Resource-Adaptable Quantum Algorithms for Scalable Simulation of the Schwinger Model

The Schwinger model (quantum electrodynamics in 1+1 dimensions) is a testbed for the study of field theories underpinning the Standard Model. Quantum computers are anticipated to enable unprecedented simulations of field theories. In this work, we give scalable and explicit digital algorithms to simulate the Schwinger model using fault-tolerant quantum computation. We upper bound a relevant metric of computational complexity, the number of T-gates, in terms of the simulation parameters, confirming that the time evolution can be simulated efficiently. Additionally, we give circuits that could be used in a nearer-term (NISQ) implementation of our simulation algorithms.