  We present a quantum Monte Carlo algorithm for the simulation of general
quantum and classical many-body models within a single unifying framework. The
algorithm builds on a power series expansion of the quantum partition function
in its off-diagonal terms and is both parameter-free and Trotter error-free. In
our approach, the quantum dimension consists of products of elements of a
permutation group. As such, it allows for the study of a very wide variety of
models on an equal footing. To demonstrate the utility of our technique, we use
it to clarify the emergence of the sign problem in the simulations of
non-stoquastic physical models. We showcase the flexibility of our algorithm
and the advantages it offers over existing state-of-the-art by simulating
transverse-field Ising model Hamiltonians and comparing the performance of our
technique against that of the stochastic series expansion algorithm. We also
study a transverse-field Ising model augmented with randomly chosen two-body
transverse-field interactions.
