Tight-Binding Energy-Phase Calculation for Topological Josephson Junction Nanowire Architecture

Abstract

The current state of Quantum computing (QC) is extremely optimistic, and we are at a point where researchers have produced highly sophisticated quantum algorithms to address far reaching problems. However, it is equally apparent that the noisy quantum environment is a larger threat than many may realize. The noisy intermediate scale quantum (NISQ) era can be viewed as an inflection point for the enterprise of QC where decoherence could stagnate progress if left unaddressed. One tactic for handling decoherence is to address the problem from a hardware level by implementing topological materials into the design. In this work, we model several Josephson junctions that are modified by the presence of topological superconducting nanowires in between the host superconductors. Our primary result is a numerical calculation of the energy-phase relationship for topological nanowire junctions which are a key parameter of interest for the dynamics of qubit circuits. In addition to this, we report on the qualitative physical behavior of the bound states as a function of superconducting phase. These results can be used to further develop and inform the construction of more complicated systems, and it is hopeful that these types of designs could manifest as a fault tolerant qubit.

14 pages, 13 figures

References in corpus (36)

• Topological Insulators with Inversion Symmetry
• Circuit Quantum Electrodynamics
• A Quantum Engineer's Guide to Superconducting Qubits
• Superconducting Qubits: Current State of Play
• Kwant: a software package for quantum transport
• Strong quantum computational advantage using a superconducting quantum processor
• Scalable Designs for Quasiparticle-Poisoning-Protected Topological Quantum Computation with Majorana Zero Modes
• New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds
• From Andreev to Majorana bound states in hybrid superconductor-semiconductor nanowires
• Transmon qubit with relaxation time exceeding 0.5 milliseconds
• Topological Quantum Computation Based on Chiral Majorana Fermions
• Josephson effect in ballistic graphene
• Single-qubit quantum memory exceeding $10$-minute coherence time
• Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers
• A Short Introduction to Topological Quantum Computation
• Solving the sampling problem of the Sycamore quantum circuits
• Interface Between Topological and Superconducting Qubits
• Dephasing of Majorana-based qubits
• Decoherence of Majorana qubits by noisy gates
• A comprehensive review on topological superconducting materials and interfaces
• Quasiparticle poisoning of Majorana qubits
• Efficient tensor network simulation of IBM's largest quantum processors
• Speed limit to the Abrikosov lattice in mesoscopic superconductors
• Majorana Superconducting Qubit
• Dephasing and leakage dynamics of noisy Majorana-based qubits: Topological versus Andreev
• Dirac Green's function approach to graphene-superconductor junctions with well defined edges
• Topological Quantum Computing Using Nanowire Devices
• Parity-to-charge conversion for readout of topological Majorana qubits
• Building topological quantum circuits: Majorana nanowire junctions
• Vortex Majorana braiding in a finite time
• Four-Majorana qubit with charge readout: dynamics and decoherence
• Tunable interfaces for realizing universal quantum computation with topological qubits
• Quasiparticle gaps in multiprobe Majorana nanowires
• Complete description of fault-tolerant quantum gate operations for topological Majorana qubit systems
• Green's functions in quantum mechanics courses
• Perturbing finite temperature multicomponent DFT 1D Kohn-Sham systems: Peierls Gap & Kohn Anomaly