# Feedback controlled heat transport in quantum devices: Theory and solid state experimental proposal

## TL;DR

This paper develops a theoretical framework for feedback-controlled heat transport in quantum systems, unifies previous results, and proposes an experimental setup using superconducting circuits to realize a Maxwell demon that manipulates heat flow via measurement and feedback.

## Contribution

It introduces a comprehensive theory of feedback-controlled heat transport in quantum devices and presents a solid-state experimental proposal for implementing a Maxwell demon.

## Key findings

- Feedback control breaks time reversal symmetry.
- Restoration of fluctuation relations requires accounting for information.
- Proposed experiment demonstrates effective inversion of temperature gradient.

## Abstract

A theory of feedback controlled heat transport in quantum systems is presented. It is based on modelling heat engines as driven multipartite systems subject to projective quantum measurements and measurement-conditioned unitary evolutions. The theory unifies various results presented in the previous literature. Feedback control breaks time reversal invariance. This in turn results in the fluctuation relation not being obeyed. Its restoration occurs by an appropriate accounting of the information gain and information use via measurements and feedback. We further illustrate an experimental proposal for the realisation of a Maxwell demon using superconducting circuits and single photon on-chip calorimetry. A two level qubit acts as a trapdoor which, conditioned on its state is coupled to either a hot resistor or a cold one. The feedback mechanism alters the temperatures felt by the qubit and can result in an effective inversion of temperature gradient, where heat flows from cold to hot thanks to information gain and use