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arXiv:1808.03309 · Physical review. B./Physical review. B

Braiding quantum circuit based on the 4 π Josephson effect

John Stenger, Michael Hatridge, Sergey Frolov, David Pekker

Published Jan 22, 2019• 29 citations
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Abstract

We propose a topological qubit in which braiding and readout are mediated by the $4\ensuremath{\pi}$ Majorana-Josephson effect. The braidonium device consists of three Majorana nanowires that come together to make a trijunction. In order to control the superconducting phase differences at the trijunction, the nanowires are enclosed in a ring made of a conventional superconductor. In order to perform initialization and readout, one of the nanowires is coupled to a fluxonium qubit through a topological Josephson junction. We analyze how flux-based control and readout protocols can be used to demonstrate braiding and qubit operation for realistic materials and circuit parameters.

DOI
10.1103/physrevb.99.035307

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We propose a topological qubit in which braiding and readout are mediated by the 4\ensuremathπ4\ensuremath{\pi}4\ensuremathπ Majorana-Josephson effect. The braidonium device consists of three Majorana nanowires that come together to make a trijunction. In order to control the superconducting phase differences at the trijunction, the nanowires are enclosed in a ring made of a conventional superconductor. In order to perform initialization and readout, one of the nanowires is coupled to a fluxonium qubit through a topological Josephson junction. We analyze how flux-based control and readout protocols can be used to demonstrate braiding and qubit operation for realistic materials and circuit parameters.
Majorana fermions hold promise for quantum computation, because their non-Abelian braiding statistics allows for topologically protected operations on quantum information. Topological qubits can be constructed from pairs of well-separated Majoranas in networks of nanowires. The coupling to a superconducting charge qubit in a transmission line resonator (transmon) permits braiding of Majoranas by external variation of magnetic fluxes. We show that readout operations can also be fully flux controlled, without requiring microscopic control over tunnel couplings. We identify the minimal circuit that can perform the initialization-braiding-measurement steps required to demonstrate non-Abelian statistics. We introduce the Random Access Majorana Memory (RAMM), a scalable circuit that can perform a joint parity measurement on Majoranas belonging to a selection of topological qubits. Such multiqubit measurements allow for the efficient creation of highly entangled states and simplify quantum error correction protocols by avoiding the need for ancilla qubits.
Topological-material-based Josephson junctions have the potential to be used to host Majorana zero modes and to construct topological qubits. For operating the topological qubits at an appropriate timescale to avoid decoherence and quasiparticle poisoning, one would eventually go to the time domain and embed the topological qubits into quantum electrodynamic circuits. Here, we constructed a topological-insulator-nanowire-based transmon qubit and demonstrated its strong coupling to a coplanar waveguide resonator. The flux-tunable spectrum and Rabi oscillations with a qubit lifetime T 1 of ∼ 0.5 μ s were observed. Such a hybrid platform, containing topological materials and quantum electrodynamic circuits, can further be used to study the physical properties such as Majorana zero modes in topological quantum circuits.
We propose a superconducting flux qubit in a dc SQUID structure, formed by a conventional insulator Josephson junction and a topological nanowire Josephson junction with Majorana bound states. The zero-energy Majorana bound states transport 4 π period Josephson currents in the nanowire junction. The interplay between this 4 π period Josephson effect and the convectional 2 π period Josephson effect in the insulator junction induces a double-well potential energy landscape in the SQUID. As a result, the two lowest-energy levels of the SQUID are isolated from the other levels. These two levels show counterpropagating supercurrents, thus can be used as a flux qubit. We reveal that this flux qubit has the merits of stability to external noises, tolerance to the deviation of system parameters, and scalability to large numbers. Furthermore, we demonstrate how to couple this flux qubit with the Majorana qubit by tuning the junction parameters, and how to use this coupling to manipulate the Majorana qubit.
Abstract Majorana bound states (MBSs) can occur in topological Josephson junction (JJ) arrays with the presence of a fractional vortex with 2π-phase winding. It has been theoretically shown that the braiding operation can be achieved by using current pulses, compatible with single flux quantum (SFQ) technology. Therefore, we designed an SFQ logic circuit for the braiding operations of the topological JJ array using single flux quanta in a conventional JJ array. Braiding operations could be realized by an SFQ logic circuit with double flux quantum driver. To obtain positive and negative current pulses using the SFQ logic circuit, we used SFQ logic circuits with ac biasing for simulation. Finally, we confirmed the CNOT operation using an array-type SFQ circuit by means of simulation and estimated the CNOT operation speed.
Proposal for a flux qubit in a dc SQUID with the 4π4π4π period Josephson effect
Constructing qubits which are suitable for quantum computation remains a notable challenge. Here, we propose a superconducting flux qubit in a dc SQUID structure, formed by a conventional insulator Josephson junction and a topological nanowire Josephson junction with Majorana bound states. The zero energy Majorana bound states transport 4π4π4π period Josephson currents in the nanowire junction. The interplay between this 4π4π4π period Josephson effect and the convectional 2π2π2π period Josephson effect in the insulator junction induces a double-well potential energy landscape in the SQUID. As a result, the two lowest energy levels of the SQUID are isolated from other levels. These two levels show contradicting circulating supercurrents, thus can be used as a flux qubit. We reveal that this flux qubit has the merits of stability to external noises, tolerance to the deviation of system parameters, and scalability to large numbers. Furthermore, we demonstrate how to couple this flux qubit with the Majorana qubit by tuning the junction parameters, and how to use this coupling to manipulate the Majorana qubit.