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Paper 1
Local Decoders for the 2D and 4D Toric Code
Nikolas P. Breuckmann, Kasper Duivenvoorden, Dominik Michels, Barbara M. Terhal
- Year
- 2016
- Journal
- arXiv preprint
- DOI
- arXiv:1609.00510
- arXiv
- 1609.00510
We analyze the performance of decoders for the 2D and 4D toric code which are local by construction. The 2D decoder is a cellular automaton decoder formulated by Harrington which explicitly has a finite speed of communication and computation. For a model of independent $X$ and $Z$ errors and faulty syndrome measurements with identical probability we report a threshold of $0.133\%$ for this Harrington decoder. We implement a decoder for the 4D toric code which is based on a decoder by Hastings arXiv:1312.2546 . Incorporating a method for handling faulty syndromes we estimate a threshold of $1.59\%$ for the same noise model as in the 2D case. We compare the performance of this decoder with a decoder based on a 4D version of Toom's cellular automaton rule as well as the decoding method suggested by Dennis et al. arXiv:quant-ph/0110143 .
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Superradiance and subradiance in extended media
Jonathan F. Schonfeld
- Year
- 2017
- Journal
- arXiv preprint
- DOI
- arXiv:1707.05237
- arXiv
- 1707.05237
In super- or subradiance, a quantum superposition of excited atoms collectively emits a photon much more or much less rapidly than an isolated atom. Superradiant and subradiant lifetimes have been derived for finite spheres of uniform media, either by simulating random samples or by expanding in spherical harmonics and analyzing Bessel functions. We introduce a simple regulator that applies to unbounded media, enabling trivial derivation and analysis of lifetimes via elementary Fourier techniques. The regulator can be interpreted as a correlation length for atomic positions; the regularized system describes localized regions of enhanced radiative activity in otherwise quiescent surroundings.
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