How quickly can anyons be braided? Or: How I learned to stop worrying about diabatic errors and love the anyon

Abstract

Topological phases of matter are a potential platform for the storage and processing of quantum information with intrinsic error rates that decrease exponentially with inverse temperature and with the length scales of the system, such as the distance between quasiparticles. However, it is less well-understood how error rates depend on the speed with which non-Abelian quasiparticles are braided. In general, diabatic corrections to the holonomy or Berry's matrix vanish at least inversely with the length of time for the braid, with faster decay occurring as the time-dependence is made smoother. We show that such corrections will not affect quantum information encoded in topological degrees of freedom, unless they involve the creation of topologically nontrivial quasiparticles. Moreover, we show how measurements that detect unintentionally created quasiparticles can be used to control this source of error.

33 pages, 18 figures, version 3: extended results to general anyon braiding

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Cited by in corpus (63)

• Scalable Designs for Quasiparticle-Poisoning-Protected Topological Quantum Computation with Majorana Zero Modes
• Roadmap to Majorana surface codes
• Search for non-Abelian Majorana braiding statistics in superconductors
• Majorana nanowires for topological quantum computation
• An experimentally accessible quality factor for Majorana wires
• Dephasing of Majorana-based qubits
• Combining Topological Hardware and Topological Software: Color Code Quantum Computing with Topological Superconductor Networks
• Topologically protected braiding in a single wire using Floquet Majorana modes
• Poor man's topological quantum gate based on the Su-Schrieffer-Heeger model
• Majorana-based fermionic quantum computation
• Dynamics of Majorana-based qubits operated with an array of tunable gates
• Braiding errors in interacting Majorana quantum wires
• Fusion protocol for Majorana modes in coupled quantum dots
• Signatures of Majorana protection in a three-site Kitaev chain
• Photon assisted braiding of Majorana fermions in a cavity
• Enhancing the excitation gap of a quantum-dot-based Kitaev chain
• Topological Quantum Computing Using Nanowire Devices
• Parity-to-charge conversion for readout of topological Majorana qubits
• Probability and (Braiding) Statistics in Majorana nanowires
• Braiding-based quantum control of a Majorana qubit built from quantum dots
• Parafermion braiding in fractional quantum Hall edge states with finite chemical potential
• Protocol Discovery for the Quantum Control of Majoranas by Differentiable Programming and Natural Evolution Strategies
• Modeling noise and error correction for Majorana-based quantum computing
• Optimal diabatic dynamics of Majorana-based quantum gates
• Error generation and propagation in Majorana-based topological qubits
• Interaction induced hybridization of Majorana zero-modes in a coupled quantum-dot hybrid-nanowire system
• $AbInitio$ Simulation of Non-Abelian Braiding Statistics in Topological Superconductors
• Emulating Majorana fermions and their braiding by Ising spin chains
• Number conserving analysis of measurement-based braiding with Majorana zero modes
• Gatemon qubit based on a thin InAs-Al hybrid nanowire
• Coherent generation of photonic fractional quantum Hall states in a cavity and the search for anyonic quasiparticles
• Many-body Majorana braiding without an exponential Hilbert space
• Feasibility of measurement-based braiding in the quasi-Majorana regime of semiconductor-superconductor heterostructures
• Diabatic errors in Majorana braiding with bosonic bath
• Optical vortex manipulation for topological quantum computation
• Majorana quasiparticles in atomic spin chains on superconductors
• Effects of decoherence on diabatic errors in Majorana braiding
• Non-Abelian Berry phase for open quantum systems: Topological protection vs geometric dephasing
• Optimal noise-canceling shortcuts to adiabaticity: application to noisy Majorana-based gates
• Demonstrating Majorana non-Abelian properties using fast adiabatic charge-transfer
• Non-Abelian Geometric Dephasing
• Optimizing the transport of Majorana zero modes in one-dimensional topological superconductors
• Measurement-only topological quantum computation without forced measurements
• Fermion-Parity-Based Computation and its Majorana-Zero-Mode Implementation
• Non-Abelian quasiholes in lattice Moore-Read states and parent Hamiltonians
• Universal quantum computing with parafermions assisted by a half fluxon
• Characterizing Dynamic Majorana Hybridization for Universal Quantum Computing
• Measuring Topological Order
• Modeling free anyons at the bosonic and fermionic ends
• Holonomic implementation of CNOT gate on topological Majorana qubits
• Readout of Majorana bound states via Landau-Zener transition
• Squeezing anyons for braiding on small lattices
• Transport probe of nonadiabatic transition caused by Majorana moving
• A new twist on the Majorana surface code: Bosonic and fermionic defects for fault-tolerant quantum computation
• Multi-particle interferometry in the time-energy domain with localized topological quasiparticles
• Braiding Majoranas in a linear quantum dot-superconductor array: Mitigating the errors from Coulomb repulsion and residual tunneling
• Bath-induced decoherence in finite-size Majorana wires at non-zero temperature
• Transport of Majorana Bound State in the presence of telegraph noise
• Universal quantum control over Majorana zero modes
• Exchangeless braiding of Majorana zero modes in weakly coupled Kitaev chains
• Majorana braiding simulations with projective measurements
• Nonadiabatic braiding of Majorana modes
• Shuttling Majorana zero modes in disordered and noisy topological superconductors