Fault tolerant quantum computation by anyons

@article{Kitaev2003FaultTQ,
  title={Fault tolerant quantum computation by anyons},
  author={Alexei Y. Kitaev},
  journal={Annals of Physics},
  year={2003},
  volume={303},
  pages={2-30}
}
  • A. Kitaev
  • Published 9 July 1997
  • Physics
  • Annals of Physics
Quantum Computation with Abelian Anyons
  • S. Lloyd
  • Physics
    Quantum Inf. Process.
  • 2002
AbstractA universal quantum computer can be constructed using abelian anyons. Two qubit quantum logic gates such as controlled-NOT operations are performed using topological effects. Single-anyon
Fault-tolerant quantum computation with high threshold in two dimensions.
We present a scheme of fault-tolerant quantum computation for a local architecture in two spatial dimensions. The error threshold is 0.75% for each source in an error model with preparation, gate,
Robustness of adiabatic quantum computation
We study the fault tolerance of quantum computation by adiabatic evolution, a quantum algorithm for solving various combinatorial search problems. We describe an inherent robustness of adiabatic
Fault-tolerant quantum computation for local non-Markovian noise
We derive a threshold result for fault-tolerant quantum computation for local non-Markovian noise models. The role of error amplitude in our analysis is played by the product of the elementary gate
A Scheme for Simulation of Quantum Gates by Abelian Anyons
Anyons can be used to realize quantum computation, because they are two-level systems in two dimensions. In this paper, we propose a scheme to simulate single-qubit gates and CNOT gate using Abelian
Quantum computation and quantum information
TLDR
A survey of all the important aspects and results that have shaped the field of quantum computation and quantum information and their applications to the general theory of information, cryptography, algorithms, computational complexity and error-correction.
From Geometry to Quantum Computation
TLDR
The aim of this paper is to introduce the idea of Holonomic Quantum Computation (Computer), which is based on both harmonic oscillators and non{linear quantum optics, not on spins of usual quantum computation and it is hoped that therefore this model may be strong for decoherence.
From 3D topological quantum field theories to 4D models with defects
(2+1) dimensional topological quantum field theories with defect excitations are by now quite well understood, while many questions are still open for (3+1) dimensional TQFTs. Here we propose a
...
...

References

SHOWING 1-10 OF 64 REFERENCES
Quantum Error Correction with Imperfect Gates
Quantum error correction can be performed fault-tolerantly This allows to store a quantum state intact (with arbitrary small error probability) for arbitrary long time at a constant decoherence rate.
"Quantum Communication, Computing, and Measurement"
TLDR
This volume brings together scientists working in the interdisciplinary fields of quantum communication science and technology on topics including quantum information theory, quantum computing, stochastic processes and filtering, and quantum measurement theory.
Threshold Estimate for Fault Tolerant Quantum Computing
TLDR
A rough estimate of the accuracy threshold for fault tolerant quantum computing with concatenated codes is made and only gate errors are considered, using the depolarizing channel error model.
Accuracy threshold for quantum computation
We have previously [11] shown that for quantum memories and quantum communication, a state can be transmitted over arbitrary distances with error (cid:15) provided each gate has error at most
Threshold Estimate for Fault Tolerant Quantum Computation
TLDR
A rough estimate of the accuracy threshold for fault tolerant quantum computing with concatenated codes is made and a simple computer simulation suggests a threshold for gate errors of the order of \epsilon 10^{-3} or better.
Concatenated Quantum Codes
TLDR
A method is given which has the property that to store or transmit a qubit with maximum error $c$ requires gates with error at most $c\epsilon$ and storage or channel elements witherror at most c, independent of how long the authors wish to store the state or how far they wish to transmit it.
Fault-tolerant quantum computation with constant error
TLDR
This paper shows how to perform fault tolerant quantum computation when the error probability, q, is smaller than some constant threshold, q.. the cost is polylogarithmic in time and space, and no measurements are used during the quantum computation.
Quantum Error Correction and Orthogonal Geometry
A group theoretic framework is introduced that simplifies the description of known quantum error-correcting codes and greatly facilitates the construction of new examples. Codes are given which map 3
Good quantum error-correcting codes exist.
  • Calderbank, Shor
  • Physics
    Physical review. A, Atomic, molecular, and optical physics
  • 1996
TLDR
The techniques investigated in this paper can be extended so as to reduce the accuracy required for factorization of numbers large enough to be difficult on conventional computers appears to be closer to one part in billions.
Fractional Statistics and the Quantum Hall Effect
The statistics of quasiparticles entering the quantum Hall effect are deduced from the adiabatic theorem. These excitations are found to obey fractional statistics, a result closely related to their
...
...