Optimal control of quantum thermal machines using machine learning

Abstract

Identifying optimal thermodynamical processes has been the essence of thermodynamics since its inception. Here, we show that differentiable programming (DP), a machine learning (ML) tool, can be employed to optimize finite-time thermodynamical processes in a quantum thermal machine. We consider the paradigmatic quantum Otto engine with a time-dependent harmonic oscillator as its working fluid, and build upon shortcut-to-adiabaticity (STA) protocols. We formulate the STA driving protocol as a constrained optimization task and apply DP to find optimal driving profiles for an appropriate figure of merit. Our ML scheme discovers profiles for the compression and expansion strokes that are superior to previously-suggested protocols. Moreover, using our ML algorithm we show that a previously-employed, intuitive energetic cost of the STA driving suffers from a fundamental flaw, which we resolve with an alternative construction for the cost function. Our method and results demonstrate that ML is beneficial both for solving hard-constrained quantum control problems and for devising and assessing their theoretical groundwork.