Multi-scale quantum simulation of quantum field theory using wavelets

TL;DR

This paper introduces a quantum simulation method for quantum field theories using wavelet bases, enabling multi-scale analysis, efficient computation of entanglement, and a natural connection to renormalization group concepts.

Contribution

It proposes encoding quantum field degrees of freedom in wavelet bases for multi-scale quantum simulation, facilitating localized particle creation and entanglement analysis.

Findings

Wavelet basis efficiently encodes field degrees of freedom.

Subsystem entanglement entropy can be computed across scales.

Long-range wavelet modes capture physics at renormalization fixed points.

Abstract

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.