Ising Meson Spectroscopy on a Noisy Digital Quantum Simulator

Abstract Quantum simulation has the potential to be an indispensable technique for the investigation of non-perturbative phenomena in strongly-interacting quantum field theories (QFTs). In the modern quantum era, with Noisy Intermediate Scale Quantum (NISQ) simulators widely available and larger-scale quantum machines on the horizon, it is natural to ask: what non-perturbative QFT problems can be solved with the existing quantum hardware? We show that existing noisy quantum machines can be used to analyze the energy spectrum of a large family of strongly-interacting 1+1D QFTs. The latter exhibit a wide-range of non-perturbative effects like ‘quark confinement’ and ‘false vacuum decay’ which are typically associated with higher-dimensional QFTs of elementary particles. We perform quench experiments on IBM’s ibmq_mumbai quantum simulator to compute the energy spectrum of 1+1D quantum Ising model with a longitudinal field. The latter model is particularly interesting due to the formation of mesonic bound states arising from a confining potential for the Ising domain-walls, reminiscent of t’Hooft’s model of two-dimensional quantum chromodynamics. Our results demonstrate that digital quantum simulation in the NISQ era has the potential to be a viable alternative to numerical techniques such as density matrix renormalization group or the truncated conformal space methods for analyzing QFTs.