Multi-scale quantum simulation of quantum field theory using wavelets

Understand

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 multi-scale description of the theory.
• Since wavelets are compact wavefunctions, this encoding allows for quantum simulations to create particle excitations with compact support and provides a natural way to associate observables in the theory to finite resolution detectors.
• We show that the wavelet basis is well suited to compute subsystem entanglement entropy by dividing the field into contributions from short-range wavelet degrees of freedom and long-range scale degrees of freedom, of which the latter act as renormalized modes which capture the essential physics at a renormalization fixed point.