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.
Chiani, M., Valentini, L. (2020). Design of Short Codes for Quantum Channels with Asymmetric Pauli Errors. Springer Nature [10.1007/978-3-030-50433-5_49].
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
