Related papers: Stabilizer quantum codes defined by trace-dependin…
We introduce a new class of evaluation linear codes by evaluating polynomials at the roots of a suitable trace function. We give conditions for self-orthogonality of these codes and their subfield-subcodes with respect to the Hermitian…
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-correcting codes aim to protect information in quantum systems to enable fault-tolerant quantum computations. The most prevalent method, stabilizer codes, has been well developed for many varieties of systems, however, largely…
We describe the theory of quantum convolutional error correcting codes. These codes are aimed at protecting a flow of quantum information over long distance communication. They are largely inspired by their classical analogs which are used…
We establish the connection between a recent new construction technique for quantum error correcting codes, based on graphs, and the so-called stabilizer codes: Each stabilizer code can be realized as a graph code and vice versa.
Controlling operational errors and decoherence is one of the major challenges facing the field of quantum computation and other attempts to create specified many-particle entangled states. The field of quantum error correction has developed…
One central theme in quantum error-correction is to construct quantum codes that have a large minimum distance. In this paper, we first present a construction of classical codes based on certain class of polynomials. Through these classical…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
Stabilizer codes form an important class of quantum error correcting codes which have an elegant theory, efficient error detection, and many known examples. Constructing stabilizer codes of length $n$ is equivalent to constructing subspaces…
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…
We present a unifying approach to quantum error correcting code design that encompasses additive (stabilizer) codes, as well as all known examples of nonadditive codes with good parameters. We use this framework to generate new codes with…
Typical stabilizer codes aim to solve the general problem of fault-tolerance without regard for the structure of a specific system. By incorporating a broader representation-theoretic perspective, we provide a generalized framework that…
We show that within any quantum stabilizer code there lurks a classical binary linear code with similar error-correcting capabilities, thereby demonstrating new connections between quantum codes and classical codes. Using this result --…
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…
New stabilizer codes with parameters better than the ones available in the literature are provided in this work, in particular quantum codes with parameters $[[127,63, \geq 12]]_2$ and $[[63,45, \geq 6]]_4$ that are records. These codes are…
In quantum coding theory, stabilizer codes are probably the most important class of quantum codes. They are regarded as the quantum analogue of the classical linear codes and the properties of stabilizer codes have been carefully studied in…
Quantum convolutional code was introduced recently as an alternative way to protect vital quantum information. To complete the analysis of quantum convolutional code, I report a way to decode certain quantum convolutional codes based on the…
We give an introduction to the theory of quantum error correction using stabilizer codes that is geared towards the working computer scientists and mathematicians with an interest in exploring this area. To this end, we begin with an…
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…
We study, by means of the stabilizer formalism, a quantum error correcting code which is alternative to the standard block codes since it embeds a qubit into a qudit. The code exploits the non-commutative geometry of discrete phase space to…