Related papers: Subsystem Code Constructions
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…
This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer…
Quantum error-correcting codes (QECCs) and decoherence-free subspace (DFS) codes provide active and passive means, respectively, to address certain types of errors that arise during quantum computation. The latter technique is suitable to…
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…
In order to correct the pair-errors generated during the transmission of modern high-density data storage that the outputs of the channels consist of overlapping pairs of symbols, a new coding scheme named symbol-pair code is proposed. The…
Quantum synchronizable error-correcting codes are special quantum error-correcting codes that are designed to correct both the effect of quantum noise on qubits and misalignment in block synchronization. It is known that in principle such a…
A subspace code is a nonempty collection of subspaces of the vector space $\mathbb{F}_q^{n}$. A pair of linear codes is called a linear complementary pair (in short LCP) of codes if their intersection is trivial and the sum of their…
Leakage is a particularly damaging error that occurs when a qubit state falls out of its two-level computational subspace. Compared to independent depolarizing noise, leaked qubits may produce many more configurations of harmful correlated…
This paper introduces a construction of quantum CSS codes from a tuple of component CSS codes and two collections of subsets. The resulting codes have parallelizable encoding and syndrome measurement circuits and built-in redundancy in the…
We describe a quantum error correction scheme aimed at protecting a flow of quantum information over long distance communication. It is largely inspired by the theory of classical convolutional codes which are used in similar circumstances…
We construct a new family of quantum MDS codes from classical generalized Reed-Solomon codes and derive the necessary and sufficient condition under which these quantum codes exist. We also give code bounds and show how to construct them…
Topological subsystem codes proposed recently by Bombin are quantum error correcting codes defined on a two-dimensional grid of qubits that permit reliable quantum information storage with a constant error threshold. These codes require…
Quantum data-syndrome (QDS) codes are a class of quantum error-correcting codes that protect against errors both on the data qubits and on the syndrome itself via redundant measurement of stabilizer group elements. One way to define a QDS…
In this paper, we address the problem of state communication in finite-level quantum systems through noise-affected channels. Our approach is based on a self-consistent theory of decoding inner products associated with the code and error…
Subspace codes have received an increasing interest recently due to their application in error-correction for random network coding. In particular, cyclic subspace codes are possible candidates for large codes with efficient encoding and…
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…
A linear code with parameters $[n, k, n-k+1]$ is called a maximum distance separable (MDS for short) code. A linear code with parameters $[n, k, n-k]$ is said to be almost maximum distance separable (AMDS for short). A linear code is said…
Surface and color codes are two forms of topological quantum error correction in two spatial dimensions with complementary properties. Surface codes have lower-depth error detection circuits and well-developed decoders to interpret and…
We use a map to quantum error-correcting codes and a subspace projection to get lower bounds for minimal homological distances in a tensor product of two chain complexes of vector spaces over a finite field. Homology groups of such a…
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…