Cooling a Qubit using n Others

TL;DR

This paper investigates how the structure of a quantum machine affects the ability and complexity of cooling a single qubit, providing new bounds and a graph-based framework for optimizing cooling protocols.

Contribution

It introduces inequalities related to the machine's energy structure that determine optimal cooling and presents a graph-based method to optimize cooling protocols.

Findings

Derived inequalities dictate optimal cooling protocols.

Established Carnot-like bounds for quantum cooling.

Proposed a bipartite graph framework for protocol optimization.

Abstract

In the task of unitarily cooling a quantum system with access to a larger quantum system, known as the machine or reservoir, how does the structure of the machine impact an agent's ability to cool and the complexity of their cooling protocol? Focusing on the task of cooling a single qubit given access to $n$ separable, thermal qubits with arbitrary energy structure, we answer these questions by giving two new perspectives on this task. Firstly, we show that a set of inequalities related to the energetic structure of the $n$ qubit machine determines the optimal cooling protocol, which parts of the machine contribute to this protocol and gives rise to a Carnot-like bound. Secondly, we show that cooling protocols can be represented as perfect matchings on bipartite graphs enabling the optimization of cost functions e.g. gate complexity or dissipation. Our results generalize the algorithmic cooling problem, establish new fundamental bounds on quantum cooling and offer a framework for designing novel autonomous thermal machines and cooling algorithms.