A simple method for sampling random Clifford operators - Van Den Berg, Ewout (2021 IEEE International Conference on Quantum Computing and Engineering (QCE), 2021)
We describe a simple algorithm for sampling n-qubit Clifford operators uniformly at random. The algorithm outputs the Clifford operators in the form of quantum circuits with at most 5n + 2n 2 elementary gates and a maximum depth of {\mathcal{O}}\left({n\,{\text{log}}\,n}\right) on fully connected topologies. The circuit can be output in a streaming fashion as the algorithm proceeds, and different parts of the circuit can be generated in parallel. The algorithm has an {\mathcal{O}}\left({{n^2}}\right) time complexity, which matches the current state of the art. The main advantage of the proposed algorithm, however, lies in its simplicity and elementary derivation.