Impact of Spatiotemporally Correlated Noise in Variational Quantum Algorithms

We present a control-theoretic analysis of variational quantum algorithms under spatiotemporally correlated noise. We employ the filter function formalism to quantify the impact of non-Markovian and stochastic errors on algorithmic performance. We demonstrate that recalculating optimal parameters in a noisy variational algorithm can suppress some, but not all, types of errors. Focusing on symmetric problem instances in the Quantum Approximate Optimization Algorithm (QAOA), such as MaxCut on complete graphs, we identify dominant error channels. By introducing perturbative symmetry-breaking, we explore how deviations from idealized problem structures influence noise resilience. Our study reveals that QAOA's sensitivity to multi-axis correlated noise is anisotropic, with ansatz-dependent dominant error channels. Therefore, we propose a new ansatz, DD-QAOA, taking inspiration from dynamical decoupling, achieving uniform suppression of multi-axis noise. Our findings underscore the importance of symmetry considerations and control strategies in enhancing QAOA's robustness, offering insights relevant to near-term quantum devices and early fault-tolerant architectures.