Related papers: Fractalizing quantum codes
In recent years, the rise of deep learning and automation requirements in the software industry has elevated Intelligent Software Engineering to new heights. The number of approaches and applications in code understanding is growing, with…
Classical coding theory contains several techniques to obtain new codes from other codes, including puncturing and shortening. For quantum codes, a form of puncturing is known, but its description is based on the code space rather than its…
We have found a quantum cloning machine that optimally duplicates the entanglement of a pair of $d$-dimensional quantum systems. It maximizes the entanglement of formation contained in the two copies of any maximally-entangled input state,…
The study of gapped quantum many-body systems in three spatial dimensions has uncovered the existence of quantum states hosting quasiparticles that are confined, not by energetics but by the structure of local operators, to move along lower…
We construct a family of exactly solvable spin models that illustrate a novel mechanism for fractionalization in topologically ordered phases, dubbed the string flux mechanism. The essential idea is that an anyon of a topological phase can…
We construct meta-intransitive systems of independent random variables of any finite order from basic tuple of random variables which generalize intransitive dice. Under this construction, the equality of some linear functional is…
A way to add an extra dimension is briefly discussed.
Expectation propagation is a general approach to fast approximate inference for graphical models. The existing literature treats models separately when it comes to deriving and coding expectation propagation inference algorithms. This comes…
We study the fractionalization of space group symmetries in two-dimensional topologically ordered phases. Specifically, we focus on Z2-fractionalized phases in two dimensions whose deconfined topological excitations transform trivially…
We review what is known about fracton phases of quantum matter. Fracton phases are characterized by excitations that exhibit restricted mobility, being either immobile under local Hamiltonian dynamics, or mobile only in certain directions.…
Gauging is a ubiquitous tool in many-body physics. It allows one to construct highly entangled topological phases of matter from relatively simple phases and to relate certain characteristics of the two. Here we develop a gauging procedure…
Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling…
Quantum spin networks overcome the challenges of traditional charge-based electronics by encoding the information into spin degrees of freedom. Although beneficial for transmitting information with minimal losses when compared to their…
It is shown that fractal dimension can be estimated seeking a solution of functional equation defined for areas of coverages of different scales. The method proposed is compared with widely known way to estimate fractal dimension via linear…
Identification of cracks is essential to assess the structural integrity of concrete infrastructure. However, robust crack segmentation remains a challenging task for computer vision systems due to the diverse appearance of concrete…
The fractal structure of real world objects is often analyzed using digital images. In this context, the compression fractal dimension is put forward. It provides a simple method for the direct estimation of the dimension of fractals stored…
The aim of this paper is to construct a fractal with the help of a finite family of generalized F-contraction mappings, a class of mappings more general than contraction mappings, defined in the setup of b-metric space. Consequently, we…
We study novel three-dimensional gapped quantum phases of matter which support quasiparticles with restricted mobility, including immobile "fracton" excitations. So far, most existing fracton models may be instructively viewed as…
In this work, we introduce a technique for reducing the length of a quantum stabilizer code, and we call this deflation of the code. Deflation can be seen as a generalization of the well-known puncturing and shortening techniques in cases…
A mathematical method for constructing fractal curves and surfaces, termed the $p\lambda n$ fractal decomposition, is presented. It allows any function to be split into a finite set of fractal discontinuous functions whose sum is equal…