One of the main problems in quantum information systems is the presence of errors due to noise. Many quantum error correcting codes have been designed to deal with generic errors. In this paper we construct new stabilizer codes able to correct a given number eg of generic Pauli X,Y and Z errors, plus a number eZ of Pauli errors of a specified type (e.g., Z errors). These codes can be of interest when the quantum channel is asymmetric, i.e., when some types of error occur more frequently than others. For example, we design a [[9,1]] quantum error correcting code able to correct up to one generic qubit error plus one Z error in arbitrary positions. According to a generalized version of the quantum Hamming bound, it is the shortest code with this error correction capability.

Design of Short Codes for Quantum Channels with Asymmetric Pauli Errors

Chiani, Marco;Valentini, Lorenzo
2020

Abstract

One of the main problems in quantum information systems is the presence of errors due to noise. Many quantum error correcting codes have been designed to deal with generic errors. In this paper we construct new stabilizer codes able to correct a given number eg of generic Pauli X,Y and Z errors, plus a number eZ of Pauli errors of a specified type (e.g., Z errors). These codes can be of interest when the quantum channel is asymmetric, i.e., when some types of error occur more frequently than others. For example, we design a [[9,1]] quantum error correcting code able to correct up to one generic qubit error plus one Z error in arbitrary positions. According to a generalized version of the quantum Hamming bound, it is the shortest code with this error correction capability.
2020
Computational Science – ICCS 2020 20th International Conference, Amsterdam, The Netherlands, June 3–5, 2020, Proceedings, Part VI
638
649
Chiani, Marco; Valentini, Lorenzo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/787994
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