Quantum

Connectivity Controls Variational Accessibility in Symmetry-Preserving Quantum Circuits

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Briefings

A new study demonstrates that minimal modifications to generator connectivity in symmetry-preserving quantum circuits can reconstruct the full orthogonal dynamical Lie algebra (DLA), significantly improving variational quantum eigensolver (VQE) performance. For the spin-1/2 XXZ model, adding one specific next-to-nearest-neighbor single-excitation connection suffices to access the full many-body symmetry sector, whereas the Hubbard model requires a single SP correlated double-excitation connection. These findings establish a direct link between generator connectivity and variational accessibility, suggesting that expanding the accessible many-body space through minimal connectivity changes is more effective than increasing circuit depth alone.

Key points

• Minimal addition of one SP next-to-NN single-excitation connection reconstructs the full orthogonal DLA for the spin-1/2 XXZ model, enabling near-unit ground-state fidelity in VQE simulations.
• The Hubbard model requires a SP correlated double-excitation connection to achieve the same reconstruction, demonstrating that connectivity can extend from spatial lattice to many-body configuration space.

Context and limitations

Results are limited to the spin-1/2 XXZ and Hubbard models; specific connectivity requirements vary by model type. Preprint status (arXiv:2610.07173v1) and uncertainty regarding generalizability beyond these two systems remain unverified.

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