Journal Article

FZJ-2020-05097

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Analytical percolation theory for topological color codes under qubit loss

Amaro, D. ; Bennett, J. ; Vodola, D. ; Müller, M. (Corresponding author)FZJ*

2020
Inst. Woodbury, NY

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Please use a persistent id in citations: http://hdl.handle.net/2128/26453  doi:10.1103/PhysRevA.101.032317

Abstract: 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.

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Contributing Institute(s):

1. Theoretische Nanoelektronik (PGI-2)

Research Program(s):

1. 144 - Controlling Collective States (POF3-144) (POF3-144)

Appears in the scientific report 2020

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Database coverage:
; ; ; Clarivate Analytics Master Journal List ; Current Contents - Electronics and Telecommunications Collection ; Current Contents - Physical, Chemical and Earth Sciences ; Ebsco Academic Search ; Essential Science Indicators ; IF < 5 ; JCR ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection

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