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.

Figure 1

(a) A semiconductor nanowire coupled by proximity with an $s$-wave superconductor, in the presence of an in-plane magnetic field $B_x$. (b) The energy dispersion for the semiconductor with spin-orbit coupling in a magnetic field, which opens the gap in the spectrum. When the chemical potential $\mu$ is in this gap, the nanowire coupled with an $s$-wave superconductor is driven into the topological phase. (c) A schematic of the proposed device used to entangle topological and conventional qubits (e.g., a Majorana wire qubit and semiconductor double-dot qubit). A flux qubit consisting of three Josephson junctions (the black strips labeled $J_1$, $J_2$, and $J_3$) supports clockwise or counterclockwise supercurrent. When $E_{J_1}=E_{J_3}$, there is interference between quantum phase slips across junctions 1 and 3. These phase slips correspond to Josephson vortex tunneling encircling the superconducting islands as shown by the dashed (red) line. Via the Aharonov-Casher effect, quantum interference of vortices around the islands produces an energy splitting for the flux qubit (at its degeneracy point) that strongly depends on the state of the topological and conventional semiconductor qubits. The topological and nontopological segments of the nanowires are represented by red (dark grey) and light grey, respectively. The latter can be achieved by driving the wire into the insulating or trivial superconducting phases.

Figure 2

A proposed setup for coherent quantum information transfer between a topological and a conventional semiconductor qubit using joint parity measurements. At the degeneracy point $\Phi =h/4e$, the splitting energy of the flux qubit depends on the total charge enclosed in the region marked by the dashed (red) line. This device allows joint parity measurements of topological-conventional, topological-topological, and conventional-conventional qubit pairs, which can be used to coherently transfer information between all the different types of qubits.