Manipulation of Majorana Kramers Qubit and its Tolerance in Time-Reversal-Invariant Topological Superconductor

Abstract

We investigate non-Abelian statistics of Majorana Kramers pairs (MKPs) in a network system of one-dimensional time-reversal invariant topological superconductors by using numerical simulations of braiding dynamics, and examine the tolerance against various perturbations which may cause decoherence of MKPs. We, first, consider effects of a magnetic field which breaks time-reversal symmetry. In contrast to a naive expectation, the non-Abelian braiding of MKPs is robust against applied magnetic fields provided that the initial and final states of a braiding process are invariant under the combination of a time reversal and a mirror reflection, even when intermediate states break the combined symmetry. Secondly, we investigate the stability of non-Abelian braidings in the case with gate-induced inhomogeneous potentials at junctions between superconducting nanowires, which generally generate a non-Majorana nearly zero-energy Andreeev bound state at the junctions. It is found that the non-Majorana nearly zero-energy states interfere with MKPs, resulting in the failure of non-Abelian braidings, when the length scale of the inhomogeneous potentials is comparable to the coherence length of the superconductors.

11pages, 9 figures

References in corpus (25)

• Non-Abelian Anyons and Topological Quantum Computation
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Classification of topological insulators and superconductors in three spatial dimensions
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Majorana bound states in a coupled quantum-dot hybrid-nanowire system
• Introduction to topological superconductivity and Majorana fermions
• Anomalous modulation of a zero bias peak in a hybrid nanowire-superconductor device
• Non-Abelian Topological Order in S-Wave Superfluids of Ultracold Fermionic Atoms
• Topological Phases of Noncentrosymmetric Superconductors: Edge States, Majorana Fermions, and the Non-Abelian Statistics
• Topology of crystalline insulators and superconductors
• Scaling of Majorana Zero-Bias Conductance Peaks
• Majorana qubit decoherence by quasiparticle poisoning
• Non-Abelian Topological Orders and Majorana Fermions in Spin-Singlet Superconductors
• Spin resonance in the d-wave superconductor CeCoIn5
• Topological Order and Non-Abelian Statistics in Noncentrosymmetric s-Wave Superconductors
• Symmetry Protected Topological Order and Spin Susceptibility in Superfluid 3He-B
• Decoherence of Majorana qubits by noisy gates
• Quasiparticle poisoning of Majorana qubits
• Majorana Braiding Dynamics on Nanowires
• Symmetry Protected Topological Superfluid ${}^3$He-B
• $AbInitio$ Simulation of Non-Abelian Braiding Statistics in Topological Superconductors
• Majorana phase-gate based on the geometric phase
• Unitary Symmetry-Protected Non-Abelian Statistics of Majorana Modes

Cited by in corpus (10)

• Theory of Majorana zero modes in unconventional superconductors
• Zero-frequency supercurrent susceptibility signatures of trivial and topological zero-energy states in nanowire junctions
• Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors
• Braiding Induced by Finite-Size Effect in One-Dimensional Topological Superconductors
• Unified model for non-Abelian braiding of Majorana and Dirac fermion zero modes
• Odd-frequency pairs and anomalous proximity effect in nematic and chiral states of superconducting topological insulators
• Noise-Tolerance of Majorana Teleportation in Mesoscopic Topological Superconductors
• Fusion Rules of Majorana-Kramer-Pairs in Time-Reversal-Invariant Topological Superconductors
• Exchangeless braiding of Majorana zero modes in weakly coupled Kitaev chains
• Engineering Majorana Kramers Pairs In Synthetic High Spin Chern Insulators