Measurement-Only Topological Quantum Computation via Tunable Interactions

Abstract

I examine, in general, how tunable interactions may be used to perform anyonic teleportation and generate braiding transformations for non-Abelian anyons. I explain how these methods are encompassed by the "measurement-only" approach to topological quantum computation. The physically most relevant example of Ising anyons or Majorana zero-modes is considered in detail, particularly in the context of Majorana nanowires.

10 pages, 8 figures; v2: correction made to discussion regarding allowed pairwise projections for generating braiding transformations, minor clarifications added; v3: minor corrections and clarifications

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• Measurement-Only Topological Quantum Computation
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Cited by in corpus (47)

• Realizing Majorana zero modes in superconductor-semiconductor heterostructures
• Scalable Designs for Quasiparticle-Poisoning-Protected Topological Quantum Computation with Majorana Zero Modes
• Symmetry Fractionalization, Defects, and Gauging of Topological Phases
• Milestones toward Majorana-based quantum computing
• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
• A Short Introduction to Topological Quantum Computation
• Theory of defects in Abelian topological states
• Classification of Topological Defects in Abelian Topological States
• Theory of Twist Liquids: Gauging an Anyonic Symmetry
• Majorana nanowires for topological quantum computation
• Stability of zero modes in parafermion chains
• Quantifying wave-function overlaps in inhomogeneous Majorana nanowires
• Superconducting analogue of the parafermion fractional quantum Hall states
• Majorana wavefunction oscillations, fermion parity switches, and disorder in Kitaev chains
• 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
• Distinguishing Majorana bound states from localized Andreev bound states by interferometry
• Criticality in Translation-Invariant Parafermion Chains
• Braiding Majorana zero modes using quantum dots
• Coupling and braiding Majorana bound states in networks defined in proximitized two-dimensional electron gases
• Time scales for Majorana manipulation using Coulomb blockade in gate-controlled superconducting nanowires
• On Defects Between Gapped Boundaries in Two-Dimensional Topological Phases of Matter
• Universal Gates via Fusion and Measurement Operations on SU$(2{)}_4$ Anyons
• Designer non-Abelian anyon platforms: from Majorana to Fibonacci
• Demonstrating non-Abelian statistics of Majorana fermions using twist defects
• 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
• Effects of disorder on Coulomb-assisted braiding of Majorana zero modes
• Charge $2e/3$ superconductivity and topological degeneracies without localized zero modes in bilayer fractional quantum Hall states
• Tunable Splitting of the Ground-State Degeneracy in 1D Parafermionic Wires
• Majorana fermions at odd junctions in a wire network of ferromagnetic impurities
• Modular transformations through sequences of topological charge projections
• Parafermions in a Kagome lattice of qubits for topological quantum computation
• Topological $\pi$-junctions from crossed Andreev reflection in the Quantum Hall regime
• Adiabatic topological quantum computing
• Feasibility of measurement-based braiding in the quasi-Majorana regime of semiconductor-superconductor heterostructures
• Instantaneous braids and Dehn twists in topologically ordered states
• Measurement-only topological quantum computation without forced measurements
• Optimizing Clifford gate generation for measurement-only topological quantum computation with Majorana zero modes
• Universal quantum computing with parafermions assisted by a half fluxon
• Correlated parity measurements as a probe of non-abelian statistics in 1D superconducting wires
• Electron-Tunneling-Assisted Non-Abelian Braiding of Rotating Majorana Bound States
• Holonomic implementation of CNOT gate on topological Majorana qubits
• Preparation of topological modes by Lyapunov control
• Topologically protected heat pumping from braiding Majorana zero modes
• Deterministic topological quantum gates for Majorana qubits without ancillary modes
• Shuttling Majorana zero modes in disordered and noisy topological superconductors