Quantum Simulation of Quantum Field Theory with Qubit Models

Quantum computers are expected to outperform classical methods in the simulation of strongly-coupled quantum field theories, as they permit the calculation of dynamic quantities in real-time and avoid the notorious sign-problem. We consider a class of qubit models which can be simulated efficiently on a fault-tolerant quantum computer, and present evidence that these models possess a rich phase diagram. One of the quantum critical points in the phase diagram may help define the traditional asymptotically free O(3) non-linear sigma model. We discuss implementation of these qubit models on both NISQ and fault-tolerant quantum computers, and provide numerical results on adiabatic ground state preparation for the O(3) sigma model. This work serves as a stepping stone towards simulating non-Abelian Kogut-Susskind type gauge theories with quantum devices.