Towards a Quantum Simulation of Nonlinear Sigma Models with a Topological Term

Abstract

We determine the mass gap of a two-dimensional $O(3)$ nonlinear sigma model augmented with a topological $\theta$-term using tensor network and digital quantum algorithms. As proof of principle, we consider the example $\theta =\pi$ and study its critical behaviour on a quantum simulator by examining the entanglement entropy of the ground state. We confirm that the quantum theory is massless in the strong-coupling regime, in agreement with analytical results. However, we also highlight the limitations of current quantum algorithms, designed for noisy intermediate-scale quantum devices, in the theory simulation at weak coupling. Finally, we compare the performance of our quantum algorithms to classical tensor network methods.

arXiv comment12 pages, 6 figures, 2 tables. v2: minor modifications, references added

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• Enhancing Quantum Field Theory Simulations on NISQ Devices with Hamiltonian Truncation
• Toward hybrid quantum simulations with qubits and qumodes on trapped-ion platforms
• State preparation of lattice field theories using quantum optimal control
• Exploring thermal equilibria of the Fermi-Hubbard model with variational quantum algorithms