Majorana braiding gates for topological superconductors in a one dimensional geometry

Abstract

We propose and analyze a physical system capable of performing topological quantum computation with Majorana zero modes (MZM) in a one-dimensional topological superconductor (1DTS). One of the leading methods to realize quantum gates in 1DTS is to use T-junctions, which allows one to maneuver MZMs such as to achieve braiding. In this paper, we propose a scheme that is in a purely one-dimensional geometry and does not require T-junctions, instead replacing it with an auxiliary qubit. We show that this allows one to perform one and two logical qubit $Z$ rotations. We first design a topologically protected logical $Z$-gate based entirely on local interactions within the 1DTS. Using an auxiliary qubit coupled to the topological superconductors, we extend the $Z$-gate to single and multiqubit arbitrary rotations with partial topological protection. Finally, to perform universal quantum computing, we introduce a scheme for performing arbitrary unitary rotations, albeit without topological protection. We develop a formalism based on unitary braids which creates transitions between different topological phases of the 1DTS system. The unitary formalism can be simply converted to an equivalent adiabatic scheme, which we numerically simulate and show that high fidelity operations should be possible with reasonable parameters.

References in corpus (46)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Unpaired Majorana fermions in quantum wires
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Quantum Computing
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Helical liquids and Majorana bound states in quantum wires
• New directions in the pursuit of Majorana fermions in solid state systems
• QuTiP 2: A Python framework for the dynamics of open quantum systems
• QuTiP: An open-source Python framework for the dynamics of open quantum systems
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Search for Majorana fermions in superconductors
• Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
• Non-Abelian statistics and topological quantum information processing in 1D wire networks
• Majorana Zero Modes and Topological Quantum Computation
• Realizing Majorana zero modes in superconductor-semiconductor heterostructures
• A Theory of Fault-Tolerant Quantum Computation
• Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid
• Observation of the e/3 Fractionally Charged Laughlin Quasiparticles
• Introduction to topological superconductivity and Majorana fermions
• Quantum Error Correction for Beginners
• Topologically-Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State
• Roads towards fault-tolerant universal quantum computation
• $2n$ Quasihole States Realize $2^{n-1}$-Dimensional Spinor Braiding Statistics in Paired Quantum Hall States
• Superconducting Quantum Computing: A Review
• Measurement of filling factor 5/2 quasiparticle interference: observation of charge e/4 and e/2 period oscillations
• A Short Introduction to Topological Quantum Computation
• Controlling non-Abelian statistics of Majorana fermions on Majorana dimer lattices
• Flux-induced Majorana modes in full-shell nanowires
• Topological superconductivity in full shell proximitized nanowires
• Flux-induced topological superconductivity in full-shell nanowires
• Efficient fault-tolerant quantum computing
• Phase signature of topological transition in Josephson Junctions
• Magnetic field-tuned Aharonov-Bohm oscillations and evidence for non-Abelian anyons at v=5/2
• Majorana fermion exchange in quasi-one-dimensional networks
• Conductance of a proximitized nanowire in the Coulomb blockade regime
• Majorana Zero Modes in Graphene
• Synthetic Topological Degeneracy by Anyon Condensation
• Non-Abelian Parton Fractional Quantum Hall Effect in Multilayer Graphene
• Sagnac interferometry with coherent vortex superposition states in exciton-polariton condensates
• Majorana quasiparticles in semiconducting carbon nanotubes
• Photoluminescence of a microcavity quantum dot system in the quantum strong-coupling regime
• Emulating Majorana fermions and their braiding by Ising spin chains
• Topological superconductivity in carbon nanotubes with a small magnetic flux
• Skyrmion quantum spin Hall effect
• Quantum Hall effect with small numbers of vortices in Bose-Einstein condensates

Cited by in corpus (7)

• Transport probe of nonadiabatic transition caused by Majorana moving
• Hong-Ou-Mandel Interference in a temporal-average-inversion-symmetric chain
• Symmetry-protected Landau-Zener-Stückelberg-Majorana interference and non-adiabatic topological transport of edge states
• Transport and fusion of Majorana zero modes in the presence of nonadiabatic transitions
• Investigating the Exchange of Ising Chains on a Digital Quantum Computer
• Non-Abelian interference of topological edge states
• Probing nontrivial fusion of Majorana zero modes via near-adiabatic coupling