Quantifying the Role of Correlated Noise in the Quantum Approximate Optimization Algorithm

The quantum approximate optimization algorithm (QAOA) is a promising application for solving optimization problems on noisy intermediate-scale quantum devices. However, their potential for quantum advantage is hindered by the presence of noise stemming from unwanted interactions between quantum systems and their environments. In prominent quantum technologies, like superconducting qubits, relevant noise sources have been found to possess both spatial and temporal correlations. While previous studies have sought to investigate the impact of noise and potential avenues for robustness in QAOA in the presence of Markovian noise, little is known about the effect of spatiotemporal correlated noise on QAOA performance. In this study, we investigate the impact of correlated noise on the QAOA variant of Grover's search using the filter function formalism. We assess the robustness of QAOA by optimizing the filter function via the variational parameters. We show that analytical error bounds relating the noise statistical properties to the approximation ratio and training error can be derived.