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2009

Learning and Testing Algorithms for the Clifford Group

Low, Richard A.

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Given oracle access to an unknown unitary C from the Clifford group and its conjugate, we give an exact algorithm for identifying C with O(n) queries, which we prove is optimal.

We then extend this to all levels of the Gottesman-Chuang hierarchy (also known as the C_k hierarchy).
Further, for unitaries not in the hierarchy itself but known to be close to an element of the hierarchy, we give a method of finding this close element.
We also present a Clifford testing algorithm that decides whether a given black-box unitary is close to a Clifford or far from every Clifford.

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A. Montanaro and T. J. Osborne, Quantum boolean functions (2008), arXiv:0810.2435
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