Quantum Computational Particle Physics: Algorithms, Resource Estimation, and Model-Building

Abstract

Quantum simulation is one of the most promising applications of quantum computers. It is anticipated that quantum simulation will accelerate scientific discovery, and advance our understanding of nature. One area that stands to benefit from quantum simulation is particle physics. This thesis contains my contributions to quantum simulation of lattice gauge theories--a well-known first-principle computational method in particle physics.

The limitations of current and near-term quantum processors, such as high error rates and small number of qubits, severely restrict the size and depth of quantum circuits that can be executed with high fidelity. Tailored to these hardware constraints, short-depth variational quantum algorithms are proposed to solve small lattice quantum electrodynamics models in two spatial dimensions. The proposal is based on, and made possible by a novel lattice quantum electrodynamics model designed to lower the simulation memory overhead.

There is no better time than now to understand and minimize fault-tolerant computational resource requirements of quantum simulations of lattice gauge theories so that they can be implemented sooner than later. To this end, complete gate-by-gate quantum algorithms with concrete fault-tolerant resource estimates are constructed to simulate lattice quantum electrodynamics and chromodynamics.

Finally, a topological 𝜃-term, directly relevant to the strong CP problem in particle physics, in the Hamiltonian formulation of lattice gauge theories is derived for future quantum simulations. Classical numerical results suggest a phase transition due to this term in a three-dimensional U(1) lattice gauge theory. Verification of this transition, and large-scale simulations of quantum chromodynamics with a 𝜃-term will likely require a quantum computer.