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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 .
Open paperPaper 2
Nonexponential quantum decay under environmental decoherence
M. Beau, J. Kiukas, I. L. Egusquiza, A. del Campo
- Year
- 2017
- Journal
- arXiv preprint
- DOI
- arXiv:1706.06943
- arXiv
- 1706.06943
An unstable quantum state generally decays following an exponential law, as environmental decoherence is expected to prevent the decay products from recombining to reconstruct the initial state. Here we show the existence of deviations from exponential decay in open quantum systems under very general conditions. Our results are illustrated with the exact dynamics under quantum Brownian motion and suggest an explanation of recent experimental observations.
Open paper