  We present a hybrid Path Integral Monte Carlo (hPIMC) algorithm to calculate
real-time quantum thermal correlation functions and demonstrate its application
to open quantum systems. The hPIMC algorithm leverages the successes of
classical PIMC as a computational tool for high-dimensional system studies by
exactly simulating dissipation using the Feynman-Vernon influence functional on
a classical computer. We achieve a quantum speed-up over the classical
algorithm by computing short-time matrix elements of the quantum propagator on
a quantum computer. We show that the component of imaginary-time evolution can
be performed accurately using the recently developed Probabilistic
Imaginary-Time Evolution (PITE) algorithm, and we introduce a novel low-depth
circuit for approximate real-time evolution under the kinetic energy operator
using a Discrete Variable Representation (DVR). We test the accuracy of the
approximation by computing the position-position thermal correlation function
of a proton transfer reaction.
