A geometric protocol for a robust Majorana magic gate

Abstract

A universal quantum computer requires a full set of basic quantum gates. With Majorana bound states one can form all necessary quantum gates in a topologically protected way, bar one. In this manuscript we present a protocol that achieves the missing, so called, $\pi /8$ 'magic' phase gate. The protocol is based on the manipulation of geometric phases in a universal manner, and does not require fine tuning for distinct physical realizations. The protocol converges exponentially with the number of steps in the geometric path. Furthermore, the magic gate protocol relies on the most basic hardware previously suggested for topologically protected gates, and can be extended to any-phase-gate, where $\pi /8$ is substituted by any $\alpha$.

14 pages, 8 figures (including appendices), v3: simplified derivation, more explicit connection between topological protection and exponential convergence

References in corpus (14)

• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Exponential Protection of Zero Modes in Majorana Islands
• A Semiconductor Nanowire-Based Superconducting Qubit
• Universal quantum computation on a semiconductor quantum wire network
• Interface Between Topological and Superconducting Qubits
• Shortcuts to nonabelian braiding
• Optimal Control of Majorana Zero Modes
• A practical phase gate for producing Bell violations in Majorana wires
• Majorana fermion exchange in strictly one dimensional structures
• Improved phase gate reliability in systems with neutral Ising anyons

Cited by in corpus (60)

• Scalable Designs for Quasiparticle-Poisoning-Protected Topological Quantum Computation with Majorana Zero Modes
• A Short Introduction to Topological Quantum Computation
• Phase-dependent chiral transport and effective non-Hermitian dynamics in a bosonic Kitaev-Majorana chain
• Roadmap to Majorana surface codes
• Majorana nanowires for topological quantum computation
• Simulation of non-Abelian braiding in Majorana time crystals
• The multi-terminal Josephson effect
• Conformal field theories are magical
• Topological Quantum Compiling with Reinforcement Learning
• Topological and holonomic quantum computation based on second-order topological superconductors
• How quickly can anyons be braided? Or: How I learned to stop worrying about diabatic errors and love the anyon
• Quantum Computing with Majorana Fermion Codes
• Combining Topological Hardware and Topological Software: Color Code Quantum Computing with Topological Superconductor Networks
• Measurement-only quantum computation with Majorana corner modes
• Quantum computation via Floquet topological edge modes
• Topologically protected braiding in a single wire using Floquet Majorana modes
• Majorana bound states in semiconducting nanostructures
• Braiding by Majorana Tracking and Long-Range CNOT Gates with Color Codes
• Universal fault-tolerant measurement-based quantum computation
• Yu-Shiba-Rusinov qubit
• Photon assisted braiding of Majorana fermions in a cavity
• Topological Quantum Computing Using Nanowire Devices
• Majorana Zero Modes Protected by Hopf Invariant in Topologically Trivial Superconductors
• Probing Robust Majorana Signatures by Crossed Andreev Reflection with a Quantum Dot
• Parafermion braiding in fractional quantum Hall edge states with finite chemical potential
• Vortex Majorana braiding in a finite time
• Robust Majorana magic gates via measurements
• Optimal diabatic dynamics of Majorana-based quantum gates
• Multi-mode architectures for noise-resilient superconducting qubits
• Emulating Majorana fermions and their braiding by Ising spin chains
• Diabatic errors in Majorana braiding with bosonic bath
• Majorana zero modes induced by superconducting phase bias
• Effects of decoherence on diabatic errors in Majorana braiding
• Non-Abelian Berry phase for open quantum systems: Topological protection vs geometric dephasing
• Non-Abelian Geometric Dephasing
• Demonstrating Majorana non-Abelian properties using fast adiabatic charge-transfer
• Fidelity and visibility reduction in Majorana qubits by entanglement with environmental modes
• Fermion-Parity-Based Computation and its Majorana-Zero-Mode Implementation
• Majorana phase-gate based on the geometric phase
• Universal quantum computing with parafermions assisted by a half fluxon
• Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors
• Characterizing Dynamic Majorana Hybridization for Universal Quantum Computing
• From edge to bulk: Cavity induced displacement of topological non-local qubits
• Unveiling non-Abelian statistics of vortex Majorana bound states in iron-based superconductors using fermionic modes
• Observation of in-gap states in a two-dimensional CrI2/NbSe2 heterostructure
• Holonomic implementation of CNOT gate on topological Majorana qubits
• Transport probe of nonadiabatic transition caused by Majorana moving
• Topologically protected heat pumping from braiding Majorana zero modes
• Braiding Induced by Finite-Size Effect in One-Dimensional Topological Superconductors
• A new twist on the Majorana surface code: Bosonic and fermionic defects for fault-tolerant quantum computation
• Topological Modes in Monitored Quantum Dynamics
• Systematic construction of topological-nontopological hybrid universal quantum gates based on many-body Majorana fermion interactions
• Braids and phase gates through high-frequency virtual tunneling of Majorana Zero Modes
• Tunable Majorana corner states driven by superconducting phase bias in a vertical Josephson junction
• Realization of the Non-endpoint Majorana Bound States in an Extended Kitaev Chain
• Pumped heat and charge statistics from Majorana braiding
• Non-Abelian holonomy of Majorana zero modes coupled to a chaotic quantum dot
• Nonadiabatic braiding of Majorana modes
• Majorana bound states with chiral magnetic textures
• Universal quantum operation of spin-3/2 Blume-Capel chains