Number conserving analysis of measurement-based braiding with Majorana zero modes

Abstract

Majorana-based quantum computation seeks to encode information non-locally in pairs of Majorana zero modes, thereby isolating qubit states from a local noisy environment. In addition to long coherence times, the attractiveness of Majorana-based quantum computing relies on achieving topologically protected Clifford gates from braiding operations. Recent works have conjectured that mean-field BCS calculations may fail to account for non-universal corrections to the Majorana braiding operations. Such errors would be detrimental to Majorana-based topological quantum computing schemes. In this work, we develop a particle-number conserving approach for measurement-based topological quantum computing and investigate the effect of quantum phase fluctuations. We demonstrate that braiding transformations are indeed topologically protected in charge-protected Majorana-based quantum computing schemes.

arXiv comment8 pages+appendices, 1 figure, v3

References in corpus (54)

• 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
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Helical liquids and Majorana bound states in quantum wires
• New directions in the pursuit of Majorana fermions in solid state systems
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Non-Abelian statistics and topological quantum information processing in 1D wire networks
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Majorana Zero Modes and Topological Quantum Computation
• Exponential Protection of Zero Modes in Majorana Islands
• Majorana bound states in a coupled quantum-dot hybrid-nanowire system
• Realizing Majorana zero modes in superconductor-semiconductor heterostructures
• Superconductor-Nanowire Devices from Tunneling to the Multichannel Regime: Zero-Bias Oscillations and Magnetoconductance Crossover
• Anomalous modulation of a zero bias peak in a hybrid nanowire-superconductor device
• Scalable Designs for Quasiparticle-Poisoning-Protected Topological Quantum Computation with Majorana Zero Modes
• Quantized Majorana conductance
• Milestones toward Majorana-based quantum computing
• Scaling of Majorana Zero-Bias Conductance Peaks
• Majorana Fermions in Semiconductor Nanowires
• Electron Teleportation via Majorana Bound States in a Mesoscopic Superconductor
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Flux-controlled quantum computation with Majorana fermions
• Coulomb-assisted braiding of Majorana fermions in a Josephson junction array
• Measurement-Only Topological Quantum Computation
• Majorana box qubits
• Majorana edge states in interacting one-dimensional systems
• Majorana Zero Modes in 1D Quantum Wires Without Long-Ranged Superconducting Order
• Braiding without Braiding: Teleportation-Based Quantum Information Processing with Majorana Zero Modes
• Universal transport signatures of Majorana fermions in superconductor-Luttinger liquid junctions
• Top-transmon: hybrid superconducting qubit for parity-protected quantum computation
• Interplay of disorder and interaction in Majorana quantum wires
• Universal quantum computation on a semiconductor quantum wire network
• A number conserving theory for topologically protected degeneracy in one-dimensional fermions
• Conductance of a proximitized nanowire in the Coulomb blockade regime
• Measurement-Only Topological Quantum Computation via Anyonic Interferometry
• Many-body characterization of topological superconductivity: The Richardson-Gaudin-Kitaev chain
• Dephasing of Majorana-based qubits
• How quickly can anyons be braided? Or: How I learned to stop worrying about diabatic errors and love the anyon
• Measurement-only quantum computation with Majorana corner modes
• Dynamics of Majorana-based qubits operated with an array of tunable gates
• Fractional Josephson Effect in Number-Conserving Systems
• What is a particle-conserving Topological Superfluid?
• The Luther-Emery liquid: Spin gap and anomalous flux period
• Number-conserving interacting fermion models with exact topological superconducting ground states
• Measurement and control of a Coulomb-blockaded parafermion box
• Measurement-only topological quantum computation without forced measurements
• Coulomb Blockade in Fractional Topological Superconductors
• Towards a Particle-Number Conserving Theory of Majorana Zero Modes in p+ip Superfluids
• Analytic ground state wavefunctions of mean-field $p_x+i{p}_y$ superconductors with vortices and boundaries
• Effect of Particle Number Conservation on the Berry Phase Resulting from Transport of a Bound Quasiparticle around a Superfluid Vortex

Cited by in corpus (16)

• Hunting for Majoranas
• Parity-to-charge conversion in Majorana qubit readout
• Superconducting diode effect in quasi-one-dimensional systems
• Pairing Obstructions in Topological Superconductors
• Protocol Discovery for the Quantum Control of Majoranas by Differentiable Programming and Natural Evolution Strategies
• Rigorous results on topological superconductivity with particle number conservation
• Parafermions in a multilegged geometry: Towards a scalable parafermionic network
• Topological symplectic Kondo effect
• Two-fluid coexistence and phase separation in a one dimensional model with pair hopping and density interactions
• Signatures of topological ground state degeneracy in Majorana islands
• Long distance coherence of Majorana wires
• Readout of Majorana bound states via Landau-Zener transition
• Topological Kondo effect with spinful Majorana fermions
• Topology of superconductors beyond mean-field theory
• Quantum Restored Symmetry Protected Topological Phases
• Majorana edge modes in isolated wires