Symmetry-guided algorithms for variational quantum optimization

arXiv:2611.05865v1 Announce Type: new Abstract: Quantum numbers associated with symmetries classify quantum states and identify the sectors relevant to a given simulation. Generic hardware-efficient ansatzes do not necessarily preserve the quantum numbers and may therefore explore states outside the target sector. We develop symmetry-guided algorithms based on the quantum-accessible Hilbert--Schmidt asymmetry (\(\AHS\)), which quantifies the deviation of a quantum state from invariance under a specified symmetry group. This quantity guides the optimization toward a highly reduced symmetry-based target sector, without enforcing the symmetry on the preparation circuit.