A general framework for recursive decompositions of unitary quantum evolutions

Author

Mehmet Dağlı , Domenico D'Alessandro and Jonathan D H Smith

Affiliations

Department of Mathematics, Iowa State University, Ames, IA, 50011 USA

E-mail

mdagli@iastate.edu daless@iastate.edu jdhsmith@math.iastate.edu

Journal

Journal of Physics A: Mathematical and Theoretical Create an alert RSS this journal

Issue

Volume 41, Number 15

Citation

Mehmet Dağlı et al 2008 J. Phys. A: Math. Theor. 41 155302

doi: 10.1088/1751-8113/41/15/155302


 
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Abstract

Decompositions of the unitary group U(n) are useful tools in quantum information theory as they allow one to decompose unitary evolutions into local evolutions and evolutions causing entanglement. Several recursive decompositions have been proposed in the literature to express unitary operators as products of simple operators with properties relevant in entanglement dynamics. In this paper, using the concept of grading of a Lie algebra, we cast these decompositions in a unifying scheme and show how new recursive decompositions can be obtained. In particular, we propose a new recursive decomposition of the unitary operator on N qubits, and give a numerical example.

 
PACS

03.67.Mn Entanglement measures, witnesses, and other characterizations

03.67.Lx Quantum computation architectures and implementations

03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.)

03.65.Fd Algebraic methods

02.20.Sv Lie algebras of Lie groups

02.20.Uw Quantum groups

MSC

22E60 Lie algebras of Lie groups (For the algebraic theory of Lie algebras, see 17Bxx)

22D10 Unitary representations of locally compact groups

17B37 Quantum groups (quantized enveloping algebras) and related deformations (See also 16W35, 20G42, 81R50, 82B23)

81R15 Operator algebra methods (See also 46Lxx, 81T05)

81P68 Quantum computation and quantum cryptography (See also 68Q05, 94A60)

81R50 Quantum groups and related algebraic methods (See also 16W35, 17B37)

Subjects

Mathematical physics

Computational physics

Quantum information and quantum mechanics

Dates

Issue 15 ( 18 April 2008)

Received 8 November 2007

Published 2 April 2008



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