Quantum error correction for beginners

By Simon J. Devitt, William J. Munro, Kae Nemoto. Reports on progress in physics. Physical Society, 2009

832 citations recorded by the source corpus.

Quantum error correction (QEC) and fault-tolerant quantum computation represent one of the most vital theoretical aspects of quantum information processing. It was well known from the early developments of this exciting field that the fragility of coherent quantum systems would be a catastrophic obstacle to the development of large-scale quantum computers. The introduction of quantum error correction in 1995 showed that active techniques could be employed to mitigate this fatal problem. However, quantum error correction and fault-tolerant computation is now a much larger field and many new codes, techniques, and methodologies have been developed to implement error correction for large-scale quantum algorithms. In response, we have attempted to summarize the basic aspects of quantum error correction and fault-tolerance, not as a detailed guide, but rather as a basic introduction. The development in this area has been so pronounced that many in the field of quantum information, specifically researchers who are new to quantum information or people focused on the many other important issues in quantum computation, have found it difficult to keep up with the general formalisms and methodologies employed in this area. Rather than introducing these concepts from a rigorous mathematical and computer science framework, we instead examine error correction and fault-tolerance largely through detailed examples, which are more relevant to experimentalists today and in the near future.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/ac9aba1ad40274295ee2c8a6b8057dc6e16448a8

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Materials challenges and opportunities for quantum computing hardware (2021, background): “Quantum error correction provides a means to account for and make use of these changes to enable low-error computations (5), but it requires significantly increased system scale and highly precise operations.”
Distributed Quantum Computing: a Survey (2022, neutral): “This is a novel approach for simulating quantum networks, adapted from quantum error correction [114].”
Simulating quantum many-body dynamics on a current digital quantum computer (2019, background): “Although this is primarily an engineering issue to increase the quality, isolation and control of the devices, there is also the theoretical contribution of error correction methods [1, 82, 83].”
Inside Quantum Repeaters (2015, methodology): “Instead one can use one-way quantum EDC or quantum error correction codes (ECC) [42], [44], [63], [64] which we schematically illustrate in Fig.”
Quantum error correction: an introductory guide (2019, background): “Many reviews have been written covering quantum error correction and its associated subfields [27–33].”
Quantum computing with atomic qubits and Rydberg interactions: progress and challenges (2016, background): “Roughly speaking larger codes can tolerate gates with higher errors[7, 8], with large scale surface codes that combine hundreds of physical qubits to create a single logical qubit having threshold error rates ∼ 0.”