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Journal of Software

How to Correct Random and Burst Quantum Errors Simultaneously

Ying Guo

Published Jan 1, 2006• 1 citation
Publisher

Abstract

A special quantum error correction scheme is proposed to protect the flow of transmitted quantum information in complex channels. Based on the derived syndrome, an algorithm is devised for the construction of the called quantum event-error correction code, which can correct simultaneously random and burst quantum errors. Moreover, the constructed code can detect the length, the number and even the exact location of the occurring errors in the listed error event.

DOI
10.1360/jos171133

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A special quantum error correction scheme is proposed to protect the flow of transmitted quantum information in complex channels. Based on the derived syndrome, an algorithm is devised for the construction of the called quantum event-error correction code, which can correct simultaneously random and burst quantum errors. Moreover, the constructed code can detect the length, the number and even the exact location of the occurring errors in the listed error event.
To simultaneously detect random and burst quantum errors which may be generalized as quantum event errors, a quantum error detection code, called the quantum event-error detection code, is first investigated in analogy to the classical event-error detection code. The proposed code can be used to detect the length, number and location of errors occurring in every error event. Two special quantum event-error detection codes are constructed by exploiting different approaches according to the derived syndrome, and their number-bound of generators of the stabilizer is also derived. Finally, the proposed theory on the quantum event-error detection code for quantum single-event error is extended to a more general case, i.e., the quantum composite-event error, so that the general quantum event-error detection code can be constructed.
A novel quantum detection code is first proposed, analogous to the classic event-error detection code, which can detect simultaneously random and burst quantum errors. The proposed code, called quantum event-error detection code, can detect the length, number and location of the quantum errors in every listed quantum error event. Especially, two kinds of quantum event-error detection codes are constructed. To construct the optimal quantum event-error detection code, the number-bound of the stabilizer generators is investigated.
In practical communication and computation systems, errors occur predominantly in adjacent positions rather than in a random manner. In this paper, we develop a stabilizer formalism for quantum burst error correction codes (QBECC) to combat such error patterns in the quantum regime. Our contributions are as follows. Firstly, we derive an upper bound for the correctable burst errors of QBECCs, the quantum Reiger bound (QRB). Secondly, we propose two constructions of QBECCs: one by heuristic computer search and the other by concatenating two quantum tensor product codes (QTPCs). We obtain several new QBECCs with better parameters than existing codes with the same coding length. Moreover, some of the constructed codes can saturate the quantum Reiger bounds. Finally, we perform numerical experiments for our constructed codes over Markovian correlated depolarizing quantum memory channels, and show that QBECCs indeed outperform standard QECCs in this scenario.