Quantum Simulation of the N flavor Gross-Neveu Model

TL;DR

This paper explores quantum simulation techniques for the N flavor Gross-Neveu model, demonstrating the feasibility of real-time scattering calculations on current NISQ devices, especially for two flavors mapped to the Hubbard model.

Contribution

It derives qubit Hamiltonians and quantum circuits for simulating the N flavor Gross-Neveu model on NISQ devices, comparing classical and quantum results for N=2 and 4.

Findings

Quantum simulations match classical results for N=2 and 4.

Real-time scattering calculations are feasible on current NISQ devices.

Mapping two flavors to the Hubbard model enables practical quantum simulation.

Abstract

We discuss the use of quantum simulation to study an $N$ flavor theory of interacting relativistic fermions in(1+1) dimensions on NISQ era machines. The case of two flavors is particularly interesting as it can be mapped to the Hubbard model. We derive the appropriate qubit Hamiltonians and associated quantum circuits. We compare classical simulation and DMRG/TEBD calculations with the results of quantum simulation on various platforms for $N$=2 and 4. We demonstrate that the four steps of the calculations of real-time scattering can actually be implemented using current NISQ devices.