TY - JOUR
T1 - Efficient simulation of quantum evolution using dynamical coarse graining
AU - Khasin, M.
AU - Kosloff, R.
PY - 2008/7/11
Y1 - 2008/7/11
N2 - A scheme to simulate the evolution of a restricted set of observables of a quantum system is proposed. The set comprises the spectrum-generating algebra of the Hamiltonian. Focusing on the simulation of the restricted set allows to drastically reduce the cost of the simulation. This reduction is the result of replacing the original unitary dynamics by a special open-system evolution. This open-system evolution can be interpreted as a process of weak measurement of the distinguished observables performed on the evolving system of interest. Under the condition that the observables are "classical" and the Hamiltonian is moderately nonlinear, the open-system dynamics displays a large time-scale separation between the relaxation of the observables and the decoherence of a generic state. This time-scale separation allows the unitary dynamics of the observables to be efficiently simulated by the open-system dynamics on the intermediate time scale. The simulation employs unraveling of the corresponding master equations into pure-state evolutions, governed by the stochastic nonlinear Schrödinger equation. The stochastic pure-state evolution can be simulated efficiently using a representation of the state in the time-dependent basis of the generalized coherent states, associated with the spectrum-generating algebra.
AB - A scheme to simulate the evolution of a restricted set of observables of a quantum system is proposed. The set comprises the spectrum-generating algebra of the Hamiltonian. Focusing on the simulation of the restricted set allows to drastically reduce the cost of the simulation. This reduction is the result of replacing the original unitary dynamics by a special open-system evolution. This open-system evolution can be interpreted as a process of weak measurement of the distinguished observables performed on the evolving system of interest. Under the condition that the observables are "classical" and the Hamiltonian is moderately nonlinear, the open-system dynamics displays a large time-scale separation between the relaxation of the observables and the decoherence of a generic state. This time-scale separation allows the unitary dynamics of the observables to be efficiently simulated by the open-system dynamics on the intermediate time scale. The simulation employs unraveling of the corresponding master equations into pure-state evolutions, governed by the stochastic nonlinear Schrödinger equation. The stochastic pure-state evolution can be simulated efficiently using a representation of the state in the time-dependent basis of the generalized coherent states, associated with the spectrum-generating algebra.
UR - http://www.scopus.com/inward/record.url?scp=47249095327&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.78.012321
DO - 10.1103/PhysRevA.78.012321
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AN - SCOPUS:47249095327
SN - 1050-2947
VL - 78
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
IS - 1
M1 - 012321
ER -