# Fractional Control Gate Protocols for Quantum Engines

## TL;DR

This paper explores using fractional control gates in quantum heat engines to improve work production and efficiency through quantum coherence and many-body correlations.

## Contribution

A novel protocol using fractional control gates achieves up to 100% efficiency in work extraction from quantum heat engines.

## Key findings

- Quantum coherence in one qubit significantly increases maximum work production and engine performance.
- Fractional control gate protocols achieve 84% to 100% efficiency in work extraction.
- Work production is strongly correlated with many-body correlations in the working medium.

## Abstract

Nth-root gates allow for a paced application of two-qubit operations. We apply them in quantum thermodynamic protocols for operating a quantum heat engine. A set of circuits for two and three qubits is compared by considering maximum work production and related efficiency. Our results show that for all circuits considered and most regions of initial parameter space, quantum coherence of one of the qubits strongly increases the maximum work production and improves the system’s performance as a quantum heat engine. In such circuits, coherence is initially imprinted into one of the qubits, improving the overall maximum extractable work. We focus here on the efficiency of such work extraction, assuming the initialisation of the qubits is a free resource. For the novel protocol that employs fractional control gates, work is generated with 84% up to 100% efficiency. Further, we uncover a strong linear correlation between work production and many-body correlations in the working medium generated by these gates.