Fully differentiable optimization protocols for non-equilibrium steady
states
- URL: http://arxiv.org/abs/2103.12604v2
- Date: Tue, 23 Nov 2021 05:11:25 GMT
- Title: Fully differentiable optimization protocols for non-equilibrium steady
states
- Authors: Rodrigo A. Vargas-Hern\'andez, Ricky T. Q. Chen, Kenneth A. Jung, Paul
Brumer
- Abstract summary: We present a novel methodology, based on automatic differentiation, capable of differentiating the steady state solution with respect to any parameter of the Liouvillian.
Our approach has a low memory cost, and is agnostic to the exact algorithm for computing the steady state.
We also present a sensitivity analysis of the steady state for energy transfer under natural incoherent light as a function of the incoherent-light pumping rate.
- Score: 7.862208848127913
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: In the case of quantum systems interacting with multiple environments, the
time-evolution of the reduced density matrix is described by the Liouvillian.
For a variety of physical observables, the long-time limit or steady state
solution is needed for the computation of desired physical observables. For
inverse design or optimal control of such systems, the common approaches are
based on brute-force search strategies. Here, we present a novel methodology,
based on automatic differentiation, capable of differentiating the steady state
solution with respect to any parameter of the Liouvillian. Our approach has a
low memory cost, and is agnostic to the exact algorithm for computing the
steady state. We illustrate the advantage of this method by inverse designing
the parameters of a quantum heat transfer device that maximizes the heat
current and the rectification coefficient. Additionally, we optimize the
parameters of various Lindblad operators used in the simulation of energy
transfer under natural incoherent light. We also present a sensitivity analysis
of the steady state for energy transfer under natural incoherent light as a
function of the incoherent-light pumping rate.
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