Thermalization of finite complexity and its application to heat bath algorithmic cooling

TL;DR

This paper presents a collision-based thermal operation framework for finite-complexity cooling, demonstrating sub-bath cooling without a machine and showing enhanced cooling with a qubit machine, advancing finite-resource cooling methods.

Contribution

It introduces a new collision model-based thermal operation framework with finite complexity constraints and demonstrates sub-bath cooling protocols, including with a qubit machine, without prior methods.

Findings

Sub-bath cooling is achievable without a machine.

A necessary condition for cooling below bath temperature is the initial lack of a well-defined effective temperature.

Introducing a qubit machine improves cooling limits and energy efficiency.

Abstract

We introduce a class of thermal operations based on the collision model, where the system sequentially interacts with uncorrelated bath molecules via energy-preserving unitaries. To ensure finite complexity, each molecule is constrained to be no larger than the system. We identify a necessary condition for cooling below the bath temperature via a single collision: the system must initially lack a well-defined effective temperature, even a negative one. By constructing a iterative protocol, we demonstrate that sub-bath cooling is achievable without a machine under these restricted thermal operations. Moreover, introducing a qubit machine further enhances both the cooling limit and energy efficiency. These findings contribute to the broader study of cooling with finite resources.