# Computational Issues of Quantum Heat Engines with Non-Harmonic Working Medium

## TL;DR

This paper develops computational methods to analyze quantum heat engines using non-harmonic oscillators, focusing on efficient and accurate simulations.

## Contribution

The novel contribution is a method to compute quantum heat engines with non-harmonic working mediums using the Schrödinger picture and error estimation techniques.

## Key findings

- Using eigenstates of a harmonic Hamiltonian provides the best computational performance for simulating non-harmonic quantum heat engines.
- A technique was developed to estimate and reduce errors introduced during the simulation of quantum heat cycles.
- The study enables numerical analysis of non-harmonic quantum heat machines with time-dependent Hamiltonians and thermal reservoir coupling.

## Abstract

In this work, we lay the foundations for computing the behavior of a quantum heat engine whose working medium consists of an ensemble of non-harmonic quantum oscillators. In order to enable this analysis, we develop a method based on the Schrödinger picture. We investigate different possible choices on the basis of expanding the density operator, as it is crucial to select a basis that will expedite the numerical integration of the time-evolution equation without compromising the accuracy of the computed results. For this purpose, we developed an estimation technique that allows us to quantify the error that is unavoidably introduced when time-evolving the density matrix expansion over a finite-dimensional basis. Using this and other ways of evaluating a specific choice of basis, we arrive at the conclusion that the basis of eigenstates of a harmonic Hamiltonian leads to the best computational performance. Additionally, we present a method to quantify and reduce the error that is introduced when extracting relevant physical information about the ensemble of oscillators. The techniques presented here are specific to quantum heat cycles; the coexistence within a cycle of time-dependent Hamiltonian and coupling with a thermal reservoir are particularly complex to handle for the non-harmonic case. The present investigation is paving the way for numerical analysis of non-harmonic quantum heat machines.