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Fault-tolerant schemes can use error correction to make a quantum computation arbitrarily ac- curate, provided that errors per physical component are smaller than a certain threshold and in- dependent of the computer size. However in…
There exists observational evidence that the interstellar medium has a fractal structure in a wide range of spatial scales. The measurement of the fractal dimension (Df) of interstellar clouds is a simple way to characterize this fractal…
This is an introduction to software methods of quantum fault tolerance. Broadly speaking, these methods describe strategies for using the noisy hardware components of a quantum computer to perform computations while continually monitoring…
A method is described for calculating the approximate fractal dimension from a set of N values y sampled from a waveform between time zero and t. The waveform was subjected to a double linear transformation that maps it into a unit square.
Algorithmic fractal dimensions -- constructs of computability theory -- have recently been used to answer open questions in classical geometric measure theory, questions of mathematical analysis whose statements do not involve computability…
We provide a rigorous study on dimensions of fractal interpolation function defined on a closed and bounded interval of $\mathbb{R}$ which is associated to a continuous function with respect to a base function, scaling functions and a…
We present a review of the history and the present state of the fractal approach to the large-scale distribution of galaxies. Angular correlation function was used as a general instrument for the structure analysis. It was realized later…
The computational cost of a Monte Carlo algorithm can only be meaningfully discussed when taking into account the magnitude of the resulting statistical error. Aiming for a fixed error per particle, we study the scaling behavior of the…
Particulate materials include powders, emulsions, composites, and many others. This is why measuring these has become important for both industry and scientific applications. For industrial applications, the greatest need is to measure…
A quantum computer -- i.e., a computer capable of manipulating data in quantum superposition -- would find applications including factoring, quantum simulation and tests of basic quantum theory. Since quantum superpositions are fragile, the…
The dimension of a bipartition matrix (BPM) is the sum of the dimensions of its indecomposable factors. The dimension of an indecomposable BPM is the sum of its row, column, and entry dimensions. To compute these dimensions, we apply four…
Characterizing and mitigating errors in current noisy intermediate-scale devices is important to improve performance of next generations of quantum hardware. In order to investigate the importance of the different noise mechanisms affecting…
Measurement fidelity matrices (MFMs) (also called error kernels) are a natural way to characterize state preparation and measurement errors in near-term quantum hardware. They can be employed in post processing to mitigate errors and…
Many young star clusters appear to be fractal, i.e. they appear to be concentrated in a nested hierarchy of clusters within clusters. We present a new algorithm for statistically analysing the distribution of stars to quantify the level of…
We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…
Recently we find several candidates of quantum algorithms that may be implementable in near-term devices for estimating the amplitude of a given quantum state, which is a core sub- routine in various computing tasks such as the Monte Carlo…
Giving a convincing experimental evidence of the quantum supremacy over classical simulations is a challenging goal. Noise is considered to be the main problem in such a demonstration, hence it is urgent to understand the effect of noise.…
In this paper we have defined two functions that have been used to construct different fractals having fractal dimensions between 1 and 2. More precisely, we can say that one of our defined functions produce the fractals whose fractal…
Scale invariance (fractality) is a prominent feature of the large-scale behavior of many stochastic systems. In this work, we construct an algorithm for the statistical identification of the Hurst distribution (in particular, the scaling…
The effect of noise on a quantum system can be described by a set of operators obtained from the interaction Hamiltonian. Recently it has been shown that generalized quantum error correcting codes can be derived by studying the algebra of…