Quantum Simulation of Quantum Field Theories

Thesis (Ph.D.)--University of Washington, 2023The theory of quantum chromodynamics (QCD) describes the nuclear forces that bind quarks into nucleons and nucleons into nuclei. The dynamics in the non-perturbative regime of QCD are of relevance for understanding inelastic hadron scattering, the behavior of quark-gluon plasma in the early universe and matter inside of extreme enviroments such as supernovae. The discretization of QCD onto a spacial lattice gives a formalism that can be used to study the non-perturbative aspects of the theory and quantum simulation offers the promise of being able to probe real time dynamics directly. The research presented in this dissertation contributes to the development of quantum simulation techniques for quantum field theory. This dissertation is organized into two parts. The first part discusses digital quantum simulation techniques which can be implemented on a universal quantum computer. This part begins with an encoding of SU(3) gauge fields onto quantum computer and a discussion of how to simulate time evolution on a quantum computer. Variational methods are then used to prepare ground states on quantum hardware. The similarity renormalization group is used to derive improved Hamiltonians that mitigate the effects of truncating the gauge fields. As a step towards simulating lattice QCD with dynamical fermions on quantum computers, a study of algorithms that can be used to simulate time evolution of a system of fermions interacting through a Coulomb interaction is performed. An algorithm is introduced to study the decay of unstable particles and total cross sections. The techniques in this section lay out a path for computing scattering observables on a quantum computer. In the second part, techniques are developed for analog quantum simulation of the O(3) non-linear $\sigma$ model on cold atoms. This part begins with the development of a method to simulate Heisenberg interactions on cold atom systems. This method is then extended to an adiabatic state preparation technique. This part concludes with a proposal for an analog simulation of the asymptotically free region of the O(3) non-linear $\sigma$ model that should be possible on currently existing cold atom quantum simulators. With the combination of long term algorithm design and near term implementation, the research in this disseration has contributed to the development of quantum simulations of quantum field theories