What does it mean to simulate a quantum field theory? This is a challenging question because a majority of the quantum field theories relevant to fundamental physics lack a fully rigourous mathematical definition. Thus it is impossible in general to compare the predictions of discretised theories with their continuum counterparts. I will discuss these challenges and advocate the use of the recently introduced operator algebraic renormalization (OAR) as a means to provide both classical and quantum simulations of quantum field theories, in particular, conformal theories. The OAR naturally provides a direct mechanism to compare predictions from a cutoff lattice with a target continuum theory.
