Enabling High Performance Debugging for Variational Quantum Algorithms using Compressed Sensing

Abstract: Variational quantum algorithms (VQAs) can potentially solve practical problems using contemporary Noisy Intermediate Scale Quantum (NISQ) computers. VQAs find near-optimal solutions in the presence of qubit errors by classically optimizing a loss function computed by parameterized quantum circuits. However, developing and testing VQAs is challenging due to the limited availability of quantum hardware, their high error rates, and the significant overhead of classical simulations. Furthermore, VQA researchers must pick the right initialization for circuit parameters, utilize suitable classical optimizer configurations, and deploy appropriate error mitigation methods. Unfortunately, these tasks are done in an ad-hoc manner today, as there are no software tools to configure and tune the VQA hyperparameters. In this paper, we present OSCAR (cOmpressed Sensing based Cost lAndscape Reconstruction) to help configure: 1) correct initialization, 2) noise mitigation techniques, and 3) classical optimizers to maximize the quality of the solution on NISQ hardware. OSCAR enables efficient debugging and performance tuning by providing users with the loss function landscape without running thousands of quantum circuits as required by the grid search. Using OSCAR, we can accurately reconstruct the complete cost landscape with up to 100X speedup. Furthermore, OSCAR can compute an optimizer function query in an instant by interpolating a computed landscape, thus enabling the trial run of a VQA configuration with considerably reduced overhead.