Topologically protected braiding in a single wire using Floquet Majorana modes

Abstract

Majorana zero modes are a promising platform for topologically protected quantum information processing. Their non-Abelian nature, which is key for performing quantum gates, is most prominently exhibited through braiding. While originally formulated for two-dimensional (2d) systems, it has been shown that braiding can also be realized using one-dimensional (1d) wires by forming an essentially two-dimensional network. Here, we show that in driven systems far from equilibrium, one can do away with the second spatial dimension altogether by instead using quasienergy as the second dimension. To realize this, we use a Floquet topological superconductor which can exhibit Majorana modes at two special eigenvalues of the evolution operator, 0 and pi, and thus can realize four Majorana modes in a single, driven quantum wire. We describe and numerically evaluate a protocol that realizes a topologically protected exchange of two Majorana zero modes in a single wire by adiabatically modulating the Floquet drive and using the pi modes as auxiliary degrees of freedom.

arXiv comment6+4 pages, 4+5 figures; updated references

References in corpus (74)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• 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
• Helical liquids and Majorana bound states in quantum wires
• New directions in the pursuit of Majorana fermions in solid state systems
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• A generic new platform for topological quantum computation using semiconductor heterostructures
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Search for Majorana fermions in superconductors
• Non-Abelian statistics and topological quantum information processing in 1D wire networks
• Topological characterization of periodically-driven quantum systems
• Majorana Zero Modes and Topological Quantum Computation
• Transport properties of non-equilibrium systems under the application of light: Photo-induced quantum Hall insulators without Landau levels
• Realizing Majorana zero modes in superconductor-semiconductor heterostructures
• Floquet Time Crystals
• On the phase structure of driven quantum systems
• Quantum Time Crystals
• Majorana Fermions in Equilibrium and Driven Cold Atom Quantum Wires
• Scalable Designs for Quasiparticle-Poisoning-Protected Topological Quantum Computation with Majorana Zero Modes
• Topological Phases of Noncentrosymmetric Superconductors: Edge States, Majorana Fermions, and the Non-Abelian Statistics
• Equilibrium states of generic quantum systems subject to periodic driving
• Long-time behavior of periodically driven isolated interacting lattice systems
• Many-body localization in periodically driven systems
• Milestones toward Majorana-based quantum computing
• Floquet-Magnus Theory and Generic Transient Dynamics in Periodically Driven Many-Body Quantum Systems
• Exponentially slow heating in periodically driven many-body systems
• Fate of many-body localization under periodic driving
• Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems
• Classical Time Crystals
• Effective Hamiltonians, prethermalization and slow energy absorption in periodically driven many-body systems
• Flux-controlled quantum computation with Majorana fermions
• Coulomb-assisted braiding of Majorana fermions in a Josephson junction array
• Periodically driven ergodic and many-body localized quantum systems
• Measurement-Only Topological Quantum Computation
• Absolute Stability and Spatiotemporal Long-Range Order in Floquet systems
• A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems
• Pre-thermal phases of matter protected by time-translation symmetry
• Majorana box qubits
• How to realize a robust practical Majorana chain in a quantum dot-superconductor linear array
• Classification of Interacting Topological Floquet Phases in One Dimension
• Classification of topological phases in periodically driven interacting systems
• Phase Structure of 1d Interacting Floquet Systems I: Abelian SPTs
• Griffiths effects and quantum critical points in dirty superconductors without spin-rotation invariance: One-dimensional examples
• A theory of many-body localization in periodically driven systems
• Geometric phases and quantum entanglement as building blocks for nonabelian quasiparticle statistics
• Efficient numerical computation of the Pfaffian for dense and banded skew-symmetric matrices
• Prethermal Floquet Steady States and Instabilities in the Periodically Driven, Weakly Interacting Bose-Hubbard Model
• Adiabatic Perturbation Theory and Geometry of Periodically-Driven Systems
• Adaptive tuning of Majorana fermions in a quantum dot chain
• Abelian Floquet symmetry-protected topological phases in one dimension
• Heating and many-body resonances in a periodically driven two-band system
• Simulation of non-Abelian braiding in Majorana time crystals
• Andreev Molecules in Semiconductor Nanowire Double Quantum Dots
• Stroboscopic prethermalization in weakly interacting periodically driven systems
• Non-adiabatic processes in Majorana qubit systems
• Complexity of quantum impurity problems
• How quickly can anyons be braided? Or: How I learned to stop worrying about diabatic errors and love the anyon
• Majorana braiding with thermal noise
• A geometric protocol for a robust Majorana magic gate
• Shortcuts to nonabelian braiding
• Quantum computation via Floquet topological edge modes
• Boosting Majorana zero modes
• Majorana Braiding Dynamics on Nanowires
• Optimal Control of Majorana Zero Modes
• Dynamics of Majorana-based qubits operated with an array of tunable gates
• Time-quasiperiodic topological superconductors with Majorana Multiplexing
• Braiding errors in interacting Majorana quantum wires
• Time scales for Majorana manipulation using Coulomb blockade in gate-controlled superconducting nanowires
• Monte Carlo studies of the properties of the Majorana quantum error correction code: is self-correction possible during braiding?
• Majorana fermion exchange in strictly one dimensional structures
• Optimal diabatic dynamics of Majorana-based quantum gates

Cited by in corpus (43)

• Floquet Higher-Order Topological Insulators with Anomalous Dynamical Polarization
• Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter
• Steady Floquet-Andreev States Probed by Tunnelling Spectroscopy
• Non-Hermitian Floquet topological superconductors with multiple Majorana edge modes
• Half-integer quantized topological response in quasiperiodically driven quantum systems
• Topological characterization and stability of Floquet Majorana modes in Rashba nanowire
• Dissipative Floquet Majorana modes in proximity-induced topological superconductors
• The quantized Hall conductance of a single atomic wire: A proposal based on synthetic dimensions
• Observing and braiding topological Majorana modes on programmable quantum simulators
• Bose-Hubbard physics in synthetic dimensions from interaction Trotterization
• Floquet Majorana bound states in voltage-biased Planar Josephson Junctions
• Topological frequency conversion in Weyl semimetals
• Engineering anomalous Floquet Majorana modes and their time evolution in helical Shiba chain
• Cross-dimensional universality classes in static and periodically driven Kitaev models
• Optimizing the transport of Majorana zero modes in one-dimensional topological superconductors
• Time-crystalline Topological Superconductors
• Stability of Floquet Majorana box qubits
• Josephson-Current Signatures of Unpaired Floquet Majorana Bound States
• Quantized Floquet topology with temporal noise
• Floquet topological insulators: from band structure engineering to novel non-equilibrium quantum phenomena
• Dynamics and Phases of Nonunitary Floquet Transverse-Field Ising Model
• Unitary Subharmonic Response and Floquet Majorana Modes
• Intrinsic dissipative Floquet superconductors beyond mean-field theory
• Self-similar phase diagram of the Fibonacci-driven quantum Ising model
• Microwave-induced conductance replicas in hybrid Josephson junctions without Floquet-Andreev states
• Robust spectral $\pi$ pairing in the random-field Floquet quantum Ising model
• Topological $\pi$ modes and beyond
• Universal Landau-Zener regimes in dynamical topological phase transitions
• Single and multi-frequency driving protocols in a Rashba nanowire proximitized to an s-wave superconductor
• Disorder induced topological phase transition in a driven Majorana chain
• Topological excitations at time vortices in periodically driven systems
• Relation between scattering matrix topological invariants and conductance in Floquet Majorana systems
• Transport of Majorana Bound State in the presence of telegraph noise
• Dynamical Chiral Symmetry and Symmetry-Class Conversion in Floquet Topological Insulators
• Non-Abelian Anyons in Periodically Driven Abelian Spin Liquids
• Rotating Majorana Zero Modes in a disk geometry
• Universal quantum control over Majorana zero modes
• Properties of dissipative Floquet Majorana modes using a quantum dot
• Generalized Majorana edge modes in a number-conserving periodically driven $p$-wave superconductor
• Shuttling Majorana zero modes in disordered and noisy topological superconductors
• Multiple tunable real-space degeneracies in graphene irradiated by twisted light
• Quantum-vacuum-protected topological edge polaritons
• Green Function Invariants for Floquet Topological Superconductivity Induced by Proximity Effects