Quantum Error Suppression via Symmetry-Averaged Virtual Distillation

Abstract: Reliable quantum simulation is limited by both algorithmic approximations and hardware noise, which usually coexist in the output of near-term and early fault-tolerant quantum devices. Existing error-suppression strategies often target these error sources separately. Here, we introduce symmetry-averaged virtual distillation (SAVD), an error-suppression protocol that applies symmetry averaging before virtual distillation and treats both imperfections at the density-matrix level. The protocol constructs a symmetry-averaged output ensemble from symmetry-labeled implementations, leaving the symmetry-invariant target contribution unchanged while averaging residual components over symmetry-related branches. Virtual distillation (VD) is then applied to this averaged ensemble, rather than to the raw output state, to amplify its dominant eigencomponent. We analyze the resulting spectral suppression mechanism and identify the role of symmetry averaging as a state-preconditioning layer for VD. Numerical demonstrations on an isotropic Heisenberg chain show improved accuracy in the presence of both coherent algorithmic errors and hardware noise. Our results provide a general symmetry-based architecture for enhancing quantum simulations.