EO-GRAPE and EO-DRLPE: Open and Closed Loop Approaches for Energy Efficient Quantum Optimal Control

TL;DR

This paper introduces two novel quantum optimal control methods, EO-GRAPE and EO-DRLPE, to optimize energy efficiency and fidelity of quantum gates, demonstrating Pareto optimality and comparing their performance under noise.

Contribution

The paper proposes two new numerical approaches for energy-efficient quantum control, including an open-loop gradient method and a closed-loop reinforcement learning method.

Findings

EO-GRAPE outperforms EO-DRLPE in most settings.

Pareto optimality between fidelity and energetic cost is demonstrated.

Correlation between Bloch sphere path length and energetic cost is shown.

Abstract

This research investigates the possibility of using quantum optimal control techniques to co-optimize the energetic cost and the process fidelity of a quantum unitary gate. The energetic cost is theoretically defined, and thereby, the gradient of the energetic cost for pulse engineering is derived. We empirically demonstrate the Pareto optimality in the trade-off between process fidelity and energetic cost. Thereafter, two novel numerical quantum optimal control approaches are proposed: (i) energy-optimized gradient ascent pulse engineering (EO-GRAPE) as an open-loop gradient-based method, and (ii) energy-optimized deep reinforcement learning for pulse engineering (EO-DRLPE) as a closed-loop method. The performance of both methods is probed in the presence of increasing noise. We find that the EO-GRAPE method performs better than the EO-DRLPE methods with and without a warm start for most experimental settings. Additionally, for one qubit unitary gate, we illustrate the correlation between the Bloch sphere path length and the energetic cost.