Construction and Performance of Quantum Burst Error Correction Codes for Correlated Errors

Abstract

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). This bound generalizes the quantum Singleton bound for standard quantum error correction codes (QECCs). 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.

Burst error-correcting quantum stabilizer codes designed from idempotents

“…The burst length of an error = ( i ) ∈ G n is defined as the largest integer 1 ≤ l ≤ n such that i = 0 and i+l−1 = 0 for some 1 ≤ i ≤ n, denoted by bl( ) = l. A code C is said to be a l burst error-correcting code if every burst error of length at most l is correctable. An important lower bound, namely the quantum Rieger bound which arose from the no-cloning theorem, was constructed in [25] and is given as follows:…”

Some Progress on Quantum Error Correction for Discrete and Continuous Error Models

“…Another kind of modified discrete error models aims for errors occurring predominantly in adjacent positions since entanglement in quantum circuits mainly exists among local qubits. The approach to correct such errors rather than errors occurring in random places is the quantum burst error correcting code [49]. The burst length bl(•) of an error E is counted by the number of places that are nonidentity consecutively.…”