Optimal control of quantum thermal machines using machine learning

Ilia Khait,Dvira Segal,Juan Carrasquilla

doi:10.1103/physrevresearch.4.l012029

Ilia Khait, Dvira Segal + Show 1 more

Open Access

https://doi.org/10.1103/physrevresearch.4.l012029

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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.

Highlights

Many problems in physics are formulated as optimization tasks by identifying a cost function that must be minimized
Using this deep learning (DL) algorithm, we show that a previously employed, intuitive energetic cost of the thermal machine driving suffers from a fundamental flaw, which we resolve with an alternative construction for the cost function
The two derivatives rise together, which results in the minimization of the energetic cost function, as we discuss

Summary

Introduction

Many problems in physics are formulated as optimization tasks by identifying a cost function that must be minimized. Since its inception, thermodynamics has been concerned with performance optimization by identifying constrains and bounds on energy conversion processes. The ideal Carnot engine is designed to reach the maximal efficiency. This upper bound is theoretically obtained for arbitrarily slow, quasistatic processes; the extracted power reduces to zero. Real thermal devices operate on finite-time cycles, and they are naturally described in terms of finite-time thermodynamics [4,5]. This theory is concerned with, e.g., how the efficiency of thermal machines erodes when heat-to-work conversion processes take place in finite-time cycles [6,7]

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