We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham Research Online
You are in:

Analytical percolation theory for topological color codes under qubit loss.

Amaro, David and Bennett, Jemma and Vodola, Davide and Müller, Markus (2020) 'Analytical percolation theory for topological color codes under qubit loss.', Physical review A., 101 (3). 032317.


Quantum information theory has shown strong connections with classical statistical physics. For example, quantum error correcting codes like the surface and the color code present a tolerance to qubit loss that is related to the classical percolation threshold of the lattices where the codes are defined. Here we explore such connection to study analytically the tolerance of the color code when the protocol introduced in Vodola et al. [Phys. Rev. Lett. 121, 060501 (2018)] to correct qubit losses is applied. This protocol is based on the removal of the lost qubit from the code, a neighboring qubit, and the lattice edges where these two qubits reside. We first obtain analytically the average fraction of edges r(p) that the protocol erases from the lattice to correct a fraction p of qubit losses. Then, the threshold pc below which the logical information is protected corresponds to the value of p at which r(p) equals the bond-percolation threshold of the lattice. Moreover, we prove that the logical information is protected if and only if the set of lost qubits does not include the entire support of any logical operator. The results presented here open a route to an analytical understanding of the effects of qubit losses in topological quantum error codes.

Item Type:Article
Full text:(VoR) Version of Record
Download PDF
Publisher Web site:
Publisher statement:Reprinted with permission from the American Physical Society: Amaro, David, Bennett, Jemma, Vodola, Davide & Müller, Markus (2020). Analytical percolation theory for topological color codes under qubit loss. Physical Review A 101(3): 032317 © 2020 by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.
Date accepted:06 February 2020
Date deposited:02 April 2020
Date of first online publication:13 March 2020
Date first made open access:02 April 2020

Save or Share this output

Look up in GoogleScholar