User-specified random sampling of quantum channels and its applications

Random samples of quantum channels have many applications in quantum information processing tasks. Due to the Choi-Jamiolkowski isomorphism, there is a well-known correspondence between channels and states, and one can imagine adapting state sampling methods to sample quantum channels. Here, we discuss such an adaptation, using the Hamiltonian Monte Carlo method, a well-known classical method capable of producing high-quality samples from arbitrary, user-specified distributions. Its implementation requires an exact parametrization of the space of quantum channels, with no superfluous parameters and no constraints. We construct such a parametrization, and demonstrate its use in three common channel sampling applications.