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Quantum computers have the potential to provide exponential speedups over their classical counterparts. Quantum principles are being applied to fields such as communications, information processing, and artificial intelligence to achieve…
In order to use quantum error-correcting codes to actually improve the performance of a quantum computer, it is necessary to be able to perform operations fault-tolerantly on encoded states. I present a general theory of fault-tolerant…
While 2-level systems, aka qubits, are a natural choice to perform a logical quantum computation, the situation is less clear at the physical level. Encoding information in higher-dimensional physical systems can indeed provide a first…
Quantum error correction protocols will play a central role in the realisation of quantum computing; the choice of error correction code will influence the full quantum computing stack, from the layout of qubits at the physical level to…
We investigate various aspects of operator quantum error-correcting codes or, as we prefer to call them, subsystem codes. We give various methods to derive subsystem codes from classical codes. We give a proof for the existence of subsystem…
Quantum error correction (QEC) is a way to protect quantum information against noise. It consists of encoding input information into entangled quantum states known as the code space. Furthermore, to classify if the encoded information is…
A new class of error-correcting quantum codes is introduced capable of stabilizing qubits against spontaneous decay arising from couplings to statistically independent reservoirs. These quantum codes are based on the idea of using an…
The main ideas of quantum error correction are introduced. These are encoding, extraction of syndromes, error operators, and code construction. It is shown that general noise and relaxation of a set of 2-state quantum systems can always be…
Recent progress in quantum cryptography and quantum computers has given hope to their imminent practical realization. An essential element at the heart of the application of these quantum systems is a quantum error correction scheme. We…
Noise is one of the central obstacles to building useful quantum computers, and quantum error correction (QEC) provides the framework for protecting quantum information against it. Unlike classical error correction, QEC must preserve…
Quantum information science strives to leverage the quantum-mechanical nature of our universe in order to achieve large improvements in certain information processing tasks. In deep-space optical communications, current receivers for the…
We introduce a generalisation of quantum error correction, relaxing the requirement that a code should identify and correct a set of physical errors on the Hilbert space of a quantum computer exactly, instead allowing recovery up to a…
Quantum error correction and the use of quantum error correction codes is likely to be essential for the realisation of practical quantum computing. Because the error models of quantum devices vary widely, quantum codes which are tailored…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
Quantum computers are a revolutionary class of computational platforms with applications in combinatorial and global optimization, machine learning, and other domains involving computationally hard problems. While these machines typically…
Codeword stabilized (CWS) codes are a general class of quantum codes that includes stabilizer codes and many families of non-additive codes with good parameters. For such a non-additive code correcting all t-qubit errors, we propose an…
We present a generalization of quantum error correction to infinite-dimensional Hilbert spaces. The generalization yields new classes of quantum error correcting codes that have no finite-dimensional counterparts. The error correction…
The constituent parts of a quantum computer are inherently vulnerable to errors. To this end we have developed quantum error-correcting codes to protect quantum information from noise. However, discovering codes that are capable of a…
Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to…
Quantum error-correction codes (QECCs) are a vital ingredient of quantum computation and communication systems. In that context it is highly desirable to design QECCs that can be represented by graphical models which possess a structure…