Efficient depth selection for the implementation of noisy quantum approximate optimization algorithm

Noise on near-term quantum devices will inevitably limit the performance of Quantum Approximate Optimization Algorithm (QAOA). One significant consequence is that the performance of QAOA may fail to monotonically improve with control depth. In principle, optimal depth can be found at a certain point where the noise effects just outweigh the benefits brought by increasing the depth. In this work, we propose to use the regularized model selection algorithm to identify the optimal depth with just a few iterations of regularization parameters. Numerical experiments show that the algorithm can efficiently locate the optimal depth under relaxation and dephasing noises. (c) 2022 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.