Connectivity Controls Variational Accessibility in Symmetry-Preserving Quantum Circuits

Abstract:Designing expressive quantum circuits for the variational quantum eigensolver (VQE) is a central challenge in simulating interacting many-body systems. Even symmetry-preserving (SP) circuits need not access the full many-body symmetry sector. We demonstrate this explicitly for the spin-$1/2$ XXZ and Hubbard models, where Hamiltonian-inspired nearest-neighbor (NN) SP circuits generate restricted dynamical Lie algebras (DLAs). While these restricted manifolds can accurately represent the ground state near the free-fermion limits, $J_z=0$ for XXZ and $U=0$ for Hubbard, interactions expose inaccessible many-body directions and severely limit VQE performance even at large circuit depth. Remarkably, a minimal modification of the generator connectivity can reconstruct the full orthogonal DLA within all relevant symmetry sectors studied in this work. For XXZ model, the addition of {\it only} one SP next-to-NN single-excitation connection triggers this dramatic reconstruction, whereas the Hubbard case requires a SP correlated double-excitation;--showing that the relevant connectivity can extend from the spatial lattice to many-body configuration space. This reconstruction enlarges the tangent space and accessibility of the energy-lowering Hamiltonian direction, leading to near-unit ground-state fidelity in VQE simulations. Our results establish a direct link between generator connectivity and variational accessibility and suggest a broader circuit-design principle: identify minimal symmetry-preserving generators that enlarge the accessible many-body space rather than increasing circuit depth alone. This perspective may have broader relevance for quantum many-body simulation at the interface of condensed-matter physics and quantum computing.

Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el)

arXiv:2610.07173 [quant-ph]

(or arXiv:2610.07173v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.07173 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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