NON-EQUILIBRIUM PROPERTIES OF QUANTUM CHROMODYNAMICS ON THE LATTICE

Abstract

Heavy-ion collisions performed at the Large Hadron Collider and the Relativistic Heavy Ion Collider have given us a tremendous insight into both the equilibrium and non-equilibrium properties of strongly coupled nuclear matter. This thesis details two theoretical frameworks for addressing particularly the non-equilibrium nature of such nuclear systems governed by quantum chromodynamics.Lattice QCD has offered non-perturbative access to observables in quantum chromodynamics. However, not much progress has been made in non-equilibrium calculations via lattice QCD compared to lattice QCD in equilibrium due to the so-called sign problem, stating that such calculations naively require a computational resource that scales exponentially with the size of the lattice. Quantum computing has the promise of performing first-principles simulations of the time-evolution of nuclear systems without such an exponential cost. This thesis details quantum algorithms for evaluating observables that are essential for understanding heavy-ion collisions: the parton distribution functions and the hydrodynamic transport coefficients. Quantum simulation of nuclear system naively requires a large-scale quantum computer which is not available at the moment. Thus it is of practical importance to pursue methods to solve sign problems and expand the frontier of the classical lattice QCD calculation of non-equilibrium observables. The second topic of this thesis is a novel approach to address sign problems, which will be referred to as complex normalizing flows. This method belongs to a family of manifold deformation methods, a long-standing approach to alleviate sign problems. The applicability of complex normalizing flows to lattice calculations of our interest, non-equilibrium QCD, will be discussed. Given that complex normalizing flows are likely to solve sign problems in bosonic theories out of equilibrium, numerical algorithms based on machine learning to solve such sign problems in the framework of complex normalizing flows will be discussed.