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A simple method for sampling random Clifford operators
E. Berg·August 13, 2020·DOI: 10.1109/QCE52317.2021.00021
Computer SciencePhysicsMathematics
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Abstract
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.