Compare Papers
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
Decoherence induced spin squeezing signatures in Greenberger-Horne-Zeilinger and W states
Kapil K. Sharma
- Year
- 2017
- Journal
- arXiv preprint
- DOI
- arXiv:1706.06273
- arXiv
- 1706.06273
We reckon the behaviour of spin squeezing in tripartite unsqueezed maximally entangled Green- berger-Horne-Zeilinger (GHZ) and W states under various decoherence channels with Kitagawa- Ueda (KU) criteria. In order to search spin squeezing sudden death (SSSD) and signatures of spin squeezing production we use bit flip, phase flip, bit-phase-flip, amplitude damping, phase damping and depolarization channels in the present study. In literature, the influence of decoherence has been studied as a destroying element. On the contrary here we investigate the positive aspect of decoherence, which produce spin squeezing in unsqueezed GHZ and W states under certain channels. Our meticulous study shows that GHZ state remain unsqueezed under aforementioned channels except bit-phase-flip and depolarization channels. While all the decoherence channels produce spin squeezing in W state. So we find, GHZ is more robust in comparison to W state in the sense of spin squeezing production under decoherence. Most importantly we find that none of the decoherence channel produce SSSD in any one of the state.
Open paper