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arXiv:2610.30270

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

Vivan Bhatt, Zhongtian Dong, Kyoungchul Kong, Kwangmin Yu

hep-phquant-phSubmitted Oct 21, 2026• Announced Oct 23, 2026• 0 citations
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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.

Comments
20 pages, 7 figures, 16 tables

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We study variational preparation of ground states and sector-resolved excited states in the (1+1)(1+1)(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 1×10−51 \times 10^{-5}1×10−5 - 2×10−42 \times 10^{-4}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 2.1×10−32.1 \times 10^{-3}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%0.35\%0.35% - 1.76%1.76\%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.
Inspired by recent advancements in simulating periodic systems on quantum computers, we develop an approach to further advance the simulation of these systems, named (SC)2{}^{2}2-ADAPT-VQE. Our approach extends the scalable-circuits ADAPT-VQE framework, which builds an ansatz from a pool of coordinate-invariant operators defined for arbitrarily large, though not arbitrarily small, volumes. Our method uses a classically tractable ``surrogate constructed'' method to remove irrelevant operators from the pool, reducing the minimum size for which the scalable circuits are defined. Bringing together the scalable circuits and the surrogate constructed approaches forms the core of the (SC)2{}^{2}2 methodology. Our approach allows for a wider set of classical computations on small volumes, which can be used for a more robust extrapolation protocol. While developed in the context of lattice models, the surrogate construction portion is applicable to a wide variety of problems where information about the relative importance of operators in the pool is available. As an example, we use it to compute the properties of the Schwinger model---quantum electrodynamics for a single, massive fermion in 1+11+11+1 dimensions---and show that our method can be used to accurately extrapolate to the continuum limit.
The study of fermionic quantum field theories is an important problem for realizing the standard model of particle physics on a quantum computer. As a step towards this goal, we consider the massive Thirring and Gross--Neveu models with arbitrary number of fermion flavors, NfN_fNf​, discretized on a spatial one-dimensional lattice of size LLL in the Hamiltonian formulation. We compute the gate complexity using the higher-order product formula and using block-encoding/qubitization and quantum singular value transformations in the limit of large NfN_fNf​ and LLL. We also prepare the ground states of both models with excellent fidelity for system sizes up to 20 qubits with Nf=1,2,3,4N_f = 1,2,3,4Nf​=1,2,3,4 using the adaptive-variational quantum imaginary time algorithm. In addition, we also classify the dynamical Lie algebras of these relativistic fermionic models and show that they belong to the same isomorphism class. Our work is a concrete step towards the quantum simulation of real-time dynamics of large NfN_fNf​ fermionic quantum field theories models relevant for chiral symmetry breaking, understanding dimensional transmutation, and exploring the conformal window of field theories on near-term and early fault-tolerant quantum computers.
We present a scalable quantum simulation framework for real-time dynamics of the multi-flavor Gross-Neveu model in 1+1 dimensions. Using superconducting quantum processors at utility scale, we develop a hardware-efficient Trotterization whose per-step circuit depth scales with fermion flavor number rather than total system size, enabling simulations beyond 100 qubits. A central contribution of this work is the Localized Diagonal Operator Approximation (LDOA), which systematically reduces the overhead associated with quartic interactions. We formulate diagonal unitary synthesis as a structured least-squares problem in phase space and obtain analytic solutions via the Moore-Penrose pseudoinverse. This formulation provides a principled and quantitatively controlled approximation: in the small Trotter-step regime, the unitary error is directly linked to the phase reconstruction error and vanishes asymptotically as the Trotter step size decreases. This establishes a clear mathematical foundation for the LDOA while significantly reducing two-qubit gate counts and circuit depth, and is broadly applicable to diagonal quantum operators with long-range structure, making it particularly well suited for quantum hardware with limited qubit connectivity. Using these techniques, we run large-scale simulations on IBM superconducting processors and study real-time observables, including density-density correlators. We benchmark against exact diagonalization and tensor network-based methods, finding strong agreement across system sizes. These results show that combining hardware-aware circuit design with rigorous approximations enables practical near-term simulation of interacting fermionic field theories and provides a scalable pathway toward more complex quantum field theory simulations.
The vacuum of the lattice Schwinger model is prepared on up to 100 qubits of IBM’s Eagle-processor quantum computers. A new algorithm to prepare the ground state of a gapped translationally invariant system on a quantum computer is presented, which we call “scalable circuits ADAPT-VQE” (SC-ADAPT-VQE). This algorithm uses the exponential decay of correlations between distant regions of the ground state, together with ADAPT-VQE, to construct quantum circuits for state preparation that can be scaled to arbitrarily large systems. These scalable circuits can be determined with use of classical computers, avoiding the challenging task of optimizing parameterized circuits on a quantum computer. SC-ADAPT-VQE is applied to the Schwinger model, and is shown to be systematically improvable, with an accuracy that converges exponentially with circuit depth. Both the structure of the circuits and the deviations of prepared wave functions are found to become independent of the number of spatial sites, L . This allows a controlled extrapolation of the circuits, determined with use of small or modest-sized systems, to arbitrarily large L . The circuits for the Schwinger model are determined on lattices up to L=14 (28 qubits) with the Qiskit classical simulator, and are subsequently scaled up to prepare the L=50 (100 qubits) vacuum on IBM’s 127-superconducting-qubit quantum computers ibm_brisbane and ibm_cusco. After introduction of an improved error-mitigation technique, which we call “operator decoherence renormalization”, the chiral condensate and charge-charge correlators obtained from the quantum computers are found to be in good agreement with classical matrix product state simulations. Published by the American Physical Society 2024
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