  I describe the first continuous space nuclear path integral quantum Monte
Carlo method, and calculate the ground state properties of light nuclei
including Deuteron, Triton, Helium-3 and Helium-4, using both local chiral
interaction up to next-to-next-to-leading-order and the Argonne $v_6'$
interaction. Compared with diffusion based quantum Monte Carlo methods such as
Green's function Monte Carlo and auxiliary field diffusion Monte Carlo, path
integral quantum Monte Carlo has the advantage that it can directly calculate
the expectation value of operators without tradeoff, whether they commute with
the Hamiltonian or not. For operators that commute with the Hamiltonian, e.g.,
the Hamiltonian itself, the path integral quantum Monte Carlo light-nuclei
results agree with Green's function Monte Carlo and auxiliary field diffusion
Monte Carlo results. For other operator expectations which are important to
understand nuclear measurements but do not commute with the Hamiltonian and
therefore cannot be accurately calculated by diffusion based quantum Monte
Carlo methods without tradeoff, the path integral quantum Monte Carlo method
gives reliable results. I show root-mean-square radii, one-particle number
density distributions, and Euclidean response functions for single-nucleon
couplings. I also systematically describe all the sampling algorithms used in
this work, the strategies to make the computation efficient, the error
estimations, and the details of the implementation of the code to perform
calculations. This work can serve as a benchmark test for future calculations
of larger nuclei or finite temperature nuclear matter using path integral
quantum Monte Carlo.
