Simplifying the design of multilevel thermal machines using virtual qubits

TL;DR

This paper extends virtual qubit models to multi-dimensional quantum systems, enabling more accurate design and analysis of complex quantum thermal machines through analytical solutions and simulations.

Contribution

It introduces multiple competing virtual qubits for modeling higher-dimensional systems and provides an analytic solution for these models, advancing quantum machine design.

Findings

General properties of reset models for multi-dimensional systems identified

Simulation results show predictive power for physical changes in complex setups

Improved three-level laser demonstrates practical application of the models

Abstract

Quantum thermodynamics often deals with the dynamics of small quantum machines interfacing with a large and complex environment. Virtual qubits, collisional models and reset master equations have become highly useful tools for predicting the qualitative behaviour of two-dimensional target systems coupled to few-qubit machines and a thermal environment. While few successes in matching the simplified model parameters for all possible physical systems are known, the qualitative predictions still allow for a general design of quantum machines irrespective of the implementation. We generalise these tools by introducing multiple competing virtual qubits for modelling multi-dimensional systems coupled to larger and more complex machines. By simulating the full physical dynamics for targets with three dimensions, we uncover general properties of reset models that can be used as `dials' to correctly predict the qualitative features of physical changes in a realistic setup and thus design autonomous quantum machines beyond a few qubits. We then present a general analytic solution of the reset model for arbitrary-dimensional systems coupled to multi-qubit machines. Finally, we showcase an improved three-level laser as an exemplary application of our results.