Network coding for distributed quantum computation over cluster and butterfly networks

Abstract

To apply network coding for quantum computation, we study the distributed implementation of unitary operations over all separated input and output nodes of quantum networks. We consider a setting of networks where quantum communication between nodes is restricted to sending just a qubit, but classical communication is unrestricted. We analyze which N-qubit unitary operations are implementable over cluster networks by investigating transformations of a given cluster network into quantum circuits. We show that any two-qubit unitary operation is implementable over the butterfly network and the grail network, which are fundamental primitive networks for classical network coding. We also analyze probabilistic implementations of unitary operations over cluster networks.

19pages, 13 figures

References in corpus (7)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Matchgates and classical simulation of quantum circuits
• Prior entanglement between senders enables perfect quantum network coding with modification
• Constructing Quantum Network Coding Schemes from Classical Nonlinear Protocols
• All unitaries having operator Schmidt rank 2 are controlled unitaries
• Quantum computation over the butterfly network
• Two-party LOCC convertibility of quadpartite states and Kraus-Cirac number of two-qubit unitaries

Cited by in corpus (6)

• Quantum network routing and local complementation
• Multicore Quantum Computing
• Modeling of Measurement-based Quantum Network Coding on IBM Q Experience Devices
• Graph-associated entanglement cost of a multipartite state in exact and finite-block-length approximate constructions
• Asymmetric quantum multicast network coding: asymmetric optimal cloning over quantum networks
• Multicast quantum network coding as optimal symmetric universal cloning over a quantum network