Related papers: Quantum-Circuit-Based Visual Fractal Image Generat…
In quantum information processing it may be possible to have efficient computation and secure communication beyond the limitations of classical systems. In a fundamental point of view, however, evolution of quantum systems by the laws of…
Scattering in complex media scrambles light, thus obscuring images and limiting applications from astronomy to microscopy. Existing computational and wavefront-shaping methods treat scattering as a linear optical-wave inversion problem that…
To help understand the underlying mechanisms of neural networks (NNs), several groups have, in recent years, studied the number of linear regions $\ell$ of piecewise linear functions generated by deep neural networks (DNN). In particular,…
The frequency of occurrence of prime numbers at unit number spacing intervals exhibits selfsimilar fractal fluctuations concomitant with inverse power law form for power spectrum generic to dynamical systems in nature such as fluid flows,…
The magnificence grandeur of quantum computing lies in the inherent nature of quantum particles to exhibit true parallelism, which can be realized by indubitably fascinating theories of quantum physics. The possibilities opened by quantum…
Two categories of results regarding quantum measurements are derived in this work and applied to the problem of collapse. The first category is concerned with local and transient features of the entanglement between a macroscopic measuring…
Quantum walks have been employed widely to develop new tools for quantum information processing recently. A natural quantum walk dynamics of interacting particles can be used to implement efficiently the universal quantum computation. In…
We explore the physical quantum properties of atoms in fractal spaces, both as a theoretical generalization of normal integer-dimensional Euclidean spaces and as an experimentally realizable setting. We identify the threshold of fractality…
When information is spatially repeated in self-similar fractal beam patterns, only a portion of the diffracted beam is needed to reconstruct the kernel data. What is unique to a fractal-encoding scheme is that the image demultiplexing…
Categorical Quantum Mechanics, and graphical calculi in particular, has proven to be an intuitive and powerful way to reason about quantum computing. This work continues the exploration of graphical calculi, inside and outside of the…
The term fractal describes a class of complex structures exhibiting self-similarity across different scales. Fractal patterns can be created by using various techniques such as finite subdivision rules and iterated function systems. In this…
The concept of self-similarity on subsets of algebraic varieties is defined by considering algebraic endomorphisms of the variety as `similarity' maps. Self-similar fractals are subsets of algebraic varieties which can be written as a…
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…
In this article, we considered a fractal image as a fractal curve, that is, as a walk on a grid in Euclidean space $\R^d$. We placed integers on the generating vectors of a grid, such that opposite directions have opposite numbers. This…
We show how local constraints can globally "shatter" Hilbert space into subsectors, leading to an unexpected dynamics with features reminiscent of both many body localization and quantum scars. A crisp example of this phenomenon is provided…
We discuss the formation of stochastic fractals and multifractals using the kinetic equation of fragmentation approach. We also discuss the potential application of this sequential breaking and attempt to explain how nature creats fractals.
Fractional evolution equations lack generally accessible and well-converged codes excepting anomalous diffusion. A particular equation of strong interest to the growing intersection of applied mathematics and quantum information science and…
A visualization scheme for quantum many-body wavefunctions is described, which we have termed qubism. Its main property is its recursivity: increasing the number of qubits reflects in an increase in the image resolution. Thus, the plots are…
The advent of Quantum Computing has influenced researchers around the world to solve multitudes of computational problems with the promising technology. Feasibility of solutions for computational problems, and representation of various…
Advances in the distribution of quantum information will likely require entanglement shared across a hybrid quantum network. Many entanglement protocols require the generation of indistinguishable photons between the various nodes of the…