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Quantum gates on hybrid qudits

Jamil Daboul1,2, Xiaoguang Wang1 and Barry C Sanders1

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We introduce quantum hybrid gates that act on qudits of different dimensions. In particular, we develop two representative two-qudit hybrid gates (SUM and SWAP) and many-qudit hybrid Toffoli and Fredkin gates. We apply the hybrid SUM gate to generating entanglement, and find that operator entanglement of the SUM gate is equal to the entanglement generated by it for certain initial states. We also show that the hybrid SUM gate acts as an automorphism on the Pauli group for two qudits of different dimensions under certain conditions. Finally, we describe a physical realization of these hybrid gates for spin systems.


PACS

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.)

03.67.Mn Entanglement measures, witnesses, and other characterizations

MSC

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

20K30 Automorphisms, homomorphisms, endomorphisms, etc.

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

Subjects

Computational physics

Quantum information and quantum mechanics

Dates

Issue 10 (14 March 2003)

Received 28 November 2002

Published 26 February 2003



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