Related papers: Entanglement-assisted quantum error-correcting cod…
We show how entanglement-assisted codes can be constructed from arbitrary quantum codes by associating them with quantum codes for erasure channels. If a subset of physical qubits is correctable for an erasure error, then it naturally forms…
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 is fundamentally important for quantum information processing and computation. Quantum error correction codes have been studied and constructed since the pioneering papers of Shor and Steane. Optimal (called MDS)…
We provide a systematic way of constructing entanglement-assisted quantum error-correcting codes via graph states in the scenario of preexisting perfectly protected qubits. It turns out that the preexisting entanglement can help beat the…
Code concatenation combines two or more component codes to design larger codes with greater noise resilience. Introducing entanglement assistance to concatenated codes provides a further advantage in terms of improved error rates and…
We propose a linear-optical implementation of a hyperentanglement-assisted quantum error-correcting code. The code is hyperentanglement-assisted because the shared entanglement resource is a photonic state hyperentangled in polarization and…
We introduce a construction for entanglement-assisted quantum error-correcting codes (EAQECCs) that saturates the classical Singleton bound with less shared entanglement than any known method for code rates below $ \frac{k}{n} = \frac{1}{3}…
Using convex optimization, we propose entanglement-assisted quantum error correction procedures that are optimized for given noise channels. We demonstrate through numerical examples that such an optimized error correction method achieves…
In this paper, we study Euclidean and Hermitian hulls of generalized Reed-Solomon codes and twisted generalized Reed-Solomon codes, as well as the Hermitian hulls of Roth-Lempel typed codes. We present explicit constructions of MDS and AMDS…
Interleaved Reed-Solomon codes admit efficient decoding algorithms which correct burst errors far beyond half the minimum distance in the random errors regime, e.g., by computing a common solution to the Key Equation for each Reed-Solomon…
Entanglement-assisted quantum error correcting codes (EAQECCs) play a significant role in protecting quantum information from decoherence and quantum noise. Recently, constructing entanglement-assisted quantum maximum distance separable…
Entanglement-assisted concatenated quantum codes (EACQCs), constructed by concatenating two quantum codes, are proposed. These EACQCs show several advantages over the standard concatenated quantum codes (CQCs). Several families of EACQCs…
Connecting multiple smaller qubit modules by generating high-fidelity entangled states is a promising path for scaling quantum computing hardware. The performance of such a modular quantum computer is highly dependent on the quality and…
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…
Fracton topological phases have a large number of materialized symmetries that enforce a rigid structure on their excitations. Remarkably, we find that the symmetries of a quantum error-correcting code based on a fracton phase enable us to…
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…
One of the central tasks in quantum error-correction is to construct quantum codes that have good parameters. In this paper, we construct three new classes of quantum MDS codes from classical Hermitian self-orthogonal generalized…
Having protected quantum information is essential to perform quantum computations. One possibility is to reduce the number of particles needing to be protected from noise and instead use systems with more states, so called qudit quantum…
Series of maximum distance quantum error-correcting codes are developed and analysed. For a given rate and given error-correction capability, quantum error-correcting codes with these specifications are constructed. The codes are explicit…
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…