Topological Quantum Buses: Coherent Quantum Information Transfer between Topological and Conventional Qubits

We propose computing bus devices that enable quantum information to be coherently transferred between topological and conventional qubits. We describe a concrete realization of such a topological quantum bus acting between a topological qubit in a Majorana wire network and a conventional semiconductor double quantum dot qubit. Specifically, this device measures the joint (fermion) parity of these two different qubits by using the Aharonov-Casher effect in conjunction with an ancilliary superconducting flux qubit that facilitates the measurement. Such a parity measurement, together with the ability to apply Hadamard gates to the two qubits, allows one to produce states in which the topological and conventional qubits are maximally entangled and to teleport quantum states between the topological and conventional quantum systems.