Canonical Decompositions of n-qubit Quantum Computations and Concurrence

Published

February 25, 2003

Author(s)

Stephen Bullock, G K. Brennen

Abstract

The two-qubit canonical decomposition SU(4) = [SU(2) SU(2)]?[SU(2) SU(2)] writes any two-qubit quantum computation as a composition of a local unitary, a relative phasing of Bell states, and a second local unitary. Using Lie theory, we generalize this to an n-qubit decomposition, the concurrence canonical decomposition (C.C.D.) SU(2n)=KAK. The group K fixes a bilinear form related to the concurrence, and in particular any computation in K preserves the n-tangle |*| (-i? ) ¿ (-i? ) |?>|2 for n even. Thus, the C.C.D. shows that any n-qubit quantum computation is a composition of a computation preserving this generalized tangle, a computation in A which applies relative phases to a set of GHZ states, and a second

Citation

Journal of Mathematical Physics

Pub Type

Journals

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Keywords

concurrence, entanglement, quantum computation

Citation

Bullock, S. and Brennen, G. (2003), Canonical Decompositions of n-qubit Quantum Computations and Concurrence, Journal of Mathematical Physics, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=50678 (Accessed October 22, 2025)