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Fast Estimation of Outcome Probabilities for Quantum Circuits

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PRX Quantum 2022年第2期3卷 020361-020361页

作者： Hakop Pashayan Oliver Reardon-Smith Kamil Korzekwa Stephen D. Bartlett Institute for Quantum Computing and Department of Combinatorics and Optimization University of Waterloo Ontario N2L 3G1 Canada Perimeter Institute for Theoretical Physics Waterloo Ontario N2L 2Y5 Canada Faculty of Physics Astronomy and Applied Computer Science Jagiellonian University Kraków 30-348 Poland Centre for Engineered Quantum Systems School of Physics The University of Sydney Sydney New South Wales 2006 Australia

We present two classical algorithms for the simulation of universal quantum circuits on n qubits constructed from c instances of Clifford gates and t arbitrary-angle Z-rotation gates such as T gates. Our algorithms complement each other by performing best in different parameter regimes. The Estimate algorithm produces an additive precision estimate of the Born-rule probability of a chosen measurement outcome with the only source of run-time inefficiency being a linear dependence on the stabilizer extent (with scaling approximately equal to 1.17t for T gates). Our algorithm is state of the art for this task: as an example, in approximately 13 h (on a standard desktop computer), we estimate the Born-rule probability to within an additive error of 0.03, for a 50-qubit, 60 non-Clifford gate quantum circuit with more than 2000 Clifford gates. Our second algorithm, Compute, calculates the probability of a chosen measurement outcome to machine precision with run time O(2t−rt), where r is an efficiently computable, circuit-specific quantity. With high probability, r is very close to min{t,n−w} for random circuits with many Clifford gates, where w is the number of measured qubits. Compute can be effective in surprisingly challenging parameter regimes, e.g., we can randomly sample Clifford+T circuits with n=55, w=5, c=105, and t=80T gates, and then compute the Born-rule probability with a run time consistently less than 10 min using a single core of a standard desktop computer. We provide a C+Python implementation of our algorithms and benchmark them using random circuits, the hidden-shift algorithm, and the quantum approximate optimization algorithm.

关键词： Quantum simulation

Low projectile density contributions in the dilute-dense CGC framework for two-particle correlations

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arXiv 2023年

作者： Kohara, Anderson Kendi Marquet, Cyrille Vila, Víctor AGH University Of Science and Technology Faculty of Physics and Applied Computer Science Mickiewicza 30 Kraków30-059 Poland CPHT CNRS École polytechnique Institut Polytechnique de Paris Palaiseau91120 France LIP Av. Prof. Gama Pinto 2 LisboaP-1649-003 Portugal Universidade de Santiago de Compostela GaliciaE-15782 Spain Institute of Nuclear Physics Polish Academy of Sciences KrakówPL-31342 Poland

At leading-order, the standard dilute-dense Color Glass Condensate formula used for two-particle correlations in proton-nucleus collisions, whose symmetries prevent the generation of odd azimuthal anisotropy harmonics, is the dilute projectile limit of the dense-dense formalism. However, when the projectile is genuinely dilute, the complete formulation contains additional contributions at the same leading order in the strong coupling constant. In this work we investigate those low projectile density contributions that are relevant when the particles are produced at forward rapidities. We find that they are responsible for nonzero odd harmonics which are negative, in qualitative agreement with recent experimental measurements at the Relativistic Heavy-Ion Collider. Copyright © 2023, The Authors. All rights reserved.

关键词： Projectiles

Constraining the bispectrum from bouncing cosmologies with Planck

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arXiv 2022年

作者： van Tent, Bartjan Delgado, Paola C.M. Durrer, Ruth Université Paris-Saclay CNRS IN2P3 IJCLab Orsay91405 France Faculty of Physics Astronomy and Applied Computer Science Jagiellonian University Krakow30-348 Poland Department of Theoretical Physics Université de Genève Quai E. Ansermet 24 Genève1211 Switzerland

Bouncing models of cosmology, as they arise e.g. in loop quantum cosmology, can be followed by an inflationary phase and generate close-to-scale-invariant fluctuation spectra as observed in the Cosmic Microwave Background (CMB). However, they are typically not Gaussian and also generate a bispectrum. These models can help to mitigate the large-scale anomalies of the CMB by considering substantial non-Gaussianities on very large scales, which decay exponentially on sub-horizon scales. It was therefore thought that this non-Gaussianity would not be visible in observations, which can only probe sub-horizon scales. In this letter we show that bouncing models with parameters such that they can significantly mitigate the large-scale anomalies of the CMB are excluded by the Planck data with high significance of, depending on the specific model, 5.4, 6.4 or 14 standard deviations. Copyright © 2022, The Authors. All rights reserved.

关键词： Cosmology

Symmetries and integrals of motion of a superintegrable deformed oscillator

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arXiv 2020年

作者： Gonera, Joanna Jasiński, Artur Kosiński, Piotr Department of Computer Science Faculty of Physics and Applied Informatics University of Lodz Poland

The symmetry structure of twodimensional nonlinear isotropic oscillator, introduced in Physica D237 (2008) 505, is discussed. It is shown that it possesses three independent integrals of motion which can be chosen in such a way that they span SU(2), E(2) or SU(1,1) algebras, depending on the value of total energy. They generate the infinitesimal canonical symmetry transformations;integrability of the latter is analyzed. The results are then generalized to the case of arbitrary number of degrees of freedom. Copyright © 2020, The Authors. All rights reserved.

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Controllable spin filtering and half metallicity in β12-borophene nanoribbons

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arXiv 2021年

作者： Norouzi, Fahimeh Farokhnezhad, Mohsen Esmaeilzadeh, Mahdi Szafran, Bartlomiej Department of Physics Iran University of Science and Technology Narmak Tehran16844 Iran Tehran19395-5531 Iran AGH University of Science and Technology Faculty of Physics and Applied Computer Science al. Mickiewicza 30 Kraków30-059 Poland

The experimental observation of the Dirac fermion states in β12-borophene sheets and the discovery of their novel topological properties have made them a promising candidate for spintronic applications. Here, by combining non-equilibrium Green's function (NEGF) and tight-binding (TB) approximation, we study the charge and spin transport properties through a β12-borophene nanoribbon (BNR) with the different edge shapes. We show when a BNR exposed to a nonlocal exchange magnetic field, the spin filtering occurs for both spin-up and spin-down so that the spin direction of transmitted electrons could be controlled by adjusting the energy of incoming electrons with the help of an external backgate voltage. It is found that an armchair BNR (ABNR) in the simultaneous presence of a transverse electric field and a nonlocal exchange field indicates a half-metallic nature which is electrically controllable. Moreover, the influence of local exchange fields is evaluated by exposing the edges of ABNR to ferromagnetic strips with parallel and anti-parallel configurations. Our findings show that the edge manipulations in ABNRs lead to the emergence of a giant magnetoresistance and a perfect spin filter. Finally, we studied the effects of edge vacancies and Anderson disorder on the spin-dependent conductance of an ABNR and find that the perfect spin polarization is not destroyed in the presence of Anderson disorder and various single vacancies. Our results reveal the outstanding spin transport properties of ABNRs for future spintronic devices. Copyright © 2021, The Authors. All rights reserved.

关键词： Nanoribbons

Development and study of the impacts of automated walking aids on the elderly

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Development and study of the impacts of automated walking ai...

International Conference on Electrical Engineering/Electronics, computer, Telecommunications and Information Technology, ECTI-CON

作者： Maleeya Tangjitjetsada Tawan Thianthong Chawalit Rakluea Wisit Loedhammacakra Paitoon Rakluea Nipont Tangthong Chatree Mahatthanajatuphat Nonchanutt Chudpooti Department of Electronics and Telecommunication Engineering Faculty of Engineering and Architecture Rajamangala University of Technology Suvarnabhumi Nonthaburi Thailand Siam Airport Ground Services Co. Ltd Bangkok Thailand Department of Electronics and Telecommunication Engineering Faculty of Engineering Rajamangala University of Technology Thanyaburi Pathum Thani Thailand Department of Electrical and Computer Engineering Faculty of Engineering King Mongkut’s University of Technology North Bangkok Bangkok Thailand Department of Industrial Physics and Medical Instrumentation Faculty of Applied Science King Mongkut’s University of Technology North Bangkok Bangkok Thailand

Since Thailand has now completely stepped into an aged society there are more than 20% of the population aged 60 years and over. There was also an increase in those who had problems with their balance. One of the main difficulties for these people is walking on their own. This paper presents an automatic walking aid for people with balance or walking problems. A specially designed automatic walking aid can be adjusted to six levels of height. It has an anti-collision warning system at a distance of up to 40 centimeters and displays GPS coordinates via SMS when falling. The experimental results of the prototype automatic walking aid showed that the walking aid could work as designed and could help people with balance problems walk more comfortably.

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Scheduling algorithms in cellular MIMO systems

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Scheduling algorithms in cellular MIMO systems

2021 International Conference Engineering and Telecommunication, En and T 2021

作者： Chernov, Alexey Matyukhin, Vladislav Zherebyatew, Maksim Teleluhin, Artem Bogdanov, Yaroslav Chernova, Julia MIPT-School of Applied Mathematics and Computer Science Moscow Institute of Physics and Technology Moscow Russia MAOU Lyceum 14 Named. Honored Teacher of the Russian Federation A.M. Kuzmina Tambow Russia Gymnasium 69 Named after Sergei Yesenin Lipetsk Russia Moscow State University Faculty of Mechanics and Mathematics Moscow Russia

ISBN: (纸本)9781728183909

In this work, we study the resource allocation problem for downlink in 5G New Radio (NR) mobile networks in the case of orthogonal frequency-division multiple access (OFDMA). One of the key features of 5G mobile networks is the usage of antenna arrays that allows them to form beams in a specific direction and send data to several users at the same transmission time interval (TTI) via the same carrier or resource block (RB). Antenna arrays usually contain up to 64 single antennas. We have been modeled the process of the data transmission from the cell to the user device or user equipment (UE), have been formulated mathematical abstraction of the resource allocation problem, and have been proposed a lightweight algorithm that uses a proportional fair metric. © 2021 IEEE.

关键词： Beamforming

Multi-Agent Economic Modeling Automation Technologies

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Multi-Agent Economic Modeling Automation Technologies

International Conference on Control, Decision and Information Technologies (CoDIT)

作者： Aleksandra A. Zhukova Nikolai P. Pilnik Ivan G. Kamenev Batyrzhan B. Iusup-Akhunov Department of Mathematical Modelling in Economic Social and Ecological Systems Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences Moscow Russian Federation Department of Mathematical Modelling of Economic Systems Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences Moscow Russian Federation Department of Applied Economics Faculty of Economic Sciences HSE University Moscow Russian Federation Department of Fundamental Sciences-11 FSBEIHE Bauman Moscow State Technical University Moscow Russian Federation The Phystech School of Applied Mathematics and Informatics Moscow Institute of Physics and Technology Moscow Region Russian Federation

Complex economic models often describe the agent's decisions, i.e. choice of some controlled variables in accordance with criteria set by agents. Unlike purely statistical ones, agent-based models allow to describe processes with different modes, in which the agent's behavior changes quali-tatively when the environment (including the actions of other agents) change. The practical use of mathematical models of complex systems with a number of interacting agents is limited by complexity of their construction and possible errors when dealing with multitude of expressions. computer tools, such as the “Ecomod” system discussed in the article, can substantially reduce the time spent on model creation and processing, and help to coordinate the work of several researchers on the model.

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Bounding and Computing Obstacle Numbers of Graphs

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arXiv 2022年

作者： Balko, Martin Chaplick, Steven Ganian, Robert Gupta, Siddharth Hoffmann, Michael Valtr, Pavel Wolff, Alexander Department of Applied Mathematics Faculty of Mathematics and Physics Charles University Czech Republic Maastricht University Netherlands Institute of Logic and Computation Technische Universität Wien Austria Department of Computer Science & Information Systems BITS Pilani Goa Campus India Department of Computer Science ETH Zürich Switzerland Institut für Informatik Universität Würzburg Germany

An obstacle representation of a graph G consists of a set of pairwise disjoint simply-connected closed regions and a one-to-one mapping of the vertices of G to points such that two vertices are adjacent in G if and only if the line segment connecting the two corresponding points does not intersect any obstacle. The obstacle number of a graph is the smallest number of obstacles in an obstacle representation of the graph in the plane such that all obstacles are simple polygons. It is known that the obstacle number of each n-vertex graph is O(nlog n) [Balko, Cibulka, and Valtr, 2018] and that there are n-vertex graphs whose obstacle number is Ω(n/(log log n)2) [Dujmović and Morin, 2015]. We improve this lower bound to Ω(n/log log n) for simple polygons and to Ω(n) for convex polygons. To obtain these stronger bounds, we improve known estimates on the number of n-vertex graphs with bounded obstacle number, solving a conjecture by Dujmović and Morin. We also show that if the drawing of some n-vertex graph is given as part of the input, then for some drawings Ω(n2) obstacles are required to turn them into an obstacle representation of the graph. Our bounds are asymptotically tight in several instances. We complement these combinatorial bounds by two complexity results. First, we show that computing the obstacle number of a graph G is fixed-parameter tractable in the vertex cover number of G. Second, we show that, given a graph G and a simple polygon P, it is NP-hard to decide whether G admits an obstacle representation using P as the only obstacle. © 2022, CC BY.

关键词： Graph theory