How to efficiently select an arbitrary Clifford group element
Abstract
We give an algorithm which produces a unique element of the Clifford group on n qubits (Cn) from an integer 0≤i<Cn (the number of elements in the group). The algorithm involves O(n3) operations and 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 Cn which are 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(n3).
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Dec 01, 2014
- Source ID
- 10.1063/1.4903507
Entities
People
- John A. Smolin
- Robert Koenig
Organizations
- IBM Thomas J. Watson Research Center
- Intelligence Advanced Research Projects Activity
- University of Waterloo