Qubit thermodynamics: Entropy production from nonadiabatic driving

TL;DR

This paper investigates entropy production in qubit control during nonadiabatic processes, revealing how entropy increases relate to the effective Hamiltonian and discussing thermodynamic implications of quantum control protocols.

Contribution

It introduces a framework to analyze nonadiabatic errors as entropy production in qubit control, using the Landau--Zener protocol and superadiabatic frames.

Findings

Entropy increases nearly monotonically with effective Hamiltonian in optimal frames

Violations of the second law are possible but require precise control

Entropy production can be understood through the loss of fine-grained information

Abstract

Adiabaticity is a cornerstone of many promising approaches to quantum control, computing, and simulation. In practice, however, there is always a trade-off. Although the deleterious effects of noise can be diminished by running a control schedule more quickly, this benefit comes at the expense of nonadiabaticity. To put these two unwanted effects on the same theoretical footing, we analyze the nonadiabatic error in qubit control as a form of entropy production, examining the mechanism by which fine-grained information is effectively lost despite the dynamics being fundamentally unitary. A crucial issue here is the question of how to define equilibrium under a time-dependent Hamiltonian. Using the Landau--Zener protocol as a test case, we show that entropy increases nearly monotonically when equilibrium is defined with respect to the effective Hamiltonian in the optimal superadiabatic frame. We then consider single-passage Landau--Zener--St\"{u}ckelberg--Majorana interferometry, in which the initial state of the qubit is arbitrary. Violations of the second law of thermodynamics are possible but require exquisite control to achieve deliberately.