Hadronic Structure with Classical and Quantum Computing

Abstract

Calculations in lattice quantum chromodynamics (QCD) — presently the only known systematically improvable approach to describe the strong nuclear force in the nonperturbative regime from first principles — are playing an increasingly important role in revealing how hadrons emerge from the interactions of the underlying degrees of freedom: quarks and gluons. With computational and theoretical advances, more fruitful connections have emerged between lattice QCD and phenomenology, and the field is now well into a stage ripe for deriving tighter constraints on hadronic structure through joint analyses of numerical lattice QCD results with experimental data. This thesis summarizes lattice QCD calculations of the Collins-Soper (CS) kernel: a nonperturbative function whose inclusion in joint analyses has the potential to advance the study of multidimensional hadronic structure. The CS kernel is an anomalous dimension of transverse-momentum-dependent (TMD) distributions describing a three-dimensional structure of ultrarelativistic hadrons as a function of quark-gluon momenta collinear with and transverse to the hadron's motion. Constraints on the CS kernel at nonperturbative transverse-momentum scales are instrumental to relate TMDs across scales and processes. The kernel differs for quark and gluon TMDs, but is otherwise universal. This thesis presents the first lattice QCD determination of the quark CS kernel with systematic control over operator mixing, quark mass, and lattice discretization, and a proof-of-principle lattice calculation of the gluon CS kernel providing the first nonperturbative constraints on this quantity. Additionally, this thesis summarizes exploratory studies on how Hamiltonian calculations — realized with quantum-computer simulations and tensor networks — may be combined with conventional Monte Carlo calculations based on Lagrangian formulations in Euclidean space. These studies examine how constructions of interpolating operators, used in conventional calculations to map between the vacuum and a ground state of interest, may be optimized in Hamiltonian calculations to increase overlap with the target state. Results, limited to the Schwinger model, support further investigations of this approach in theories more closely resembling QCD as quantum-computing and tensor-network technologies continue to mature.