Creation of Wave Packets for Quantum Chromodynamics on Quantum Computers

TL;DR

This paper develops a method for creating particle wave packets in lattice gauge theories, including three-dimensional QCD, enabling real-time quantum simulations of scattering processes on quantum computers.

Contribution

It extends previous work to generate general particle wave packets in lattice gauge theories, including 3D QCD, using the LCU technique and Haag-Ruelle theory.

Findings

Successful wave packet creation from vacuum in lattice gauge theories.

Implementation of wave packet preparation using LCU technique.

Preparation probability decreases polynomially with key parameters.

Abstract

One of the most ambitious goals of quantum simulation of quantum field theory is the description of scattering in real time, which would allow not only for computation of scattering amplitudes, but also for studying the collision process step by step. The initial state of such simulation is made of typically two wave packets of stable particles moving on top of the vacuum, whose preparation is difficult. Here we extend a previous work to create wave packets of a general kind of particle from the vacuum in lattice gauge theories in various dimensions, including three-dimensional QCD for the first time. The conceptual foundation of this approach is the Haag-Ruelle scattering theory, and the only theoretical limitation is given by the presence of massless particles. In the context of digital quantum computation, the wave packet creation from the vacuum is implemented with the technique known as LCU (linear combination of unitaries). The preparation is performed successfully upon measuring an ancillary register with a certain probability, which vanishes polynomially in the lattice spacing, the wave-packet energy and the momentum narrowness.