Quantum channels over graph states using generalized measurement-based quantum computation framework

Abstract

Measurement-based quantum computation (MBQC) is an alternative way of quantum information processing that describes the unitary evolution of a quantum state using the cluster state and well-defined sequential measurements. We give a closed form expression for the unitary evolution that a state goes through in terms of the network parameters and measurement outcomes on various qubits of the network. We extend the framework of MBQC to describe quantum channels. Using the new framework, we define a valid quantum unital channel between any two nodes of a graph consisting of nodes connected by edges. We describe the channel in terms of the network parameters and initial state. Our generalization consists of modifying the unitary operation, measurement operators, initial arbitrary state of the qubits at all the nodes of the network. We also study the inverse problem of devising an appropriate approximate unitary in the generalized MBQC to create any given quantum channel