Multiscale quantum simulation of quantum field theory using wavelets

A successful approach to understand field theories is to resolve the physics into different length or energy scales using the renormalization group framework. We propose a quantum simulation of quantum field theory which encodes field degrees of freedom in a wavelet basis - a multiscale description of the theory. Since wavelet families can be constructed to have compact support at all resolutions, this encoding allows for quantum simulations to create particle excitations which are local at some chosen scale and provides a natural way to associate observables in the theory to finite-resolution detectors.