The Clifford group, stabilizer states, and linear and quadratic operations over GF(2)

2003/04/18 by Jeroen Dehaene, Bart De Moor · 3 citations
Physics and Astronomy · #quant-ph

paper · pdf · doi:10.1103/physreva.68.042318

published as Phys. Rev. A 68, 042318 (2003) · 9 pages

arxiv created 2003/04/18 · arxiv updated 2009/12/01

Abstract

We describe stabilizer states and Clifford group operations using linear operations and quadratic forms over binary vector spaces. We show how the n-qubit Clifford group is isomorphic to a group with an operation that is defined in terms of a (2n+1)x(2n+1) binary matrix product and binary quadratic forms. As an application we give two schemes to efficiently decompose Clifford group operations into one and two-qubit operations. We also show how the coefficients of stabilizer states and Clifford group operations in a standard basis expansion can be described by binary quadratic forms. Our results are useful for quantum error correction, entanglement distillation and possibly quantum computing.

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