Related papers: Codes as fractals and noncommutative spaces
We consider a model of non-commutative Quantum Mechanics given by two harmonic oscillators over a non-commutative two dimensional configuration space. We study possible ways of removing the non-commutativity based on the classical limit…
We present a construction of self-orthogonal codes using product codes. From the resulting codes, one can construct both block quantum error-correcting codes and quantum convolutional codes. We show that from the examples of convolutional…
While stabilizer tableaus have proven exceptionally useful as a descriptive tool for additive quantum codes, they offer little guidance for concrete constructions or coding algorithm analysis. We introduce a representation of stabilizer…
In this paper, some nonbinary quantum codes using classical codes over Gaussian integers are obtained. Also, some of our quantum codes are better than or comparable with those known before, (for instance [[8; 2; 5]]4+i).
Quantum correlations can be naturally formulated in a classical statistical system of infinitely many degrees of freedom. This realizes the underlying non-commutative structure in a classical statistical setting. We argue that the quantum…
Quantum synchronizable codes are kinds of quantum error-correcting codes that can not only correct the effects of quantum noise on qubits but also the misalignment in block synchronization. In this paper, the quantum synchronizable codes…
We formally define homological quantum rotor codes which use multiple quantum rotors to encode logical information. These codes generalize homological or CSS quantum codes for qubits or qudits, as well as linear oscillator codes which…
Stabilizer codes form an important class of quantum error correcting codes which have an elegant theory, efficient error detection, and many known examples. Constructing stabilizer codes of length $n$ is equivalent to constructing subspaces…
The use of geometric methods has proved useful in the hamiltonian description of classical constrained systems. In this note we provide the first steps toward the description of the geometry of quantum constrained systems. We make use of…
We construct explicitly two infinite families of genuine nonadditive 1-error correcting quantum codes and prove that their coding subspaces are 50% larger than those of the optimal stabilizer codes of the same parameters via the linear…
We construct an infinite-dimensional analog of the HaPPY code as a growing series of stabilizer codes defined respective to their Hilbert spaces. The Hilbert spaces are related by isometric maps, which we define explicitly. We construct a…
The discovery of holographic codes established a surprising connection between quantum error correction and the anti-de Sitter-conformal field theory correspondence. Recent technological progress in artificial quantum systems renders the…
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.…
This study analyzes the geometrical relationship between a classical string and its semi-classical quantum model. From an arbitrary $(2+1)-$dimensional geometry, a specific ansatz for a classical string is used to generate a semi-classical…
Matrix configurations coming from matrix models comprise many important aspects of modern physics. They represent special quantum spaces and are thus strongly related to noncommutative geometry. In order to establish a semiclassical limit…
We present a quantum compilation algorithm that maps Clifford encoders, encoding maps for stabilizer quantum codes, to a unique graphical representation in the ZX calculus. Specifically, we develop a canonical form in the ZX calculus and…
We combine the coordinate method and Erlangen program in the framework of noncommutative geometry through an investigation of symmetries of noncommutative coordinate algebras. As the model we use the coherent states construction and the…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
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…
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…