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IEEE Transactions on Applied Superconductivity

Braiding Operations for a Topological Josephson Junction Array Using a Bipolar Current Pulse Generator Controlled by SFQ Logic Circuits

Hiroaki Myoren, Takuro Funazawa, Kitaru Oba, Yuki Shimizu, Masato Naruse

Published Mar 4, 2024• 1 citation
Publisher

Abstract

Majorana bound states can occur in a topological Josephson junction (JJ) array in the presence of a fractal vortex with 2$\pi$-phase winding. The braiding operation was theoretically demonstrated using current pulses, compatible with the single flux quantum (SFQ) technology. Herein, we designed an SFQ logic circuit for braiding operations of a topological JJ array using single flux quanta. Braiding operations could be realized using a bipolar current pulse generator controlled by an SFQ logic circuit.

DOI
10.1109/tasc.2024.3372865

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Majorana bound states can occur in a topological Josephson junction (JJ) array in the presence of a fractal vortex with 2π\piπ-phase winding. The braiding operation was theoretically demonstrated using current pulses, compatible with the single flux quantum (SFQ) technology. Herein, we designed an SFQ logic circuit for braiding operations of a topological JJ array using single flux quanta. Braiding operations could be realized using a bipolar current pulse generator controlled by an SFQ logic circuit.
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.
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.
We report low-power single-flux-quantum (SFQ) circuits fabricated with a lowered critical current density process and low-voltage design. We selected 250 A/cm2^{2}2to obtain 2–10 μA Josephson junctions (JJs) easily using conventional facilities. Our numerical simulation shows that the expected operating frequency is 10 GHz and that we can reduce the bias voltage to 0.1–0.5 mV; power consumption can be reduced to around 1 nW per JJ. We newly developed a fabrication process featuring four planarized Nb layers and a Pd resistor layer. We obtained the correct operation of several basic SFQ circuit elements designed with the lowered critical currents to 1/2 of the conventional circuits at 4.2 K. We also evaluated the Josephson junction critical currents, specific capacitance, resistance, and inductance at 3 K and 300 mK. We observed an increase of 7% in the critical currents at 300 mK, while the other parameters were unchanged. We demonstrated a 0.5-mV Josephson transmission line where we lowered the critical currents to 1/10. We expect such low-power SFQ circuits to operate at 20 mK, providing classical, general-purpose digital processing near quantum bits.
Field-programmable gate arrays (FPGAs) provide a significantly cheaper solution for various applications in traditional semiconductor electronics. Single flux quantum (SFQ) technologies are developing rapidly and the availability of SFQ-specific FPGA will be very useful. Towards developing such an SFQ-specific FPGA, new designs of FPGA subcircuits for both synchronous and asynchronous operation of SFQ circuits are presented in this paper. Magnetic Josephson junctions (MJJs) are used as bias limiting junctions in energy-efficient rapid SFQ (ERSFQ) biasing to implement programmable switches in various subcircuits of the proposed FPGA fabric. Designs of all FPGA subcircuits are developed and are verified through circuit simulation. Verilog hardware description language (HDL) models are also developed for all FPGA circuit blocks to facilitate large-scale FPGA simulations for the implementation of the desired circuit on the proposed FPGA fabric. Designs of a few subcircuits with switches based on nondestructive readout cell are also given in the current paper for better comparison with MJJ switch based counterparts. Programming of MJJ-based switches is based on the ability to control the critical current of MJJs externally. Recent implementations of SFQ decoder is proposed for accessing individual MJJs through the current lines in a crossbar structure. Estimations for the area and power consumption are much better in comparison to previous attempts at designing an SFQ specific FPGA.
We designed several single flux quantum (SFQ) flip-flops and logic gates composed of Josephson junctions (JJs) and π-shifted JJs (π-JJs) to quantitatively evaluate effectiveness of introduction of π-JJs into the SFQ logic circuit. One-output flip-flops and logic gates were designed on the basis of the circuit design methodology we built for the SFQ circuit containing π-JJs. The designed flip-flops and logic gates have wide operating margins, the dc-bias margins of larger than ±30%, and device parameter margins of ±18%, though the static power consumption are reduced compared to conventional ones composed of JJs. We found that the difference in the critical current density between JJs and π-JJs does not affect the operating margins of the SFQ flip-flop composed of JJs and π-JJs. We devised a circuit structure of the delay flip-flop with complementary outputs composed of JJs and π-JJs (π-DFFC). The analog circuit simulation shows the dc-bias margin of the π-DFFC is larger than ±33%. These results indicate that the large-scale SFQ logic circuit system can be implemented using the flip-flops and logic gates containing π-JJs.
A new current-injection Josephson latch employing a single-flux quantum is proposed. It has a master-slave circuit configuration and operates under ac power supply. In the circuit, data are stored as a circulating current in a superconducting loop consisting of a single junction and inductances. A two-junction interferometer gate directly coupled to the loop reads out the stored data. Dual-rail signals are generated from the read-out data by Josephson junctions and resister-coupled Josephson logic gates. The isolation between a master circuit and a slave circuit is realized using high-impedance states in the Josephson junctions. The circuit design and computer-simulation results on the circuit operation are described in this paper.