Majorana Fermion Surface Code for Universal Quantum Computation

Abstract

We introduce an exactly solvable model of interacting Majorana fermions realizing $Z_2$ topological order with a $Z_2$ fermion parity grading and lattice symmetries permuting the three fundamental anyon types. We propose a concrete physical realization by utilizing quantum phase slips in an array of Josephson-coupled mesoscopic topological superconductors, which can be implemented in a wide range of solid state systems, including topological insulators, nanowires or two-dimensional electron gases, proximitized by $s$-wave superconductors. Our model finds a natural application as a Majorana fermion surface code for universal quantum computation, with a single-step stabilizer measurement requiring no physical ancilla qubits, increased error tolerance, and simpler logical gates than a surface code with bosonic physical qubits. We thoroughly discuss protocols for stabilizer measurements, encoding and manipulating logical qubits, and gate implementations.

17 pages, 13 figures

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Cited by in corpus (93)

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• InAs-Al Hybrid Devices Passing the Topological Gap Protocol
• Braiding without Braiding: Teleportation-Based Quantum Information Processing with Majorana Zero Modes
• Towards realistic implementations of a Majorana surface code
• Entanglement and dynamics of diffusion-annihilation processes with Majorana defects
• Roadmap to Majorana surface codes
• Majorana nanowires for topological quantum computation
• Universal Quantum Computation with Hybrid Spin-Majorana Qubits
• Hunting for Majoranas
• All Majorana Models with Translation Symmetry are Supersymmetric
• Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter
• Three-dimensional surface codes: Transversal gates and fault-tolerant architectures
• Quantum Computing with Majorana Fermion Codes
• Combining Topological Hardware and Topological Software: Color Code Quantum Computing with Topological Superconductor Networks
• Majorana qubits in topological insulator nanoribbon architecture
• Weak measurement protocols for Majorana bound state identification
• Readout of Majorana Qubits
• Higher order topological superconductors as generators of quantum codes
• Parity-controlled $2\pi$ Josephson effect mediated by Majorana Kramers pairs
• Braiding errors in interacting Majorana quantum wires
• Braiding by Majorana Tracking and Long-Range CNOT Gates with Color Codes
• Interacting Majorana Fermions
• Jordan-Wigner Dualities for Translation-Invariant Hamiltonians in Any Dimension: Emergent Fermions in Fracton Topological Order
• Physical Implementation of a Majorana Fermion Surface Code for Fault-Tolerant Quantum Computation
• Low-field Topological Threshold in Majorana Double Nanowires
• Exact master equation and decoherence dynamics of Majorana zero modes under the gate-induced charge fluctuation
• Equivalence between fermion-to-qubit mappings in two spatial dimensions
• Driven Dissipative Majorana Dark Spaces
• Majorana Quantum Lego, a Route Towards Fracton Matter
• A decoder for the triangular color code by matching on a Möbius strip
• Lifetime of Majorana qubits in Rashba nanowires with non-uniform chemical potential
• Quantum Computing with Majorana Kramers Pairs
• Demonstrating non-Abelian statistics of Majorana fermions using twist defects
• Towards dark space stabilization and manipulation in driven dissipative Majorana platforms
• Electron Teleportation in Multi-Terminal Majorana Islands: Statistical Transmutation and Fractional Quantum Conductance
• Degeneracy lifting of Majorana bound states due to electron-phonon interactions
• Vortex Majorana braiding in a finite time
• Kondo physics from quasiparticle poisoning in Majorana devices
• Evidence of Majorana Zero Modes in Josephson Trijunctions
• Majorana Spin Liquids, Topology and Superconductivity in Ladders
• Modeling noise and error correction for Majorana-based quantum computing
• Dissipative topological systems
• $AbInitio$ Simulation of Non-Abelian Braiding Statistics in Topological Superconductors
• Majorana-Hubbard model on the honeycomb lattice
• Majorana Zero-Modes in a Two-Dimensional $p$-Wave Superconductor
• Simulating topological tensor networks with Majorana qubits
• Fault-tolerant fermionic quantum computation based on color code
• Tricritical Ising phase transition in two-ladder Majorana fermion lattice
• Optimal noise-canceling shortcuts to adiabaticity: application to noisy Majorana-based gates
• Changing anyonic ground degeneracy with engineered gauge fields
• Fidelity and visibility reduction in Majorana qubits by entanglement with environmental modes
• Noise threshold and resource cost of fault-tolerant quantum computing with Majorana fermions in hybrid systems
• Engineering Yang-Lee anyons via Majorana bound states
• Proximity induced time-reversal topological superconductivity in Bi2Se3 films without phase tuning
• Scalable Fermionic Error Correction in Majorana Surface Codes
• Two-Channel Kondo Physics in a Majorana Island Coupled to a Josephson Junction
• Quantum phase transitions of the Majorana toric code in the presence of finite Cooper-pair tunneling
• Topological classification of intrinsic 3D superconductors using anomalous surface construction
• Universal quantum computing with parafermions assisted by a half fluxon
• Dispersive sensing in hybrid InAs/Al nanowires
• Non-Abelian defects in Fracton phase of matter
• Nonlocal discrete time crystals in periodically driven surface codes
• Extracting topological orders of generalized Pauli stabilizer codes in two dimensions
• Interference and parity blockade in transport through a Majorana box
• Structured volume-law entanglement in an interacting, monitored Majorana spin liquid
• Quantum transport in coupled Majorana box systems
• Engineering Quantum Spin Liquids and Many-Body Majorana States with a Driven Superconducting Box Circuit
• Supersymmetry in an interacting Majorana model on the kagome lattice
• Long distance coherence of Majorana wires
• Encoding Majorana codes
• Exfoliated hexagonal BN as gate dielectric for InSb nanowire quantum dots with improved gate hysteresis and charge noise
• Segmented Composite Design of Robust Single-Qubit Quantum Gates
• A new twist on the Majorana surface code: Bosonic and fermionic defects for fault-tolerant quantum computation
• Topological ordering in the Majorana Toric Code
• Entangled Cloning of Stabilizer Codes and Free Fermions
• Quantum transport theory of hybrid superconducting systems
• Charge response of the Majorana toric code
• A graph-based formalism for surface codes and twists
• The differential conductance tunnel spectroscopy in an analytical solvable two-terminal Majorana device
• Erasure conversion in Majorana qubits via local quasiparticle detection
• Triangular lattice Majorana-Hubbard model: Mean field theory and DMRG on a width-4 torus
• Majorana braiding simulations with projective measurements
• Transport-based fusion that distinguishes between Majorana and Andreev bound states
• 1D Error Correcting Code for Majorana Qubits
• Theory of Topological Superconductivity in Doped IV-VI Semiconductors
• Topological in-gap chiral edge states in superconducting Haldane model with spin-orbit coupling
• Interplay of Tilt and Axion Fields in Topological Superconductors: Anisotropy in the Meissner Effect
• Gap reopening as a possible signature of coupling between Majorana zero modes in Sn-(Bi,Sb)2(Te,S)3-based Josephson trijunctions
• Partons from stabilizer codes
• Parity readout in Majorana box qubits from the dispersive to the resonant regime
• Effects of dilution in a 2D topological magnon insulator