  Simulations of high-energy particle collisions, such as those used at the
Large Hadron Collider, are based on quantum field theory; however, many
approximations are made in practice. For example, the simulation of the parton
shower, which gives rise to objects called `jets', is based on a semi-classical
approximation that neglects various interference effects. While there is a
desire to incorporate interference effects, new computational techniques are
needed to cope with the exponential growth in complexity associated to quantum
processes. We present a classical algorithm called the quantum trellis to
efficiently compute the un-normalized probability density over N-body phase
space including all interference effects, and we pair this with an MCMC-based
sampling strategy. This provides a potential path forward for classical
computers and a strong baseline for approaches based on quantum computing.
