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Canonical Decompositions of n-qubit Quantum Computations and Concurrence
Published
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
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 August 31, 2024)