A simple method for sampling random Clifford operators

Understand

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 $\mathcal{O}(n\log n)$ 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 $\mathcal{O}(n^2)$ time complexity, which matches the current state of the art.