Quantum Simulation of the Real-time Dynamics in the multi-flavor Gross-Neveu Model at the utility scale using Superconducting Quantum Computers

TL;DR

This paper introduces a scalable quantum simulation framework for the multi-flavor Gross-Neveu model using superconducting quantum computers, featuring a novel Localized Diagonal Operator Approximation that reduces circuit complexity.

Contribution

The work develops a hardware-efficient Trotterization and the LDOA method, enabling large-scale fermionic simulations with reduced gate counts on superconducting quantum hardware.

Findings

Successfully simulated real-time dynamics of the model on IBM quantum processors.

Achieved strong agreement with exact and tensor network methods across various system sizes.

Demonstrated the scalability and practicality of the approach for near-term quantum hardware.

Abstract

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.