Non-Markovian Noise in Symmetry-Preserving Quantum Dynamics

Near-term quantum devices are a promising tool for solving complex problems impractical for classical computers in optimization, chemistry and machine learning. However, the utility of a quantum system is hindered by noise, particularly spatio-temporally correlated noise. In this work, we develop a formalism to quantify the effects of temporally correlated noise on symmetric quantum evolution. We demonstrate analytically that symmetry-preserving noise maintains the computational subspace while inducing decoherence within it. Conversely, we show that non-symmetric noise, albeit resulting in decoherent leakage outside the computational subspace, leads to highly specific errors channels. For this purpose, we construct a novel basis for calculating filter functions informed by the system symmetries. We support our results with a numerical study of a noisy Ising model. Our results are broadly applicable, providing new insights into the design of noise-resilient quantum computation and error protection strategies for the NISQ era and beyond.