Related papers: Accuracy of the box-counting algorithm for noisy f…
The main challenge of quantum computing on its way to scalability is the erroneous behaviour of current devices. Understanding and predicting their impact on computations is essential to counteract these errors with methods such as quantum…
We formulate a scheme for fault-tolerant quantum computation that works effectively against highly biased noise, where dephasing is far stronger than all other types of noise. In our scheme, the fundamental operations performed by the…
We have developed a fast, accurate and generally applicable method for inferring the power spectrum and its uncertainties from maps of the cosmic microwave background (CMB) in the presence of inhomogeneous and correlated noise. For maps…
The box counting dimension $d_C$ and the correlation dimension $d_G$ change with the number of numerically generated points forming the attractor. At a sufficiently large number of points the fractal dimension tends to a finite value. The…
Guessing random additive noise decoding (GRAND) algorithm has emerged as an excellent decoding strategy that can meet both the high reliability and low latency constraints. This paper proposes a successive addition-subtraction algorithm to…
We study the kinetics of random sequential adsorption of a mixture of particles with continuous distribution of sizes for different deposition rules. It appears in the long time limit the resulting system can be described using the fractal…
Measurement based quantum computation (MBQC) is an effective paradigm for universal quantum computation. In this scheme, the universal set of quantum gates are realized by only local measurements on the prior prepared cluster states. The…
Fractal dimension is defined on the base of entropy, including macro state entropy and information entropy. The generalized correlation dimension of multifractals is based on Renyi entropy. However, the mathematical transform from entropy…
Forthcoming high-resolution observations of the Cosmic Microwave Background (CMB) radiation will generate datasets many orders of magnitude larger than have been obtained to date. The size and complexity of such datasets presents a very…
It has recently been observed that a stochastic (infinite degree of freedom) time series with a $1/f^\alpha$ power spectrum can exhibit a finite correlation dimension, even for arbitrarily large data sets. [A.R. Osborne and A.~Provenzale,…
The estimation of parameters characterizing dynamical processes is central to science and technology. The estimation error changes with the number N of resources employed in the experiment (which could quantify, for instance, the number of…
Quantum advantage requires overcoming noise-induced degradation of quantum systems. Conventional methods for reducing noise such as error mitigation face scalability issues in deep circuits. Specifically, noise hampers the extraction of…
Fractals such as the Cantor set can be equipped with intrinsic arithmetic operations (addition, subtraction, multiplication, division) that map the fractal into itself. The arithmetics allows one to define calculus and algebra intrinsic to…
Sampling from the output distribution of chaotic quantum evolutions, and of pseudo-random universal quantum circuits in particular, has been proposed as a prominent milestone for near-term quantum supremacy. The same paper notes that…
The fractal or Hausdorff dimension is a measure of roughness (or smoothness) for time series and spatial data. The graph of a smooth, differentiable surface indexed in $\mathbb{R}^d$ has topological and fractal dimension $d$. If the surface…
We study the fractal scaling of iso-levels sets of a passive scalar mixed by three-dimensional homogeneous and isotropic turbulence at high Reynolds numbers. The Schmidt number is unity. A fractal box-counting dimension $D_F$ can be…
The development of algorithmic fractal dimensions in this century has had many fruitful interactions with geometric measure theory, especially fractal geometry in Euclidean spaces. We survey these developments, with emphasis on connections…
We present a number models describing the sequential deposition of a mixture of particles whose size distribution is determined by the power-law $p(x) \sim \alpha x^{\alpha-1}$, $x\leq l$ . We explicitly obtain the scaling function in the…
As quantum computing hardware steadily increases in qubit count and quality, one important question is how to allocate these resources to mitigate the effects of hardware noise. In a transitional era between noisy small-scale and fully…
Cohesive particles form agglomerates that are usually very porous. Their geometry, particularly their fractal dimension, depends on the agglomeration process (diffusion-limited or ballistic growth by adding single particles or…