Dominant Eigenstate Isolation through Symmetry-Orbit Decoupling

arXiv:2606.21962v2 Announce Type: replace Abstract: We address the problem of extracting a target eigenstate from an approximate pure state. Our approach, symmetry-orbit decoupling, exploits symmetries that preserve the target state while acting differently on the residual. Averaging over the resulting orbit suppresses the target--residual coherence without reducing the target population, thereby exposing a spectral structure that is hidden in the original pure state. When the target is sufficiently separated from the residual modes, it becomes the principal mode of the orbit-averaged state and can be identified through the orbit Gram matrix. Numerical VQE simulations performed with QuESTlink for six- and eight-qubit Heisenberg and Fermi--Hubbard chains show substantial improvements in ground-state energy estimation. The remaining accuracy is limited by residual components that are indistinguishable from the target under the chosen symmetry.