Fully differentiable optimization protocols for non-equilibrium steady states

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.

Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe

“…In open quantum systems, quantum trajectories instead of the density matrix formalism and automatic differentiation have been used [253,256,372,373] to speed up optimization and reduce the computation complexity. Steady states of dissipative dynamics including non-equilibrium states can be targeted by optimal control via implicit differentiation [585,586]. Optimal control has been combined with time-convolutionless master equations [55,627] which allowed for studying, respectively, qubit reset and instantaneous tracking under non-Markovian dynamics.…”

Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe

“…In open quantum systems, quantum trajectories instead of the density matrix formalism and automatic differentiation have been used [248,368,369] to speed up optimization and reduce the computation complexity. Steady states of dissipative dynamics including non-equilibrium states can be targeted by optimal control via implicit differentiation [579,580]. Optimal control has been combined with timeconvolutionless master equations [53,621] which allowed for studying, respectively, qubit reset and instantaneous tracking under non-Markovian dynamics.…”

Inverse molecular design and parameter optimization with Hückel theory using automatic differentiation

“…Along these lines, there are auto-differentiable versions of Hartree-Fock, 18,19 density functional theory (DFT), [19][20][21][22][23] excited state mean-field theory, 24 and other applications in physical sciences. 21,[25][26][27][28][29][30][31][32][33][34][35] Over all, AD has been used to accelerate the calculation of gradient physical methods and to blend with ML algorithms. AD has also been fundamental for constructing more accurate semiempirical methods when combined with ML algorithms.…”