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
A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer. Unitary transformations can be performed by moving the excitations around each other. Measurements can be performed by joining excitations in pairs and observing the result of fusion. Such computation is fault-tolerant by its physical nature. 
Quantum Computation with Abelian Anyons
  • S. Lloyd
  • Physics, Computer Science
  • 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-anyonExpand
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,Expand
A fault-tolerant one-way quantum computer
We describe a fault-tolerant one-way quantum computer on cluster states in three dimensions. The presented scheme uses methods of topological error correction resulting from a link between clusterExpand
Quantum Computing: a Quantum Group Approach
There is compelling theoretical evidence that quantum physics will change the face of information science. Exciting progress has been made during the last two decades towards the building of a largeExpand
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 adiabaticExpand
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 gateExpand
A Survey on quantum computing technology
TLDR
The most recent results of quantum computation technology are reviewed and the open problems of the field are addressed. Expand
Toward Realizable Quantum Computers
The work in this thesis splits naturally into two parts: (1) experimentally oriented work consisting of experimental proposals for systems that could be used to implement quantum information tasksExpand
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 AbelianExpand
Almost any quantum spin system with short-range interactions can support toric codes
Inspired by Kitaev's argument that physical error correction is possible in a system of interacting anyons, we demonstrate that such "self-correction" is fairly common in spin systems with classicalExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 23 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. Expand
Fault-tolerant quantum computation
  • P. Shor
  • Computer Science, Physics
  • Proceedings of 37th Conference on Foundations of Computer Science
  • 1996
TLDR
For any quantum computation with t gates, it is shown how to build a polynomial size quantum circuit that tolerates O(1/log/sup c/t) amounts of inaccuracy and decoherence per gate, for some constant c; the previous bound was O( 1/t). Expand
Threshold Accuracy for Quantum Computation
We have previously (quant-ph/9608012) shown that for quantum memories and quantum communication, a state can be transmitted over arbitrary distances with error $\epsilon$ provided each gate has errorExpand
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. Expand
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. Expand
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. Expand
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 3Expand
Good quantum error-correcting codes exist.
  • Calderbank, Shor
  • Physics, Medicine
  • 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. Expand
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 theirExpand
...
1
2
3
...