of the p-spin model but note that a recently introduced protocol ("h-gain"), which implements adiabatic reverse annealing, may lead to improved performance.
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U2 - 10.1103/PhysRevA.100.052321
DO - 10.1103/PhysRevA.100.052321
M3 - Article
AN - SCOPUS:85075513037
VL - 100
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
SN - 1050-2947
IS - 5
M1 - 052321
ER -