Braiding errors in interacting Majorana quantum wires

Abstract

Avenues of Majorana bound states (MBSs) have become one of the primary directions towards a possible realization of topological quantum computation. For a Y-junction of Kitaev quantum wires, we numerically investigate the braiding of MBSs while considering the full quasi-particle background. The two central sources of braiding errors are found to be the fidelity loss due to the incomplete adiabaticity of the braiding operation as well as the hybridization of the MBS. The explicit extraction of the braiding phase in the low-energy Majorana sector from the full many-particle Hilbert space allows us to analyze the breakdown of the independent-particle picture of Majorana braiding. Furthermore, we find nearest-neighbor interactions to significantly affect the braiding performance to the better or worse, depending on the sign and magnitude of the coupling.

10 pages, 5 figures

References in corpus (20)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a 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
• Scalable Designs for Quasiparticle-Poisoning-Protected Topological Quantum Computation with Majorana Zero Modes
• Majorana box qubits
• Interaction Effects in Topological Superconducting Wires Supporting Majorana Fermions
• Majorana edge states in interacting one-dimensional systems
• High-resolution studies of the Majorana atomic chain platform
• Ballistic superconductivity in semiconductor nanowires
• Braiding without Braiding: Teleportation-Based Quantum Information Processing with Majorana Zero Modes
• Roadmap to Majorana surface codes
• Non-Abelian Statistics in a Quantum Antiferromagnet
• Shortcuts to nonabelian braiding
• Majorana Braiding Dynamics on Nanowires
• Optimal Control of Majorana Zero Modes

Cited by in corpus (32)

• From Andreev to Majorana bound states in hybrid superconductor-semiconductor nanowires
• Majorana nanowires for topological quantum computation
• Topologically protected braiding in a single wire using Floquet Majorana modes
• Poor man's topological quantum gate based on the Su-Schrieffer-Heeger model
• Dynamics of Majorana-based qubits operated with an array of tunable gates
• Majorana Braiding in Realistic Nanowire Y-Junctions and Tuning Forks
• Topological Quantum Computing Using Nanowire Devices
• Double-frequency Aharonov-Bohm effect and non-Abelian braiding properties of Jackiw-Rebbi zero-mode
• Braiding-based quantum control of a Majorana qubit built from quantum dots
• Degeneracy lifting of Majorana bound states due to electron-phonon interactions
• Parafermion braiding in fractional quantum Hall edge states with finite chemical potential
• $AbInitio$ Simulation of Non-Abelian Braiding Statistics in Topological Superconductors
• Majorana zero modes in Y-shape interacting Kitaev wires
• Many-body Majorana braiding without an exponential Hilbert space
• Majorana quasiparticles in atomic spin chains on superconductors
• Optimal noise-canceling shortcuts to adiabaticity: application to noisy Majorana-based gates
• Optimizing the transport of Majorana zero modes in one-dimensional topological superconductors
• Manipulation of Majorana Kramers Qubit and its Tolerance in Time-Reversal-Invariant Topological Superconductor
• Demonstrating Majorana non-Abelian properties using fast adiabatic charge-transfer
• Effect of impurities and disorder on the braiding dynamics of Majorana zero modes
• Majorana phase-gate based on the geometric phase
• Characterizing Dynamic Majorana Hybridization for Universal Quantum Computing
• Transport probe of nonadiabatic transition caused by Majorana moving
• Majorana Zero Modes in Nanowires with Combined Triangular and Hexagonal Geometry
• Bath-induced decoherence in finite-size Majorana wires at non-zero temperature
• Transport of Majorana Bound State in the presence of telegraph noise
• Altermagnet-Superconductor Heterostructure: a Scalable Platform for Braiding of Majorana Modes
• Transport and fusion of Majorana zero modes in the presence of nonadiabatic transitions
• Exchangeless braiding of Majorana zero modes in weakly coupled Kitaev chains
• Shuttling Majorana zero modes in disordered and noisy topological superconductors
• Sub-gap Fano resonances in a topological superconducting wire with on-site Coulomb interactions
• Dynamical simulation of the injection of vortices into a Majorana edge mode