A simple method for sampling random Clifford operators

• Published in: 2021 IEEE International Conference on Quantum Computing and Engineering (QCE) pp. 54 - 59
• Main Author: Van Den Berg, Ewout
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.10.2021
• Subjects: Clifford circuits; Conferences; Logic gates; Quantum circuit; random sampling; tableau representation; Time complexity; Topology
• DOI: 10.1109/QCE52317.2021.00021

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.