Open and Closed Loop Approaches for Energy Efficient Quantum Optimal Control

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. The Pareto optimality is empirically demonstrated 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. It is found 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, the correlation between the Bloch sphere path length and the energetic cost is illustrated.