Related papers: A Construction of Quantum Stabilizer Codes from Cl…
Divisible codes are defined by the property that codeword weights share a common divisor greater than one. They are used to design signals for communications and sensing, and this paper explores how they can be used to protect quantum…
Universal quantum computation requires the implementation of a logical non-Clifford gate. In this paper, we characterize all stabilizer codes whose code subspaces are preserved under physical $T$ and $T^{-1}$ gates. For example, this could…
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…
In this paper, we introduce a new family of stabilizer quantum LDPC codes derived from the classical linear codes $L_k$ and $L_k^{+}$, defined via sub-exceding functions. In previous work, these codes demonstrated strong performance in…
The standard stabilizer formalism provides a setting to show that quantum computation restricted to operations within the Clifford group are classically efficiently simulable: this is the content of the well-known Gottesman-Knill theorem.…
In this work, we define Generalized Monomial Cartesian Codes (GMCC), which constitute a natural extension of generalized Reed-Solomon codes. We describe how two different generalized Reed-Solomon codes can be combined to construct one GMCC.…
We characterize the affine-invariant maximal extended cyclic codes. Then by the CSS construction, we derive from these codes a family of pure quantum codes. Also for ordnq even, a new family of degenerate quantum stabilizer codes is derived…
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…
We show how good quantum error-correcting codes can be constructed using generalized concatenation. The inner codes are quantum codes, the outer codes can be linear or nonlinear classical codes. Many new good codes are found, including both…
The CSS code construction is a powerful framework used to express features of a quantum code in terms of a pair of underlying classical codes. Its subsystem extension allows for similar expressions, but the general case has not been fully…
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…
Convolutional stabilizer codes promise to make quantum communication more reliable with attractive online encoding and decoding algorithms. This paper introduces a new approach to convolutional stabilizer codes based on direct limit…
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…
Random classical linear codes are widely believed to be hard to decode. While slightly sub-exponential time algorithms exist when the coding rate vanishes sufficiently rapidly, all known algorithms at constant rate require exponential time.…
There has been a lot of effort to construct good quantum codes from the classical error correcting codes. Constructing new quantum codes, using Hermitian self-orthogonal codes, seems to be a difficult problem in general. In this paper,…
Two methods for constructing quantum LDPC codes are presented. We explain how to overcome the difficulty of finding a set of low weight generators for the stabilizer group of the code. Both approaches are based on some graph representation…
Construction of quantum codes and entanglement-assisted quantum codes with good parameters via classical codes is an important task for quantum computing and quantum information. In this paper, by a family of one-generator quasi-cyclic…
We construct toric codes on various high-dimensional manifolds. Assuming a conjecture in geometry we find families of quantum CSS stabilizer codes on $N$ qubits with logarithmic weight stabilizers and distance $N^{1-\epsilon}$ for any…
Quantum replacer codes are codes that can be protected from errors induced by a given set of quantum replacer channels, an important class of quantum channels that includes the erasures of subsets of qubits that arise in quantum error…
Implementing robust quantum error correction (QEC) is imperative for harnessing the promise of quantum technologies. We introduce a framework that takes {\it any} classical code and explicitly constructs the corresponding QEC code. Our…