scholarly journals Accelerating Shor’s factorization algorithm on GPUs

2018 ◽  
Vol 96 (7) ◽  
pp. 759-761 ◽  
Author(s):  
I. Savran ◽  
M. Demirci ◽  
A.H. Yılmaz

Shor’s quantum algorithm is very important for cryptography, because it can factor large numbers much faster than classical algorithms. In this study, we implement a simulator for Shor’s quantum algorithm on graphic processor units (GPU) and compare our results with Liquid, which is a Microsoft quantum simulation platform, and two classical CPU implementations. We evaluate 10 benchmarks for comparing our GPU implementation with Liquid and single-core implementation. The analysis shows that GPU vector operations are more suitable for Shor’s quantum algorithm. Our GPU kernel function is compute-bound, due to all threads in a block reaching the same element of the state vector. Our implementation has 52.5× speedup over single-core algorithm and 20.5× speedup over Liquid.

2020 ◽  
Vol 224 ◽  
pp. 01016
Author(s):  
Larissa Cherckesova ◽  
Olga Safaryan ◽  
Pavel Razumov ◽  
Irina Pilipenko ◽  
Yuriy Ivanov ◽  
...  

This report discusses Shor’s quantum factorization algorithm and ρ–Pollard’s factorization algorithm. Shor’s quantum factorization algorithm consists of classical and quantum parts. In the classical part, it is proposed to use Euclidean algorithm, to find the greatest common divisor (GCD), but now exist large number of modern algorithms for finding GCD. Results of calculations of 8 algorithms were considered, among which algorithm with lowest execution rate of task was identified, which allowed the quantum algorithm as whole to work faster, which in turn provides greater potential for practical application of Shor’s quantum algorithm. Standard quantum Shor’s algorithm was upgraded by replacing the binary algorithm with iterative shift algorithm, canceling random number generation operation, using additive chain algorithm for raising to power. Both Shor’s algorithms (standard and upgraded) are distinguished by their high performance, which proves much faster and insignificant increase in time in implementation of data processing. In addition, it was possible to modernize Shor’s quantum algorithm in such way that its efficiency turned out to be higher than standard algorithm because classical part received an improvement, which allows an increase in speed by 12%.


2016 ◽  
pp. 4039-4042
Author(s):  
Viliam Malcher

The interpretation problems of quantum theory are considered. In the formalism of quantum theory the possible states of a system are described by a state vector. The state vector, which will be represented as |ψ> in Dirac notation, is the most general form of the quantum mechanical description. The central problem of the interpretation of quantum theory is to explain the physical significance of the |ψ>. In this paper we have shown that one of the best way to make of interpretation of wave function is to take the wave function as an operator.


Author(s):  
Оlena Fedorіvna Caracasidi

The article deals with the fundamental, inherent in most of the countries of the world transformation of state power, its formation, functioning and division between the main branches as a result of the decentralization of such power, its subsidiarity. Attention is drawn to the specifics of state power, its func- tional features in the conditions of sovereignty of the states, their interconnec- tion. It is emphasized that the nature of the state power is connected with the nature of the political system of the state, with the form of government and many other aspects of a fundamental nature.It is analyzed that in the middle of national states the questions of legitima- cy, sovereignty of transparency of state power, its formation are acutely raised. Concerning the practical functioning of state power, a deeper study now needs a problem of separation of powers and the distribution of power. The use of this principle, which ensures the real subsidiarity of the authorities, the formation of more effective, responsible democratic relations between state power and civil society, is the first priority of the transformation of state power in the conditions of modern transformations of countries and societies. It is substantiated that the research of these problems will open up much wider opportunities for the provi- sion of state power not as a center authority, but also as a leading political structure but as a power of the people and the community. In the context of global democratization processes, such processes are crucial for a more humanistic and civilized arrangement of human life. It is noted that local self-government, as a specific form of public power, is also characterized by an expressive feature of a special subject of power (territorial community) as a set of large numbers of people; joint communal property; tax system, etc.


2018 ◽  
Vol 15 (1) ◽  
pp. 12-22
Author(s):  
V. M. Artyushenko ◽  
D. Y. Vinogradov

The article reviewed and analyzed the class of geometrically stable orbits (GUO). The conditions of stability in the model of the geopotential, taking into account the zonal harmonics. The sequence of calculation of the state vector of GUO in the osculating value of the argument of the latitude with the famous Ascoli-royski longitude of the ascending node, inclination and semimajor axis. The simulation is obtained the altitude profiles of SEE regarding the all-earth ellipsoid model of the gravitational field of the Earth given 7 and 32 zonal harmonics.


2016 ◽  
Author(s):  
Jean M. Bergeron ◽  
Mélanie Trudel ◽  
Robert Leconte

Abstract. The potential of data assimilation for hydrologic predictions has been demonstrated in many research studies. Watersheds over which multiple observation types are available can potentially further benefit from data assimilation by having multiple updated states from which hydrologic predictions can be generated. However, the magnitude and time span of the impact of the assimilation of an observation varies according not only to its type, but also to the variables included in the state vector. This study examines the impact of multivariate synthetic data assimilation using the Ensemble Kalman Filter (EnKF) into the spatially distributed hydrologic model CEQUEAU for the mountainous Nechako River located in British-Columbia, Canada. Synthetic data includes daily snow cover area (SCA), daily measurements of snow water equivalent (SWE) at three different locations and daily streamflow data at the watershed outlet. Results show a large variability of the continuous rank probability skill score over a wide range of prediction horizons (days to weeks) depending on the state vector configuration and the type of observations assimilated. Overall, the variables most closely linearly linked to the observations are the ones worth considering adding to the state vector. The performance of the assimilation of basin-wide SCA, which does not have a decent proxy among potential state variables, does not surpass the open loop for any of the simulated variables. However, the assimilation of streamflow offers major improvements steadily throughout the year, but mainly over the short-term (up to 5 days) forecast horizons, while the impact of the assimilation of SWE gains more importance during the snowmelt period over the mid-term (up to 50 days) forecast horizon compared with open loop. The combined assimilation of streamflow and SWE performs better than its individual counterparts, offering improvements over all forecast horizons considered and throughout the whole year, including the critical period of snowmelt. This highlights the potential benefit of using multivariate data assimilation for streamflow predictions in snow-dominated regions.


2021 ◽  
Vol 13 (17) ◽  
pp. 3389
Author(s):  
Pei Ye ◽  
Meng-Dao Xing ◽  
Xiang-Gen Xia ◽  
Guang-Cai Sun ◽  
Yachao Li ◽  
...  

In a short observation time, after the range alignment and phase adjustment, the motion of a target can be approximated as a uniform rotation. The radar observing process can be simply described as multiplying an observation matrix on the ISAR image, which can be thought of as a linear system. It is known that the longer observation time is, the higher cross-range resolution is. In order to deal with the conflict between short observation time and high cross-range resolution, we introduce Kalman filtering (KF) into the ISAR imaging and propose a novel method to reconstruct a high-resolution image with short time observed data. As KF has excellent reconstruction performance, it leads to a good application in ISAR image reconstruction. At each observation aperture, the reconstructed image denotes the state vector in KF at the aperture time. It is corrected by a two-step KF process: prediction and update. As iteration continues, the state vector is gradually corrected to a well-focused high-resolution image. Thus, the proposed method can obtain a high-resolution image in a short observation time. Both simulated and real data are applied to demonstrate the performance of the proposed method.


1974 ◽  
Vol 19 (2) ◽  
pp. 169-170 ◽  
Author(s):  
G. Bertoni ◽  
S. Beghelli ◽  
G. Capitani ◽  
M. Tibaldi

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