**by Yu Yamashiro, Masaki Ohkuwa, Hidetoshi Nishimori, Daniel A.
Lidar**

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.

**by Masayuki Ohzeki**

Quantum annealing (QA) is a generic method for solving optimization
problems using fictitious quantum fluctuation. The current device
performing QA involves controlling the transverse field; it is
classically simulatable by using the standard technique for mapping
the quantum spin systems to the classical ones. In this sense, the
current system for QA is not powerful despite utilizing quantum
fluctuation. Hence, we developed a system with a time-dependent
Hamiltonian consisting of a combination of the formulated Ising model
and the “driver” Hamiltonian with only quantum fluctuation. In the
previous study, for a fully connected spin model, quantum fluctuation
can be addressed in a relatively simple way. We proved that the fully
connected antiferromagnetic interaction can be transformed into a
fluctuating transverse field and is thus classically simulatable at
sufficiently low temperatures. Using the fluctuating transverse field,
we established several ways to simulate part of the nonstoquastic
Hamiltonian on classical computers. We formulated a message-passing
algorithm in the present study. This algorithm is capable of assessing
the performance of QA with part of the nonstoquastic Hamiltonian
having a large number of spins. In other words, we developed a
different approach for simulating the nonstoquastic Hamiltonian
without using the quantum Monte Carlo technique. Our results were
validated by comparison to the results obtained by the replica method.