161 research outputs found
Quantum annealing with Jarzynski equality
We show a practical application of the Jarzynski equality in quantum
computation. Its implementation may open a way to solve combinatorial
optimization problems, minimization of a real single-valued function, cost
function, with many arguments. We consider to incorpolate the Jarzynski
equality into quantum annealing, which is one of the generic algorithms to
solve the combinatorial optimization problem. The ordinary quantum annealing
suffers from non-adiabatic transitions whose rate is characterized by the
minimum energy gap of the quantum system under
consideration. The quantum sweep speed is therefore restricted to be extremely
slow for the achievement to obtain a solution without relevant errors. However,
in our strategy shown in the present study, we find that such a difficulty
would not matter.Comment: 4 pages, to appear in Phys. Rev. Let
Nonequilibrium work on spin glasses in longitudinal and transverse fields
We derive a number of exact relations between equilibrium and nonequilibrium
quantities for spin glasses in external fields using the Jarzynski equality and
gauge symmetry. For randomly-distributed longitudinal fields, a lower bound is
established for the work done on the system in nonequilibrium processes, and
identities are proven to relate equilibrium and nonequilibrium quantities. In
the case of uniform transverse fields, identities are proven between physical
quantities and exponentiated work done to the system at different parts of the
phase diagram with the context of quantum annealing in mind. Additional
relations are given, which relate the exponentiated work in quantum and
simulated (classical) annealing. It is also suggested that the Jarzynski
equality may serve as a guide to develop a method to perform quantum annealing
under non-adiabatic conditions.Comment: 17 pages, 5 figures, submitted to JPS
Proposal of a Checking Parameter in the Simulated Annealing Method Applied to the Spin Glass Model
We propose a checking parameter utilizing the breaking of the Jarzynski
equality in the simulated annealing method using the Monte Carlo method. This
parameter is based on the Jarzynski equality. By using this parameter, to
detect that the system is in global minima of the free energy under gradual
temperature reduction is possible. Thus, by using this parameter, one is able
to investigate the efficiency of annealing schedules. We apply this parameter
to the +-J Ising spin glass model. The application to the Gaussian Ising spin
glass model is also mentioned. We discuss that the breaking of the Jarzynski
equality is induced by the system being trapped in local minima of the free
energy. By performing Monte Carlo simulations of the +-J Ising spin glass model
and a glassy spin model proposed by Newman and Moore, we show the efficiency of
the use of this parameter.Comment: 14 pages, 2 figures. v6: this is the final versio
Quantum fluctuation theorem to benchmark quantum annealers
Near term quantum hardware promises unprecedented computational advantage.
Crucial in its development is the characterization and minimization of
computational errors. We propose the use of the quantum fluctuation theorem to
benchmark the performance of quantum annealers. This versatile tool provides
simple means to determine whether the quantum dynamics are unital, unitary, and
adiabatic, or whether the system is prone to thermal noise. Our proposal is
experimentally tested on two generations of the D-Wave machine, which
illustrates the sensitivity of the fluctuation theorem to the smallest
aberrations from ideal annealing.Comment: 5 pages, 4 figur
Nonequilibrium relations in spin glasses
The applications of nonequilbrium relations such as the Jarzynski equality
and the fluctuation theorem to spin glasses are considered. The spin glass is a
basic platform where we consider an application of an approximate solver of
combinatorial optimization problems, simulated annealing. We find a novel
relationship between an average through a nonequilibrium process where the
temperature changes as in simulated annealing and a thermal average in
equilibrium with different amounts of quenched randomness. The results shown in
the present study may serve as an alternative way to overcome critical slowing
down in spin glasses. It means that this way may mitigate difficulties in
several hard optimization problems.Comment: 4 pages, Proceeding of International Symposium on Nanoscience and
Quantum Physics (nanoPHYS'09) Version 3 is the final on
Equilibrium Sampling From Nonequilibrium Dynamics
We present some applications of an Interacting Particle System (IPS)
methodology to the field of Molecular Dynamics. This IPS method allows several
simulations of a switched random process to keep closer to equilibrium at each
time, thanks to a selection mechanism based on the relative virtual work
induced on the system. It is therefore an efficient improvement of usual
non-equilibrium simulations, which can be used to compute canonical averages,
free energy differences, and typical transitions paths
Work Statistics, Loschmidt Echo and Information Scrambling in Chaotic Quantum Systems
Characterizing the work statistics of driven complex quantum systems is
generally challenging because of the exponential growth with the system size of
the number of transitions involved between different energy levels. We consider
the quantum work distribution associated with the driving of chaotic quantum
systems described by random matrix Hamiltonians and characterize exactly the
work statistics associated with a sudden quench for arbitrary temperature and
system size. Knowledge of the work statistics yields the Loschmidt echo
dynamics of an entangled state between two copies of the system of interest,
the thermofield double state. This echo dynamics is dictated by the spectral
form factor. We discuss its relation to frame potentials and its use to assess
information scrambling.Comment: 11+6pp, 5 figures. v3: version accepted for publication in Quantu
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