Symmetry-protected gates of Majorana qubits in a high-$T_c$ superconductor platform

Abstract

We propose a platform for braiding Majorana non-Abelian anyons based on a heterostructure between a $d$-wave high-$T_c$ superconductor and a quantum spin-Hall insulator. It has been recently shown that such a setup for a quantum spin-Hall insulator leads to a pair of Majorana zero modes at each corner of the sample, and thus can be regarded as a higher-order topological superconductor. We show that upon applying a Zeeman field in the region, these Majorana modes split in space and can be manipulated for braiding processes by tuning the field and pairing phase. We show that such a setup can achieve full braiding, exchanging, and arbitrary phase gates (including the $\pi /8$ magic gates) of the Majorana zero modes, all of which are robust and protected by symmetries. As many of the ingredients of our proposed platform have been realized in recent experiments, our results provide a new route toward universal topological quantum computation.

arXiv comment49 pages, 5 figures

References in corpus (60)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• 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
• 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
• Reflection symmetric second-order topological insulators and superconductors
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Topology of crystalline insulators and superconductors
• $2n$ Quasihole States Realize $2^{n-1}$-Dimensional Spinor Braiding Statistics in Paired Quantum Hall States
• Theta, Time Reversal, and Temperature
• Second-order topological insulators and superconductors with an order-two crystalline symmetry
• 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
• Fractional topological insulators
• Higher-order bulk-boundary correspondence for topological crystalline phases
• Majorana corner modes in a high-temperature platform
• Surface State Magnetization and Chiral Edge States on Topological Insulators
• High-Temperature Majorana Corner States
• Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
• Higher Order Topological Phases: A General Principle of Construction
• Controlling non-Abelian statistics of Majorana fermions on Majorana dimer lattices
• Weak-Pairing Higher Order Topological Superconductors
• Classification and analysis of two dimensional abelian fractional topological insulators
• Topological Quadrupolar Semimetals
• Minimal model for higher-order topological insulators and phosphorene
• Theory of defects in Abelian topological states
• Fractional topological superconductors with fractionalized Majorana fermions
• Fractional disclination charge in two-dimensional $C_n-$symmetric topological crystalline insulators
• Lattice models with exactly solvable topological hinge and corner states
• Higher-order topological odd-parity superconductors
• Classification of Topological Defects in Abelian Topological States
• Universal quantum computation on a semiconductor quantum wire network
• Second-order Dirac superconductors and magnetic field induced Majorana hinge modes
• Higher order symmetry-protected topological states for interacting bosons and fermions
• Interface Between Topological and Superconducting Qubits
• Connecting higher-order topological insulators to lower-dimensional topological insulators
• Electron pairing in the presence of incipient bands in iron-based superconductors
• Topological and holonomic quantum computation based on second-order topological superconductors
• Braiding Majorana corner modes in a second-order topological superconductor
• Higher-order topological superconductors in $\mathcal{P}$-, $\mathcal{T}$-odd quadrupolar Dirac materials
• Canted Spin Texture and Quantum Spin Hall Effect in WTe2
• Higher-Order Topological Dirac Superconductors
• All-electrically tunable networks of Majorana bound states
• Resilient nodeless $d$-wave superconductivity in monolayer FeSe
• Vortex and Surface Phase Transitions in Superconducting Higher-order Topological Insulators
• `Unhinging' the surfaces of higher-order topological insulators and superconductors
• Kramers pairs of Majorana corner states in a topological insulator bilayer
• Second-Order Bulk-Boundary Correspondence in Rotationally Symmetric Topological Superconductors from Stacked Dirac Hamiltonians
• Topological superconductivity and Majorana fermions in hybrid structures involving cuprate high-T_c superconductors
• A practical phase gate for producing Bell violations in Majorana wires
• Braiding properties of Majorana Kramers Pairs
• Majorana zero modes and their bosonization
• Higher-order topological phase without crystalline symmetry
• Braiding Majorana zero modes in spin space: from worldline to worldribbon

Cited by in corpus (1)

• Surface Bogoliubov-Dirac cones and helical Majorana hinge modes in superconducting Dirac semimetals