# Measurement-Only Topological Quantum Computation via Anyonic Interferometry

@article{Bonderson2008MeasurementOnlyTQ,
title={Measurement-Only Topological Quantum Computation via Anyonic Interferometry},
author={Parsa Bonderson and Michael H. Freedman and C. Nayak},
journal={arXiv: Quantum Physics},
year={2008}
}
• Published 14 August 2008
• Physics
• arXiv: Quantum Physics
58 Citations

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## References

SHOWING 1-10 OF 110 REFERENCES
Measurement-only topological quantum computation.
• Medicine, Physics
Physical review letters
• 2008
By using an anyonic analog of quantum state teleportation, it is shown how the braiding transformations used to generate computational gates may be produced through a series of topological charge measurements.
Tilted Interferometry Realizes Universal Quantum Computation in the Ising TQFT without Overpasses
• Physics
• 2007
We show how a universal gate set for topological quantum computation in the Ising TQFT, the non-Abelian sector of the putative effective field theory of the $\nu=5/2$ fractional quantum Hall state,
Experimental quantum teleportation
• Physics, Biology
Nature
• 1997
It is shown that during teleportation, one of a pair of entangled photons are subjected to a measurement such that the second photon of the entangled pair acquires the polarization of the initial photon.
Universal quantum computation with the v=5/2 fractional quantum Hall state
We consider topological quantum computation (TQC) with a particular class of anyons that are believed to exist in the fractional quantum Hall effect state at Landau-level filling fraction v =5/2.
Computation by measurements: A unifying picture
• Physics
• 2004
The ability to perform a universal set of quantum operations based solely on static resources and measurements presents us with a striking viewpoint for thinking about quantum computation and its
Topological Quantum Computation
• Physics, Computer Science
QCQC
• 1998
The connection between fault-tolerant quantum computation and nonabelian quantum statistics in two spatial dimensions is explored and it is shown that if information is encoded in pairs of quasiparticles, then the Aharonov-Bohm interactions can be adequate for universal fault-Tolerance quantum computation.
Topological Quantum Computation
• Mathematics, Physics
• 2001
The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones poly-
Towards universal topological quantum computation in the ν = 5 2 fractional quantum Hall state
• Physics
• 2006
The Pfaffian state, which may describe the quantized Hall plateau observed at Landau level filling fraction $\ensuremath{\nu}=\frac{5}{2}$, can support topologically-protected qubits with extremely