Quantum computation over the butterfly network

Abstract

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.

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

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Cited by in corpus (7)

• Experimental Quantum Network Coding
• Entanglement-efficient bipartite-distributed quantum computing
• Photonic multipartite entanglement conversion using nonlocal operations
• Network coding for distributed quantum computation over cluster and butterfly networks
• Exploring the limitations of quantum networking through butterfly-based networks
• Multicast quantum network coding as optimal symmetric universal cloning over a quantum network
• Effect of Quantum correlation on Perfect K pair Quantum Network Coding