QBEL: Quantum Burst Error Locating Codes

Burst errors, which involve the corruption of consecutive symbols, are a more realistic and common type of error in many communication and storage systems. While classical codes for burst correction are well-established, quantum errorcorrecting codes that handle burst errors and error localization have been less explored. In this paper, we present constructions of quantum codes designed to locate and correct burst errors. We introduce a nearly optimal quantum error-locating burst code, which can identify an interval of $2 b$ qubits containing a burst of quantum errors of length at most $b$, improving upon previous constructions in terms of redundancy. This code leverages a stabilizer framework that is not based on the CSS (Calderbank-Shor-Steane) construction, offering a more efficient error-locating capability. Additionally, our construction can correct a large structured set of burst errors, specifically those of length $b$ that do not end with a $Y$ Pauli operator. We prove that the redundancy of this code is optimal with respect to this error set.