Symmetry-Preserving and Scalable Variational Circuits for the Lattice Gross-Neveu Model

Year: 2026

Type: preprint

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 $1 \times 10^{-5}$ - $2 \times 10^{-4}$, 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 $2.1 \times 10^{-3}$. 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.30270

Authors: Bhatt, Vivan, Dong, Zhongtian, Kong, Kyoungchul, Yu, Kwangmin

Institutions: University of Kansas, Peking University, Brookhaven National Laboratory

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, U.S. Department of Energy, National Energy Research Scientific Computing Center, Office of Science, University of California, San Diego, Laboratory Directed Research and Development, Brookhaven National Laboratory

OpenAlex ID: W7223362866