Quantum adiabatic Markovian master equations

By Tameem Albash, Sergio Boixo, Daniel A. Lidar, Paolo Zanardi. 2012

266 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/781d4b9998fdc90de77282fef1da8f42b772142e

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe (2022, background): “For slow external driving in the adiabatic limit, the free evolution generator composed from the commutator of the instantaneous Hamiltonian and the dissipative generators commute [10, 23, 167].”
Quantum feedback: theory, experiments, and applications (2014, methodology): “ control, either by using methods for exact simulation of open-system dynamics (see e.g. [446– 449]) or by obtaining approximate master equations that correctly model noise for time-dependent systems [450]. A key question regarding the relationship between various kinds of feedback is whether one ki”
Decoherence in adiabatic quantum computation (2015, methodology): “[14] by including the factor g2 in the definitions of γαβ(ω) and Sαβ(ω) instead of pulling it out as in Eqs.”
Dynamics of non-Markovian open quantum systems (2015, unknown): “…n e−i n(t−t ′)|n(t)〉〈n(t′)|, (76) A second tractable situation is when the system undergoes an exact adiabatic evolution, which allows us to express (75) as (Albash et al., 2012; Mostafazadeh, 1997) Uads (t, t′) = ∑ n e−iµn(t,t ′)|n(t)〉〈n(t′)|, (77) where µn(t, t ′) = ∆n(t, t ′) − γn(t, t′), with…”