Quantum computation over the butterfly network

Akihito Soeda, Yoshiyuki Kinjo, Peter S. Turner, Mio Murao

Research output: Contribution to journalArticle (Academic Journal)peer-review

16 Citations (Scopus)


In order to investigate distributed quantum computation under restricted network resources, we introduce a quantum computation task over the butterfly network where both quantum and classical communications are limited. We consider deterministically performing a two-qubit global unitary operation on two unknown inputs given at different nodes, with outputs at two distinct nodes. By using a particular resource setting introduced by M. Hayashi [Phys. Rev. A \textbf{76}, 040301(R) (2007)], which is capable of performing a swap operation by adding two maximally entangled qubits (ebits) between the two input nodes, we show that unitary operations can be performed without adding any entanglement resource, if and only if the unitary operations are locally unitary equivalent to controlled unitary operations. Our protocol is optimal in the sense that the unitary operations cannot be implemented if we relax the specifications of any of the channels. We also construct protocols for performing controlled traceless unitary operations with a 1-ebit resource and for performing global Clifford operations with a 2-ebit resource.
Original languageEnglish
JournalPhysical Review A: Atomic, Molecular and Optical Physics
Publication statusPublished - 2011

Bibliographical note

12 pages, 12 figures, the second version has been significantly expanded, and author ordering changed and the third version is a minor revision of the previous version


  • quant-ph


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