Related papers: Automated searching for quantum subsystem codes
The most general method for encoding quantum information is not to encode the information into a subspace of a Hilbert space, but to encode information into a subsystem of a Hilbert space. Recently this notion has led to a more general…
We present a method of concatenated quantum error correction in which improved classical processing is used with existing quantum codes and fault-tolerant circuits to more reliably correct errors. Rather than correcting each level of a…
Operator quantum error correction provides a unified framework for the known techniques of quantum error correction such as the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method.…
A promising approach to overcome decoherence in quantum computing schemes is to perform active quantum error correction using topology. Topological subsystem codes incorporate both the benefits of topological and subsystem codes, allowing…
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…
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…
The essential insight of quantum error correction was that quantum information can be protected by suitably encoding this quantum information across multiple independently erred quantum systems. Recently it was realized that, since the most…
Due to the fragility of quantum mechanical effects, real quantum computers are plagued by frequent noise effects that cause errors during computations. Quantum error-correcting codes address this problem by providing means to identify and…
Quantum error correction codes are usually designed to correct errors regardless of their physical origins. In large-scale devices, this is an essential feature. In smaller-scale devices, however, the main error sources are often…
Performing experiments on small-scale quantum computers is certainly a challenging endeavor. Many parameters need to be optimized to achieve high-fidelity operations. This can be done efficiently for operations acting on single qubits as…
Proposals for quantum computing devices are many and varied. They each have unique noise processes that make none of them fully reliable at this time. There are several error correction/avoidance techniques which are valuable for reducing…
Construction of a fault-tolerant quantum computer remains a challenging problem due to unavoidable noise in quantum states and the fragility of quantum entanglement. However, most of the error-correcting codes increases the complexity of…
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…
In this paper we investigate the encoding of operator quantum error correcting codes i.e. subsystem codes. We show that encoding of subsystem codes can be reduced to encoding of a related stabilizer code making it possible to use all the…
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…
The importance of quantum error correction in paving the way to build a practical quantum computer is no longer in doubt. This dissertation makes a threefold contribution to the mathematical theory of quantum error-correcting codes.…
Quantum error correction is a set of methods to protect quantum information--that is, quantum states--from unwanted environmental interactions (decoherence) and other forms of noise. The information is stored in a quantum error-correcting…
Quantum error correcting codes have been developed to protect a quantum computer from decoherence due to a noisy environment. In this paper, we present two methods for optimizing the physical implementation of such error correction schemes.…
Quantum error correction protects quantum information against environmental noise. When using qubits, a measure of quality of a code is the maximum number of errors that it is able to correct. We show that a suitable notion of ``number of…
Active quantum error correction using qubit stabilizer codes has emerged as a promising, but experimentally challenging, engineering program for building a universal quantum computer. In this review we consider the formalism of qubit…