Topologically protected quantum gates for computation with non-Abelian anyons in the Pfaffian quantum Hall state

Abstract

We extend the topological quantum computation scheme using the Pfaffian quantum Hall state, which has been recently proposed by Das Sarma et al., in a way that might potentially allow for the topologically protected construction of a universal set of quantum gates. We construct, for the first time, a topologically protected Controlled-NOT gate which is entirely based on quasihole braidings of Pfaffian qubits. All single-qubit gates, except for the pi/8 gate, are also explicitly implemented by quasihole braidings. Instead of the pi/8 gate we try to construct a topologically protected Toffoli gate, in terms of the Controlled-phase gate and CNOT or by a braid-group based Controlled-Controlled-Z precursor. We also give a topologically protected realization of the Bravyi-Kitaev two-qubit gate g_3.

6 pages, 7 figures, RevTeX; version 3: introduced section names, new reference added; new comment added about the embedding of the one- and two- qubit gates into a three-qubit system

References in corpus (22)

• Fault-tolerant quantum computation by anyons
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• An Electronic Mach-Zehnder Interferometer
• Topologically-Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State
• $2n$ Quasihole States Realize $2^{n-1}$-Dimensional Spinor Braiding Statistics in Paired Quantum Hall States
• Transition from quantum Hall to compressible states in the second Landau level: new light on the $\nu$=5/2 enigma
• Incompressible paired Hall state, stripe order and the composite fermion liquid phase in half-filled Landau levels
• Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State
• Proposed experiments to probe the non-abelian ν=5/2 quantum Hall state
• Electron correlation in the second Landau level; a competition between many, nearly degenerate quantum phases
• Insulating and Fractional Quantum Hall States in the N=1 Landau Level
• Braiding Operators are Universal Quantum Gates
• Towards Universal Topological Quantum Computation in the $\nu =5/2$ Fractional Quantum Hall State
• Observation of Aharonov-Bohm Superperiod in a Laughlin Quasiparticle Interferometer
• Probing Non-Abelian Statistics with QuasiParticle Interferometry
• Proposal for reading out anyon qubits in non-abelian $\nu =12/5$ quantum Hall state
• Quantum computation with quasiparticles of the Fractional Quantum Hall Effect
• The nu=5/2 quantum Hall state revisited: spontaneous breaking of the chiral fermion parity and phase transition between abelian and non-abelian statistics
• Nonabelian braid statistics versus projective permutation statistics
• Aharonov-Bohm effect in the non-Abelian quantum Hall fluid

Cited by in corpus (41)

• Non-Abelian Anyons and Topological Quantum Computation
• Introduction to topological superconductivity and Majorana fermions
• Majorana Fermions and Topology in Superconductors
• Universal Quantum Computation with Hybrid Spin-Majorana Qubits
• Qutrit Magic State Distillation
• Catalysis and activation of magic states in fault tolerant architectures
• Non-Abelian Braiding of Lattice Bosons
• Braiding of Atomic Majorana Fermions in Wire Networks and Implementation of the Deutsch-Josza Algorithm
• Implementation of Clifford gates in the Ising-anyon topological quantum computer
• Controlled-NOT for multiparticle qubits and topological quantum computation based on parity measurements
• Non-Abelian Fractional Chern Insulators from Long-Range Interactions
• Braiding Majorana Fermions and Creating Quantum Logic Gates with Vortices on a Periodic Pinning Structure
• Noise Thresholds for Higher Dimensional Systems using the Discrete Wigner Function
• Using hybrid topological-spin qubit systems for two-qubit-spin gates
• Towards a universal set of topologically protected gates for quantum computation with Pfaffian qubits
• Topological Quantum Computing Using Nanowire Devices
• Skein Theory and Topological Quantum Registers: Braiding Matrices and Topological Entanglement Entropy of Non-Abelian Quantum Hall States
• Tight Noise Thresholds for Quantum Computation with Perfect Stabilizer Operations
• Many-body Majorana braiding without an exponential Hilbert space
• Hybrid Topological Quantum Computation with Majorana Fermions: A Cold Atom Setup
• Bell's inequality and universal quantum gates in a cold atom chiral fermionic p-wave superfluid
• 3- and 4-body Interactions from 2-body interactions in Spin Models: A Route to Abelian and Non-Abelian Fractional Chern Insulators
• Majorana quasiparticles in atomic spin chains on superconductors
• Nonlocality as a Benchmark for Universal Quantum Computation in Ising Anyon Topological Quantum Computers
• Noise threshold and resource cost of fault-tolerant quantum computing with Majorana fermions in hybrid systems
• Engineering Yang-Lee anyons via Majorana bound states
• Braid Matrices and Quantum Gates for Ising Anyons Topological Quantum Computation
• Unified approach to topological quantum computation with anyons: From qubit encoding to Toffoli gate
• Ultimate braid-group generators for coordinate exchanges of Ising anyons from the multi-anyon Pfaffian wave functions
• Complete description of fault-tolerant quantum gate operations for topological Majorana qubit systems
• Topological Mid-gap States of px+ipy Topological Superconductor with Vortex superlattice
• Realizing Universal Majorana Fermionic Quantum Computation
• Systematic construction of topological-nontopological hybrid universal quantum gates based on many-body Majorana fermion interactions
• Correlated transport of FQHE quasiparticles in a double-antidot system
• Topologically protected qubits as minimal Josephson junction arrays with non trivial boundary conditions: a proposal
• Braiding properties of paired spin-singlet and non-abelian hierarchy states
• Topological superconductor from superconducting topological surface states and fault-tolerant quantum computing
• Dissipationless topological quantum computation for Majorana objects in sparse-dense mixed encoding process
• Phase diagrams of superconducting topological surface states
• Computational equivalence of the two inequivalent spinor representations of the braid group in the Ising topological quantum computer
• Topological Quantum Computation with the universal R matrix for Ising anyons