Finite steps optimise dissipation in stochastically controlled quantum systems

TL;DR

This paper analyzes the thermodynamic costs of quantum control protocols under stochastic influences, deriving optimal step numbers and minimal dissipation using quantum thermodynamic length.

Contribution

It introduces a framework for quantifying dissipation in stochastic quantum control and determines optimal steps and minimal work for such processes.

Findings

Weak Gaussian noise increases dissipation linearly with steps.

Finite optimal steps minimize average dissipated work.

Demonstrated with Landau-Zener and Ising model examples.

Abstract

Motivated by the need for precise, energy-efficient, and experimentally realistic quantum control protocols, we investigate the thermodynamic cost of performing quantum step-equilibration processes under the influence of classical stochastic control fields. Whereas purely deterministic protocols exhibit dissipation that scales inversely with the number of steps, we show that weak Gaussian noise in the control variables induces dissipative contributions that grow linearly with the number of steps. Consequently, we derive the finite optimal number of steps and minimal achievable average dissipated work and its variance using the quantum thermodynamic length. These results are demonstrated using two paradigmatic examples: a Landau-Zener sweep of a qubit strongly coupled to a thermal bath and the erasure of a transverse-field Ising model.