Measurement-only topological quantum computation without forced measurements
arXiv:1607.07475 · doi:10.1088/1367-2630/aa50bb
Abstract
We investigate the measurement-only topological quantum computation (MOTQC) approach proposed by Bonderson et al. [Phys. Rev. Lett. 101, 010501 (2008)] where the braiding operation is shown to be equivalent to a series of topological charge "forced measurements" of anyons. In a forced measurement, the charge measurement is forced to yield the desired outcome (e.g. charge 0) via repeatedly measuring charges in different bases. This is a probabilistical process with a certain success probability for each trial. In practice, the number of measurements needed will vary from run to run. We show that such an uncertainty associated with forced measurements can be removed by simulating the braiding operation using a fixed number of three measurements supplemented by a correction operator. Furthermore, we demonstrate that in practice we can avoid applying the correction operator in hardware by implementing it in software. Our findings greatly simplify the MOTQC proposal and only require the capability of performing charge measurements to implement topologically protected transformations generated by braiding exchanges without physically moving anyons.
Published version with the section of software-implemented correction operator significantly rewritten
References in corpus (55)
- Non-Abelian Anyons and Topological Quantum Computation
- Anyons in an exactly solved model and beyond
- 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
- Surface codes: Towards practical large-scale quantum computation
- 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
- Universal Quantum Computation with ideal Clifford gates and noisy ancillas
- Observation of the fractional ac Josephson effect: the signature of Majorana particles
- Exponential Protection of Zero Modes in Majorana Islands
- Anomalous modulation of a zero bias peak in a hybrid nanowire-superconductor device
- Topologically-Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State
- Milestones toward Majorana-based quantum computing
- A fault-tolerant one-way quantum computer
- Exotic non-Abelian anyons from conventional fractional quantum Hall states
- Topological Order with a Twist: Ising Anyons from an Abelian Model
- 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
- Coulomb-assisted braiding of Majorana fermions in a Josephson junction array
- Parafermionic edge zero modes in Z_n-invariant spin chains
- Measurement-Only Topological Quantum Computation
- Topological phases with parafermions: theory and blueprints
- Genons, twist defects, and projective non-Abelian braiding statistics
- Topological Nematic States and Non-Abelian Lattice Dislocations
- Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
- Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
- Fractional topological superconductors with fractionalized Majorana fermions
- Anyonic interferometry without anyons: How a flux qubit can read out a topological qubit
- Magic state distillation in all prime dimensions using quantum Reed-Muller codes
- Projective non-Abelian Statistics of Dislocation Defects in a Z_N Rotor Model
- Fractional Helical Liquids and Non-Abelian Anyons in Quantum Wires
- Interferometry of non-Abelian Anyons
- Kramers Pairs of Majorana Fermions and Parafermions in Fractional Topological Insulators
- Topological quantum buses: coherent quantum information transfer between topological and conventional qubits
- Parafermions in Interacting Nanowire Bundle
- Interface Between Topological and Superconducting Qubits
- High efficiency deterministic Josephson Vortex Ratchet
- Observing Majorana bound states of Josephson vortices in topological superconductors
- How quickly can anyons be braided? Or: How I learned to stop worrying about diabatic errors and love the anyon
- Aharonov-Casher-Effect Suppression of Macroscopic Tunneling of Magnetic Flux
- Synthetic Topological Qubits in Conventional Bilayer Quantum Hall Systems
- Quantum Computing with Parafermions
- Implementing arbitrary phase gates with Ising anyons
- Assembling Fibonacci Anyons From a Parafermion Lattice Model
- Measurement-Only Topological Quantum Computation via Tunable Interactions
- Topological Entanglement Entropy with a Twist
- Demonstrating non-Abelian statistics of Majorana fermions using twist defects
- Improved phase gate reliability in systems with neutral Ising anyons
- A family of stabilizer codes for anyons and Majorana modes
- Braiding of non-Abelian anyons using pairwise interactions
- Parafermions in a Kagome lattice of qubits for topological quantum computation
- Topological blockade and measurement of topological charge
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- A comparative study of universal quantum computing models: towards a physical unification
- Optimizing Clifford gate generation for measurement-only topological quantum computation with Majorana zero modes
- Parafermions in a multilegged geometry: Towards a scalable parafermionic network
- Fermion-Parity-Based Computation and its Majorana-Zero-Mode Implementation
- Universal quantum computing with parafermions assisted by a half fluxon
- Holonomic implementation of CNOT gate on topological Majorana qubits
- Readout of Majorana bound states via Landau-Zener transition
- Deterministic topological quantum gates for Majorana qubits without ancillary modes