# User-specified random sampling of quantum channels and its applications

## TL;DR

This paper introduces a novel method for sampling quantum channels using Hamiltonian Monte Carlo, leveraging a new parameterization of the channel space, with applications demonstrated in three scenarios.

## Contribution

It develops an exact parameterization of quantum channels enabling efficient Hamiltonian Monte Carlo sampling, adapting classical state sampling techniques to quantum channels.

## Key findings

- Successful implementation of the sampling method
- Application to three quantum channel sampling tasks
- High-quality samples generated from user-specified distributions

## Abstract

Random samples of quantum channels have many applications in quantum information processing tasks. Due to the Choi--Jamio\l{}kowski isomorphism, there is a well-known correspondence between channels and states, and one can imagine adapting \emph{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 parameterization of the space of quantum channels, with no superfluous parameters and no constraints. We construct such a parameterization, and demonstrate its use in three common channel sampling applications.