Related papers: Stabilizer quantum codes from $J$-affine variety c…
We develop a framework for the classification of invertible translation-invariant stabilizer codes modulo condensation and stabilization with simple codes. We introduce generalizations of the Pauli groups of local unitaries for quantum…
We solve one of the oldest problems in the theory of quantum stabilizer codes by proving the non-existence of quantum [[13,5,4]]-codes.
Quantum synchronizable codes are quantum error-correcting codes designed to correct the effects of both quantum noise and block synchronization errors. While it is known that quantum synchronizable codes can be constructed from cyclic codes…
New infinite families of quantum symmetric and asymmetric codes are constructed. Several of these are MDS. The codes obtained are shown to have parameters which are better than previously known. A number of known codes are special cases of…
Entanglement is essential for quantum information processing, but is limited by noise. We address this by developing high-yield entanglement distillation protocols with several advancements. (1) We extend the 2-to-1 recurrence entanglement…
We consider the problem of a generic stabilizer Hamiltonian under local, incoherent Pauli errors. Using two different approaches -- (i) Haah's polynomial formalism arXiv:1204.1063 and (ii) the homological perspective on CSS codes -- we…
We present an algorithm for manipulating quantum information via a sequence of projective measurements. We frame this manipulation in the language of stabilizer codes: a quantum computation approach in which errors are prevented and…
We provide a construction for quantum codes (hermitian-self-orthogonal codes over GF(4)) starting from cyclic codes over GF(4^m). We also provide examples of these codes some of which meet the known bounds for quantum codes.
We classify the time complexities of three important decoding problems for quantum stabilizer codes. First, regardless of the channel model, quantum bounded distance decoding is shown to be NP-hard, like what Berlekamp, McEliece and Tilborg…
A new type of local-check additive quantum code is presented. Qubits are associated with edges of a 2-dimensional lattice whereas the stabilizer operators correspond to the faces and the vertices. The boundary of the lattice consists of…
We present a geometric framework for constructing additive and non-additive stabiliser codes which encompasses stabiliser codes and graphical non-additive stabiliser codes.
In this paper, by using matrix product codes, several classes of new quantum codes are obtained. Moreover, some of them have better parameters than the previous quantum codes available.
We report new construction of nine-qubit error-correcting code, which introduces two new nine-qubit codes and one new three-qubit code. Because both the new two nine-qubit codes have the normal logical operators, as opposed to the…
While stabilizer tableaus have proven useful as a descriptive tool for additive quantum codes, they otherwise offer little guidance for concrete constructions or algorithm analysis. We introduce a representation of stabilizer codes as…
To implement a quantum error correction protocol, we first need a scheme to prepare our state in the correct subspace of the code, and this can be done using a unitary encoding circuit. Majorana codes are special since any gates that…
To improve the efficiency of the encoding and the decoding is the important problem in the quantum error correction. In a preceding work, a general algorithm for decoding the stabilizer code is shown. This paper will show an decoding which…
Classical BCH codes that contain their (Euclidean or Hermitian) dual codes can be used to construct quantum stabilizer codes; this correspondence studies the properties of such codes. It is shown that a BCH code of length n can contain its…
Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…
Calderbank, Rains, Shor and Sloane (see \cite{Sloane}) showed that error-correction is possible in the context of quantum computations. Quantum stabilizer codes are a class of additive quaternary codes in binary projective spaces, which are…
The performance of quantum error correction can be significantly improved if detailed information about the noise is available, allowing to optimize both codes and decoders. It has been proposed to estimate error rates from the syndrome…