Quantum simulation of massive Thirring and Gross--Neveu models for arbitrary number of flavors

TL;DR

This paper advances quantum simulation techniques for fermionic quantum field theories, specifically the massive Thirring and Gross--Neveu models, by analyzing gate complexity, state preparation, and algebraic structures for various system sizes and flavors.

Contribution

It introduces methods for simulating these models on quantum computers, including ground state preparation and algebra classification, for arbitrary flavors and system sizes.

Findings

Gate complexity computed using product formula and qubitization methods.

Ground states prepared with high fidelity for systems up to 20 qubits.

Classified the dynamical Lie algebras, showing they belong to the same isomorphism class.

Abstract

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, $N_f$, discretized on a spatial one-dimensional lattice of size $L$ 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 $N_f$ and $L$. We also prepare the ground states of both models with excellent fidelity for system sizes up to 20 qubits with $N_f = 1,2,3,4$ 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 $N_f$ 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.