Symmetry-Preserving and Scalable Variational Circuits for the Lattice Gross-Neveu Model
Abstract
We study variational preparation of ground states and sector-resolved excited states in the (1+1)-dimensional lattice Gross-Neveu model. We construct fixed circuits preserving either total fermion number or every flavor number, and a problem-specific scalable-circuit adaptive variational quantum eigensolver (SC-ADAPT-VQE). Classical circuit benchmarks cover massless and massive systems through 30 qubits, using exact-diagonalization and tensor-network reference results. Imposing flavor-number conservation improves the achieved energies in the completed two-flavor comparisons. Selected massive fixed-ansatz benchmarks with one to four flavors have relative energy errors of approximately 1 × 10−5 - 2 × 10−4, smaller than the quoted literature errors where available, although discretizations and computational resources differ. The adaptive pool combines translated bulk and boundary-sensitive generators with an interaction-sensitive cross-flavor family. Selected massive SC-ADAPT benchmarks with one to three flavors have relative energy errors below 2.1 × 10−3. For one flavor, matrix-product-state evaluations extend the transferred circuits to 60-400 qubits without target-side operator selection or parameter optimization, giving energy deviations of approximately 0.35% - 1.76% from density-matrix renormalization-group reference values at maximum bond dimension 256. At fixed flavor number, range caps, and append count, the adaptive construction has a precompilation local-factor count linear in volume and a volume-independent shared-parameter count; fixed-accuracy performance at arbitrary volumes remains unestablished. Sequential deflation also prepares low-lying states within a fixed flavor-number sector, with projector fidelities providing a basis-independent assessment of degenerate target eigenspaces.
Related
- Connectivity Controls Variational Accessibility in Symmetry-Preserving Quantum Circuits
- BAHAMAS: A Control Plane for Optimization and Execution of Variational Quantum Circuits
- Quantum Hierarchical Reinforcement Learning via Variational Quantum Circuits
- Subspace Controllability in Variational Quantum Circuits: Maximising Expressivity and Increasing Search Efficiency with Dynamical Lie Algebras
- Operator Learning with Variational Quantum Circuits
BibTeX
@misc{bhatt2026symmetrypreserving,
title = {{Symmetry-Preserving and Scalable Variational Circuits for the Lattice Gross-Neveu Model}},
author = {Vivan Bhatt and Zhongtian Dong and Kyoungchul Kong and Kwangmin Yu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30270},
eprint = {2610.30270},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30270},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Symmetry-Preserving and Scalable Variational Circuits for the Lattice Gross-Neveu Model
AU - Vivan Bhatt
AU - Zhongtian Dong
AU - Kyoungchul Kong
AU - Kwangmin Yu
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30270
UR - https://arxiv.org/abs/2610.30270
AB - We study variational preparation of ground states and sector-resolved excited states in the (1+1)-dimensional lattice Gross-Neveu model. We construct fixed circuits preserving either total fermion number or every flavor number, and a problem-specific scalable-circuit adaptive variational quantum eigensolver (SC-ADAPT-VQE). Classical circuit benchmarks cover massless and massive systems through 30 qubits, using exact-diagonalization and tensor-network reference results. Imposing flavor-number conservation improves the achieved energies in the completed two-flavor comparisons. Selected massive fixed-ansatz benchmarks with one to four flavors have relative energy errors of approximately 1 × 10^−5 - 2 × 10^−4, smaller than the quoted literature errors where available, although discretizations and computational resources differ. The adaptive pool combines translated bulk and boundary-sensitive generators with an interaction-sensitive cross-flavor family. Selected massive SC-ADAPT benchmarks with one to three flavors have relative energy errors below 2.1 × 10^−3. For one flavor, matrix-product-state evaluations extend the transferred circuits to 60-400 qubits without target-side operator selection or parameter optimization, giving energy deviations of approximately 0.35% - 1.76% from density-matrix renormalization-group reference values at maximum bond dimension 256. At fixed flavor number, range caps, and append count, the adaptive construction has a precompilation local-factor count linear in volume and a volume-independent shared-parameter count; fixed-accuracy performance at arbitrary volumes remains unestablished. Sequential deflation also prepares low-lying states within a fixed flavor-number sector, with projector fidelities providing a basis-independent assessment of degenerate target eigenspaces.
ER -