Quantum Computation of the Massive Thirring Model

TL;DR

This paper demonstrates a hybrid classical-quantum approach to calculate energy levels of the massive Thirring model, a fundamental relativistic fermionic theory, showing promising results with error mitigation near the massive regime.

Contribution

It introduces a novel hybrid quantum-classical method to compute the mass gap of the massive Thirring model on a small lattice, including error mitigation techniques.

Findings

Results agree with classical calculations with error mitigation

Approach extends to near massless limit with significant errors

Comparison with perturbation theory confirms accuracy in certain regimes

Abstract

Relativistic fermionic field theories constitute the fundamental description of all observable matter. The simplest of the models provide a useful, classically verifiable benchmark for noisy intermediate scale quantum computers. We calculate the energy levels of the massive Thirring model - a model of Dirac fermions with four-fermion interactions - on a lattice in 1 + 1 space-time dimensions. We employ a hybrid classical-quantum computation scheme to obtain the mass gap in this model for three spatial sites. With error mitigation the results are in good agreement with exact classical calculations. Our calculations extend to the vicinity of the massless limit where chiral symmetry emerges, however relative errors for quantum computations in this regime are significant. We compare our results with an analytical calculation using perturbation theory.