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, Jz=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.
Related
- Symmetry-Preserving and Scalable Variational Circuits for the Lattice Gross-Neveu Model
- From Trainability Diagnostics to Optimization Claims: Boundaries and Controls in Variational Quantum Optimization
- PT-invariant nonlocal variable-coefficient Fokas-Lenells equation: nonstandard Hirota bilinearization, symmetry-preserving and breaking multi-soliton solutions
- Fate of average symmetry-protected topological states under symmetry-preserving quantum operations
- Symmetry-Preserving Local Representation for Short-Range Interaction in Complex Materials
BibTeX
@misc{reja2026connectivity,
title = {{Connectivity Controls Variational Accessibility in Symmetry-Preserving Quantum Circuits}},
author = {Sahinur Reja},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07173},
eprint = {2610.07173},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07173},
}
RIS
TY - UNPB
TI - Connectivity Controls Variational Accessibility in Symmetry-Preserving Quantum Circuits
AU - Sahinur Reja
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.07173
UR - https://arxiv.org/abs/2610.07173
AB - 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.
ER -