A survey on quantum error correcting codes

Josu Etxezarreta Martínez, Patricio Fuentes, Pedro M. Crespo +1 more

Quantum information is prone to suffer from errors caused by the so-called decoherence, which describes the loss in coherence of quantum states associated to their interactions with the surrounding environment. This decoherence phenomenon is present in every quantum information task, be it transmission, processing or even storage of quantum information. Consequently, the protection of quantum information via quantum error correction codes (QECC) is of paramount importance to construct fully operational quantum computers. Understanding environmental decoherence processes and the way they are modeled is fundamental in order to construct effective error correction methods capable of protecting quantum information. Moreover, quantum channel models that are efficiently implementable and manageable on classical computers are required in order to design and simulate such error correction schemes. In this article, we present a survey of decoherence models, reviewing the manner in which these models can be approximated into quantum Pauli channel models, which can be efficiently implemented on classical computers. We also explain how certain families of quantum error correction codes can be entirely simulated in the classical domain, without the explicit need of a quantum computer. A quantum error correction code for the approximated channel is also a correctable code for the original channel, and its performance can be obtained by Monte Carlo simulations on a classical computer.

Shayan Srinivasa Garani, Priya J. Nadkarni, Ankur Raina

Bei Zeng, Xie Chen, D. L. Zhou +1 more

Linh Nguyen, Quoc Bao Phan, Ivan B. Djordjević +1 more

In the era of sixth-generation (6G) communications, quantum technologies are expected to serve as foundational components for future network infrastructure. However, the inherently fragile nature of quantum states, susceptible to environmental noise and hardware operational errors, creates an urgent demand for effective mechanisms to protect information. This article provides a comprehensive survey of quantum error correction codes (QECCs), spanning from the inception of the field through 2026, with a specific focus on their role as an essential reliability layer within the 6G ecosystem. The survey presents an overview of the transition from classical ECC to QECC, while systematically organizing the foundations, evolution, and classification of key QECC families. We conduct an in-depth analysis of their structural properties in relation to scalability, locality, and distributed operation. Furthermore, the article delves into a detailed discussion of encoding techniques, syndrome extraction, and practical implementation challenges. In particular, we emphasize the approach of hardware-software co-design and analyze the bandwidth-latency trade-offs inherent in distributed quantum communication environments. By identifying open challenges and emerging trends leading up to 2026, this article outlines a strategic roadmap for integrating reliability mechanisms into the infrastructure of the future quantum internet.

Giuliano G. La Guardia

Zunaira Babar, Daryus Chandra, Hung Viet Nguyen +4 more

Quantum error correction codes (QECCs) can be constructed from the known classical coding paradigm by exploiting the inherent isomorphism between the classical and quantum regimes, while also addressing the challenges imposed by the strange laws of quantum physics. In this spirit, this paper provides deep insights into the duality of quantum and classical coding theory, hence aiming for bridging the gap between them. Explicitly, we survey the rich history of both classical as well as quantum codes. We then provide a comprehensive slow-paced tutorial for constructing stabilizer-based QECCs from arbitrary binary as well as quaternary codes, as exemplified by the dual-containing and non-dual-containing Calderbank-Shor-Steane (CSS) codes, non-CSS codes and entanglement-assisted codes. Finally, we apply our discussions to two popular code families, namely to the family of Bose-Chaudhuri-Hocquenghem as well as of convolutional codes and provide detailed design examples for both their classical as well as their quantum versions.