  Understanding the interactions between elementary particles and mapping out
the internal structure of the hadrons are of fundamental importance in high
energy nuclear and particle physics. This thesis concentrates on the strong
interaction, described by Quantum Chromodynamics (QCD). We introduce a novel
concept called "polarized jet fragmentation functions" and develop the
associated theory framework known as QCD factorization which allows us to
utilize jet substructure to probe spin dynamics of hadrons, especially
nucleon's three-dimensional imaging. Furthermore, non-perturbative QCD studies,
particularly of the QCD phase diagram, are important for understanding the
properties of hadrons. The development of quantum computing and simulators can
potentially improve the accuracy of finite-temperature simulations and allow
researchers to explore extreme temperatures and densities in more detail. In
this thesis, I present my work in two aspects of QCD studies: (1) investigating
the nucleon structure using polarized jet fragmentation functions and (2)
illustrating how to apply quantum computing techniques for studying phase
diagram of a low energy QCD model. The first category investigates phenomena
such as hadron production inside jets, spin asymmetries, etc., providing
valuable insight into the behavior of quarks and gluons in hadrons. The second
category provides potential applications of quantum computing in QCD and
explores the non-perturbative nature of QCD.
