Quantum adiabatic Markovian master equations

Abstract

Abstract. 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.

Performance of two different quantum annealing correction codes

“…For sufficiently high γ a non-decodable state becomes lower in energy than a decodable state. This coincides with the optimal γ value from a quantum adiabatic master equation simulation [46]. When the EP strategy is used instead of EM, the optimal γ occurs at a larger value as shown in Fig.…”

Experimental signature of programmable quantum annealing

“…In Fig. 5 we compare a numerical simulation of open system QA, using an adiabatic Markovian master equation 19 , with classical thermalization. The quantum prediction of increasing p s is confirmed experimentally, as shown in Fig.…”

“…If the change is sufficiently slow and there is no environment, the adiabatic theorem of quantum mechanics predicts that the system will remain in its ground state, and an optimal solution is obtained 12,13 . Realistically, one should include the effects of coupling to a thermal environment, that is, consider open system quantum adiabatic evolution [14][15][16][17][18][19] . An implementation of open system QA has recently been reported in a programmable architecture of superconducting flux qubits [20][21][22][23] , and applied to relatively simple protein folding and number theory problems 24,25 .…”

Geometric phaselike effects in a quantum heat engine

“…Within an adiabatic approximation, a weakly coupled quantum system's dynamics is governed by the quantum Liouville equation, |ρ(t) =L(t)|ρ(t) , where |ρ(t) is the time rate of change of the reduced density vector for the system [45].L(t) is the Liouvillian superoperator containing the time dependent driving and is responsible for system's evolution. Using standard perturbation theory within the Born-Markov approximation, the reduced density vector for the QHE is |ρ = {ρ 11 , ρ 22 , ρ aa , ρ bb , (ρ 12 )}, where ρ ii , i = 1, 2, a, b represent populations of the system's many body states and (ρ 12 ) is the thermally (noise) induced coherence between the degenerate states |1 and |2 .…”