Functions of Random Operators

1984 ◽  
pp. 30-60
Author(s):  
A. V. Skorohod
Keyword(s):  
Random Operators

scholarly journals Gaussian Elimination versus Greedy Methods for the Synthesis of Linear Reversible Circuits

2021 ◽  
Vol 2 (3) ◽  
pp. 1-26
Author(s):  
Timothée Goubault De Brugière ◽  
Marc Baboulin ◽  
Benoît Valiron ◽  
Simon Martiel ◽  
Cyril Allouche
Keyword(s):  
Quantum Computing ◽  
State Of The Art ◽  
Gaussian Elimination ◽  
Random Operators ◽  
Lu Factorization ◽  
Large Problem ◽  
Computational Costs ◽  
Elimination Algorithm ◽  
Reversible Circuits ◽  
Greedy Methods

Linear reversible circuits represent a subclass of reversible circuits with many applications in quantum computing. These circuits can be efficiently simulated by classical computers and their size is polynomially bounded by the number of qubits, making them a good candidate to deploy efficient methods to reduce computational costs. We propose a new algorithm for synthesizing any linear reversible operator by using an optimized version of the Gaussian elimination algorithm coupled with a tuned LU factorization. We also improve the scalability of purely greedy methods. Overall, on random operators, our algorithms improve the state-of-the-art methods for specific ranges of problem sizes: The custom Gaussian elimination algorithm provides the best results for large problem sizes (n > 150), while the purely greedy methods provide quasi optimal results when n < 30. On a benchmark of reversible functions, we manage to significantly reduce the CNOT count and the depth of the circuit while keeping other metrics of importance (T-count, T-depth) as low as possible.

scholarly journals THE COMPARABLY ALMOST (S,T)- STABILITY FOR RANDOM JUNGCK-TYPE ITERATIVE SCHEMES

2019 ◽  
pp. 175
Author(s):  
Dhekra M. Albaqeri ◽  
Rashwan A. Rashwan
Keyword(s):  
Random Operators ◽  
Stochastic Version ◽  
Iterative Schemes

The purpose of this paper is to introduce the concept of generalized - weakly con-tractive random operators and study a new concept of stability introduced by Kim [15] which is alled comparably almost stability and then prove the comparably almost (S,T)- stability for the  Jungck-type random iterative schemes. Our results extend, improve and unify the recent results in  [15], [19], [32] and many others. We also give stochastic version of many important known results.

scholarly journals A db-Scan Hybrid Algorithm: An Application to the Multidimensional Knapsack Problem

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 507 ◽  
Author(s):  
José García ◽  
Paola Moraga ◽  
Matias Valenzuela ◽  
Hernan Pinto
Keyword(s):  
Transfer Function ◽  
Unsupervised Learning ◽  
Knapsack Problem ◽  
Hybrid Algorithm ◽  
Transfer Functions ◽  
Random Operators ◽  
Multidimensional Knapsack Problem ◽  
Multidimensional Knapsack ◽  
Learning Technique ◽  
Binarization Method

This article proposes a hybrid algorithm that makes use of the db-scan unsupervised learning technique to obtain binary versions of continuous swarm intelligence algorithms. These binary versions are then applied to large instances of the well-known multidimensional knapsack problem. The contribution of the db-scan operator to the binarization process is systematically studied. For this, two random operators are built that serve as a baseline for comparison. Once the contribution is established, the db-scan operator is compared with two other binarization methods that have satisfactorily solved the multidimensional knapsack problem. The first method uses the unsupervised learning technique k-means as a binarization method. The second makes use of transfer functions as a mechanism to generate binary versions. The results show that the hybrid algorithm using db-scan produces more consistent results compared to transfer function (TF) and random operators.

An integer-valued bilinear time series model via two random operators

2019 ◽  
Vol 25 (4) ◽  
pp. 429-446 ◽  
Author(s):  
M. Mohammadpour ◽  
Hassan S. Bakouch ◽  
S. Ramzani
Keyword(s):  
Time Series ◽  
Time Series Model ◽  
Random Operators

The Wegner estimate and the integrated density of states for some random operators

2002 ◽  
Vol 112 (1) ◽  
pp. 31-53 ◽  
Author(s):  
J. M. Combes ◽  
P. D. Hislop ◽  
Frédéric Klopp ◽  
Shu Nakamura
Keyword(s):  
Density Of States ◽  
Integrated Density Of States ◽  
Random Operators ◽  
Wegner Estimate
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