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

Tags

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.

Technology Areas

  • Quantum Computing