Related papers: MDS Stabilizer Poset Codes
Quantum error-correcting codes with good parameters can be constructed by evaluating polynomials at the roots of the polynomial trace. In this paper, we propose to evaluate polynomials at the roots of trace-depending polynomials (given by a…
Subsystem codes are the most versatile class of quantum error-correcting codes known to date that combine the best features of all known passive and active error-control schemes. The subsystem code is a subspace of the quantum state space…
Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. It is very hard to construct quantum MDS codes with relatively large minimum distance. In this paper, based on classical constacyclic codes, we…
Quantum maximum-distance-separable (MDS) codes are an important class of quantum codes. In this paper, using constacyclic codes and Hermitain construction, we construct some new quantum MDS codes of the form $q=2am+t$,…
Stabilizer codes obtained via CSS code construction and Steane's enlargement of subfield-subcodes and matrix-product codes coming from generalized Reed-Muller, hyperbolic and affine variety codes are studied. Stabilizer codes with good…
Let $q$ be a prime power. Let $\lambda>1$ be a divisor of $q-1$, and let $\tau>1$ and $\rho>1$ be divisors of $q+1$. Under certain conditions we prove that there exists an MDS stabilizer quantum code with length $n=\lambda \tau \sigma$…
The concept of generalized concatenated quantum codes (GCQC) provides a systematic way for constructing good quantum codes from short component codes. We introduce a stabilizer formalism for GCQCs, which is achieved by defining quantum…
We propose two types, namely Type-I and Type-II, quantum stabilizer codes using quadratic residue sets of prime modulus given by the form $p=4n\pm1$. The proposed Type-I stabilizer codes are of cyclic structure and code length $N=p$. They…
Symbol-pair codes are block codes with symbol-pair metrics designed to protect against pair-errors that may occur in high-density data storage systems. MDS symbol-pair codes are optimal in the sense that it can attain the highest pair-error…
In this paper we consider stabilizer codes over local Frobenius rings. First, we study the relative minimum distances of a stabilizer code and its reduction onto the residue field. We show that for various scenarios, a free stabilizer code…
In this paper, we establish the Singleton bound for pomset block codes ($(Pm,\pi)$-codes) of length $N$ over the ring $\mathbb{Z}_m$. We give a necessary condition for a code to be MDS in the pomset (block) metric and prove that every MDS…
Stabilizer codes are the most widely studied class of quantum error-correcting codes and form the basis of most proposals for a fault-tolerant quantum computer. A stabilizer code is defined by a set of parity-check operators, which are…
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…
Magic State Distillation (MSD) has been a research focus for fault-tolerant quantum computing due to the need for non-Clifford resource in gaining quantum advantage. Although many of the MSD protocols so far are based on stabilizer codes…
We define a multi-partite entanglement measure for stabilizer states, which can be computed efficiently from a set of generators of the stabilizer group. Our measure applies to qubits, qudits and continuous variables.
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…
General isometries of cyclic codes, including multipliers and translations, are introduced; and isometrically self-dual cyclic codes are defined. In terms of Type-I duadic splittings given by multipliers and translations, a necessary and…
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…
Quantum error correction requires the use of error syndromes derived from measurements that may be unreliable. Recently, quantum data-syndrome (QDS) codes have been proposed as a possible approach to protect against both data and syndrome…
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…