A simple method for sampling random Clifford operators

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 O(n log n) 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 O(n(2)) 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.