Measurement-only quantum computation with Majorana corner modes

Abstract

Majorana modes, typically arising at the edges of one-dimensional topological superconductors, are considered to be a promising candidate for encoding nonlocal qubits in fault-tolerant quantum computation. Here we propose to exploit the two-dimensional geometry of Majorana corner modes in second-order topological superconductors to realize measurement-only quantum computation. In particular, a periodically modulated topological superconducting system may host eight Majorana corner modes, through which two logical qubits as well as one ancilla qubit can be constructed and topologically protected gate operations can be implemented by a series of Majorana parity measurements. The measurements are achieved via Mach-Zehnder type interference in the conductance of a semiconductor based topological superconductor. Our proposal represents a scenario in which single- and two-qubit gate operations can be carried out in a minimal setup that may provide a natural building block for Majorana-based qubit architectures.

arXiv comment21 pages (4 pages main text + 17 pages Supplemental Material), 5 figures. Comments are welcome

References in corpus (77)

• 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
• Helical liquids and Majorana bound states in quantum wires
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Quantized Electric Multipole Insulators
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Non-Abelian statistics and topological quantum information processing in 1D wire networks
• Higher-Order Topological Insulators
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Topolectrical circuit realization of topological corner modes
• Reflection symmetric second-order topological insulators and superconductors
• Observation of a phononic quadrupole topological insulator
• On the phase structure of driven quantum systems
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Higher-Order Topology in Bismuth
• Demonstration of a quantized microwave quadrupole insulator with topologically protected corner states
• Majorana Fermions in Equilibrium and Driven Cold Atom Quantum Wires
• Scalable Designs for Quasiparticle-Poisoning-Protected Topological Quantum Computation with Majorana Zero Modes
• Topological protection of photonic mid-gap cavity modes
• Schrieffer-Wolff transformation for quantum many-body systems
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Quantized Majorana conductance
• Second-order photonic topological insulator with corner states
• Scaling of Majorana Zero-Bias Conductance Peaks
• Second-order topological insulators and superconductors with an order-two crystalline symmetry
• Electron Teleportation via Majorana Bound States in a Mesoscopic Superconductor
• Coulomb-assisted braiding of Majorana fermions in a Josephson junction array
• Measurement-Only Topological Quantum Computation
• Majorana corner modes in a high-temperature platform
• Majorana box qubits
• Bulk--Boundary Correspondence for Chiral Symmetric Quantum Walks
• High-Temperature Majorana Corner States
• Universal Quantum Computation with the nu=5/2 Fractional Quantum Hall State
• A Short Introduction to Topological Quantum Computation
• Symmetries, Topological Phases and Bound States in the One-Dimensional Quantum Walk
• Majorana Kramers pairs in higher-order topological insulators
• Classification of Two Dimensional Topological Crystalline Superconductors and Majorana Bound States at Disclinations
• An anomalous higher-order topological insulator
• Topological Quadrupolar Semimetals
• Tunable Majorana corner states in a two-dimensional second-order topological superconductor induced by magnetic fields
• Majorana corner states in a two-dimensional magnetic topological insulator on a high-temperature superconductor
• Braiding without Braiding: Teleportation-Based Quantum Information Processing with Majorana Zero Modes
• Lattice models with exactly solvable topological hinge and corner states
• Towards realistic implementations of a Majorana surface code
• Higher-order Floquet topological phases with corner and bulk bound states
• Coupled-wire construction of static and Floquet second-order topological insulators
• Roadmap to Majorana surface codes
• Towards Universal Topological Quantum Computation in the $\nu =5/2$ Fractional Quantum Hall State
• Poking holes and cutting corners to achieve Clifford gates with the surface code
• Second-order Dirac superconductors and magnetic field induced Majorana hinge modes
• Simulation of non-Abelian braiding in Majorana time crystals
• Connecting higher-order topological insulators to lower-dimensional topological insulators
• Measurement-Only Topological Quantum Computation via Anyonic Interferometry
• Multi-channel Kondo impurity dynamics in a Majorana device
• Orbital effect of magnetic field on the Majorana phase diagram
• Majorana braiding with thermal noise
• A geometric protocol for a robust Majorana magic gate
• Floquet Perturbation Theory: Formalism and Application to Low-Frequency Limit
• Quantum computation via Floquet topological edge modes
• Implementing arbitrary phase gates with Ising anyons
• Measurement-Only Topological Quantum Computation via Tunable Interactions
• Braiding of Atomic Majorana Fermions in Wire Networks and Implementation of the Deutsch-Josza Algorithm
• Majorana Superconducting Qubit
• Direct prediction of corner state configurations from edge winding numbers in 2D and 3D chiral-symmetric lattice systems
• Braiding by Majorana Tracking and Long-Range CNOT Gates with Color Codes
• Monte Carlo studies of the properties of the Majorana quantum error correction code: is self-correction possible during braiding?
• Quantum Computing with Majorana Kramers Pairs
• Line nodes and surface Majorana flat bands in static and kicked p-wave superconducting Harper model
• Topological Corner States on Kagome Lattice Based Chiral Higher-Order Topological Insulator
• Majorana Entanglement Bridge
• Measurement-only topological quantum computation without forced measurements
• Measuring Majorana fermions qubit state and non-Abelian braiding statistics in quenched inhomogeneous spin ladders
• Braids and phase gates through high-frequency virtual tunneling of Majorana Zero Modes

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• Classical higher-order topological insulators
• Higher-order topological odd-parity superconductors
• Topological and holonomic quantum computation based on second-order topological superconductors
• Majorana corner and hinge modes in second-order topological insulator-superconductor heterostructures
• Floquet generation of Second Order Topological Superconductor
• All-electrically tunable networks of Majorana bound states
• Floquet higher order topological insulator in a periodically driven bipartite lattice
• Observation of pi/2 modes in an acoustic Floquet system
• Hierarchy of higher-order topological superconductors in three dimensions
• Non-Hermitian Floquet Topological Matter -- A Review
• Non-Hermitian Floquet second order topological insulators in periodically quenched lattices
• Floquet engineering of topological localization transitions and mobility edges in one-dimensional non-Hermitian quasicrystals
• Phonon-induced Floquet second-order topological phases protected by space-time symmetries
• Time-induced second-order topological superconductors
• Helical Liquids in Semiconductors
• Non-Hermitian higher-order topological superconductors in two-dimension: statics and dynamics
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Floquet Second Order Topological Superconductor based on Unconventional Pairing
• Arbitrary entangled state transfer via a topological qubit chain
• Square-root Floquet topological phases and time crystals
• Floquet higher-order Weyl and nexus semimetals
• Symmetry Analysis of Anomalous Floquet Topological Phases
• Floquet topological phases with fourfold-degenerate edge modes in a driven spin-1/2 Creutz ladder
• Dynamical construction of Quadrupolar and Octupolar topological superconductors
• Corner- and sublattice-sensitive Majorana zero modes on the kagome lattice
• Superconductors with anomalous Floquet higher-order topology
• Number conserving analysis of measurement-based braiding with Majorana zero modes
• High-fidelity and long-distance entangled-state transfer with Floquet topological edge modes
• $Z_4$ parafermion $\pm \pi /2$ modes in interacting periodically driven superconducting chain
• Surface Bogoliubov-Dirac cones and helical Majorana hinge modes in superconducting Dirac semimetals
• Higher-order Weyl superconductors with anisotropic Weyl-point connectivity
• Floquet topological superconductors with many Majorana edge modes: topological invariants, entanglement spectrum and bulk-edge correspondence
• Correlation Effects in Quadrupole Insulators: a Quantum Monte Carlo Study
• Stability of Floquet Majorana box qubits
• Entanglement spectrum and entropy in Floquet topological matter
• Floquet band engineering with Bloch oscillations
• Fermion-Parity-Based Computation and its Majorana-Zero-Mode Implementation
• Anomalous topological edge modes in a periodically-driven trimer lattice
• Topological classification of intrinsic 3D superconductors using anomalous surface construction
• Topological and dynamical features of periodically driven spin ladders
• Time evolution of Majorana corner modes in Floquet second-order topological superconductor
• Generating many Majorana corner modes and multiple phase transitions in Floquet second-order topological superconductors
• Dynamical Fragile Topology in Floquet Crystals
• Combating quasiparticle poisoning with multiple Majorana fermions in a periodically-driven quantum wire
• Floquet higher-order topological phases in momentum space
• Gapless higher-order topology and corner states in Floquet systems
• Readout of Majorana bound states via Landau-Zener transition
• Theory of Anomalous Floquet Higher-Order Topology: Classification, Characterization, and Bulk-Boundary Correspondence
• Topological $\pi$ modes and beyond
• Non-Abelian Anyons in Periodically Driven Abelian Spin Liquids
• Engineering Majorana corner modes from two-dimensional hexagonal crystals
• Generalized Majorana edge modes in a number-conserving periodically driven $p$-wave superconductor
• Nonadiabatic braiding of Majorana modes
• Universal quantum control over Majorana zero modes
• Quantum-vacuum-protected topological edge polaritons
• Zero and Nonzero Energy Majorana Modes in an Extended Kitaev Chain
• Dynamical Symmetry Indicators for Floquet Crystals
• Symmetry-protected topological corner modes in a periodically driven interacting spin lattice
• $q$th-root non-Hermitian Floquet topological insulators
• Floquet topological properties in the Non-Hermitian long-range system with complex hopping amplitudes