4 research outputs found
Quantum Adiabatic Markovian Master Equations
We develop from first principles Markovian master equations suited for
studying the time evolution of a system evolving adiabatically while coupled
weakly to a thermal bath. We derive two sets of equations in the adiabatic
limit, one using the rotating wave (secular) approximation that results in a
master equation in Lindblad form, the other without the rotating wave
approximation but not in Lindblad form. The two equations make markedly
different predictions depending on whether or not the Lamb shift is included.
Our analysis keeps track of the various time- and energy-scales associated with
the various approximations we make, and thus allows for a systematic inclusion
of higher order corrections, in particular beyond the adiabatic limit. We use
our formalism to study the evolution of an Ising spin chain in a transverse
field and coupled to a thermal bosonic bath, for which we identify four
distinct evolution phases. While we do not expect this to be a generic feature,
in one of these phases dissipation acts to increase the fidelity of the system
state relative to the adiabatic ground state.Comment: 31 pages, 9 figures. v2: Generalized Markov approximation bound.
Included a section on thermal equilibration. v3: Added text that appears in
NJP version. Generalized Lindblad ME to include degenerate subspaces. v3.
Corrections made to Appendix E and F. We thank Kabuki Takada and Hidetoshi
Nishimori for pointing out the errors. v4: Corrected a typo in Eqt. B
Quantum Simulations of Classical Annealing Processes
We describe a quantum algorithm that solves combinatorial optimization
problems by quantum simulation of a classical simulated annealing process. Our
algorithm exploits quantum walks and the quantum Zeno effect induced by
evolution randomization. It requires order steps to find an
optimal solution with bounded error probability, where is the minimum
spectral gap of the stochastic matrices used in the classical annealing
process. This is a quadratic improvement over the order steps
required by the latter.Comment: 4 pages - 1 figure. This work differs from arXiv:0712.1008 in that
the quantum Zeno effect is implemented via randomization in the evolutio