Papers โบ How to efficiently select an arbitrary Clifford group element
How to efficiently select an arbitrary Clifford group element
Robert Koenig, John A. Smolin
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We give an algorithm which produces a unique element of the Clifford group ๐โ on n qubits from an integer 0โคi < |๐โ| (the number of elements in the group). The algorithm involves O(nยณ) operations. It is a variant of the subgroup algorithm by Diaconis and Shahshahani which is commonly applied to compact Lie groups. We provide an adaption for the symplectic group Sp(2n,๐ฝโ) which provides, in addition to a canonical mapping from the integers to group elements g, a factorization of g into a sequence of at most 4n symplectic transvections. The algorithm can be used to efficiently select random elements of ๐โ which is often useful in quantum information theory and quantum computation. We also give an algorithm for the inverse map, indexing a group element in time O(nยณ).
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