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Chemically Motivated Simulation Problems are Efficiently Solvable by a Quantum computer

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arXiv 2024年

作者： Schleich, Philipp Kristensen, Lasse Bjørn Campos-Gonzalez-Angulo, Jorge A. Aldossary, Abdulrahman Avagliano, Davide Bagherimehrab, Mohsen Gorgulla, Christoph Fitzsimons, Joe Aspuru-Guzik, Alán Department of Computer Science University of Toronto TorontoONM5S 3G4 Canada Vector Institute of Artificial Intelligence TorontoONM5G 1M1 Canada Department of Chemistry University of Toronto TorontoONM5S 3H6 Canada Department of Computer Science University of Copenhagen CopenhagenDK-2100 Denmark Paris75005 France Department of Structural Biology St. Jude Children’s Research Hospital MemphisTN38105 United States Department of Physics Harvard University CambridgeMA02138 United States Horizon Quantum Computing Singapore138565 Singapore Department of Chemical Engineering & Applied Chemistry University of Toronto TorontoONM5S 3E5 Canada Department of Materials Science & Engineering University of Toronto TorontoONM5S 3E4 Canada Acceleration Consortium TorontoONM5S 3H6 Canada Canadian Institute for Advanced Research TorontoONM5G 1Z8 Canada Canadian Institute for Advanced Research TorontoONM5S 1M1 Canada

Simulating chemical systems is highly sought after and computationally challenging, as the number of degrees of freedom increases exponentially with the size of the system. Quantum computers have been proposed as a computational means to overcome this bottleneck, thanks to their capability of representing this amount of information efficiently. Most efforts so far have been centered around determining the ground states of chemical systems. However, hardness results and the lack of theoretical guarantees for efficient heuristics for initial-state generation shed doubt on the feasibility. Here, we propose a heuristically guided approach that is based on inherently efficient routines to solve chemical simulation problems, requiring quantum circuits of size scaling polynomially in relevant system parameters. If a set of assumptions can be satisfied, our approach finds good initial states for dynamics simulation by assembling them in a scattering tree. In particular, we investigate a scattering-based state preparation approach within the context of mergo-association. We discuss a variety of quantities of chemical interest that can be measured after the quantum simulation of a process, e.g., a reaction, following its corresponding initial state preparation. © 2024, CC BY.

关键词： Association reactions

Quantum linear algebra is all you need for Transformer architectures

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arXiv 2024年

作者： Guo, Naixu Yu, Zhan Choi, Matthew Agrawal, Aman Nakaji, Kouhei Aspuru-Guzik, Alán Rebentrost, Patrick Centre for Quantum Technologies National University of Singapore 117543 Singapore Department of Computer Science University of Toronto TorontoONM5S 2E4 Canada Vector Institute for Artificial Intelligence TorontoONM5S 1M1 Canada Department of Mathematics National University of Singapore 119076 Singapore Department of Chemistry University of Toronto TorontoONM5G 1Z8 Canada 1-1-1 Umezono Ibaraki Tsukuba305-8568 Japan Quantum Computing Center Keio University 3-14-1 Hiyoshi Kohoku-ku Kanagawa Yokohama223-8522 Japan Department of Materials Science & Engineering University of Toronto TorontoONM5S 3E4 Canada Department of Chemical Engineering & Applied Chemistry University of Toronto TorontoONM5S 3E5 Canada Canadian Institute for Advanced Research TorontoONM5G 1Z8 Canada School of Computing National University of Singapore 117417 Singapore

Generative machine learning methods such as large-language models are revolutionizing the creation of text and images. While these models are powerful they also harness a large amount of computational resources. The transformer is a key component in large language models that aims to generate a suitable completion of a given partial sequence. In this work, we investigate transformer architectures under the lens of fault-tolerant quantum computing. The input model is one where trained weight matrices are given as block encodings and we construct the query, key, and value matrices for the transformer. We show how to prepare a block encoding of the self-attention matrix, with a new subroutine for the row-wise application of the softmax function. In addition, we combine quantum subroutines to construct important building blocks in the transformer, the residual connection and layer normalization, and the feed-forward neural network. Our subroutines prepare an amplitude encoding of the transformer output, which can be measured to obtain a prediction. Based on common open-source large-language models, we provide insights into the behavior of important parameters determining the run time of the quantum algorithm. We discuss the potential and challenges for obtaining a quantum advantage. © 2024, CC BY.

关键词： Network architecture

Optimization of Correlation Filters Using Extended Particle Swarm Optimization Technique

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Computational and Mathematical Methods in Medicine 2021年 2021卷 6321860页

作者： Masood, Haris Zafar, Amad Ali, Muhammad Umair Khan, Muhammad Attique Iqbal, Kashif Tariq, Usman Kadry, Seifedine Wah Engineering College University of Wah Wah Cantt Pakistan Department of Electrical Engineering University of Lahore Islamabad Campus Pakistan Department of Unmanned Vehicle Engineering Sejong University Seoul05006 Korea Republic of Department of Computer Science HITEC University Taxila Taxila47040 Pakistan College of Computer Engineering and Sciences Prince Sattam Bin Abdulaziz University Al-Khraj Saudi Arabia Faculty of Applied Computing and Technology Noroff University College Kristiansand Norway

In the past few decades, the field of image processing has seen a rapid advancement in the correlation filters, which serves as a very promising tool for object detection and recognition. Mostly, complex filter equations are used for deriving the correlation filters, leading to a filter solution in a closed loop. Selection of optimal tradeoff (OT) parameters is crucial for the effectiveness of correlation filters. This paper proposes extended particle swarm optimization (EPSO) technique for the optimal selection of OT parameters. The optimal solution is proposed based on two cost functions. The best result for each target is obtained by applying the optimization technique separately. The obtained results are compared with the conventional particle swarm optimization method for various test images belonging from different state-of-the-art datasets. The obtained results depict the performance of filters improved significantly using the proposed optimization method. © 2021 Haris Masood et al.

关键词： Cost functions

Lagrange–chebyshev interpolation for image resizing

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arXiv 2021年

作者： Occorsio, Donatella Ramella, Giuliana Themistoclakis, Woula Department of Mathematics and Computer Science University of Basilicata Viale dell’Ateneo Lucano 10 Potenza85100 Italy C.N.R. National Research Council of Italy Institute for Applied Computing "Mauro Picone" Via P. Castellino 111 Naples80131 Italy

Image resizing is a basic tool in image processing and in literature we have many methods, based on different approaches, which are often specialized in only upscaling or downscaling. In this paper, independently of the (reduced or enhanced) size we aim to get, we approach the problem at a continuous scale where the underlying continuous image is globally approximated by the tensor product Lagrange polynomial interpolating at a suitable grid of first kind Chebyshev zeros. This is a well–known approximation tool that is widely used in many applicative fields, due to the optimal behavior of the related Lebesgue constants. Here we show how Lagrange–Chebyshev interpolation can be fruitfully applied also for resizing an arbitrary digital image in both downscaling and upscaling. The performance of the proposed method has been tested in terms of the standard SSIM and PSNR metrics. The results indicate that, in upscaling, it is almost comparable with the classical Bicubic resizing method with slightly better metrics, but in downscaling a much higher performance has been observed in comparison with Bicubic and other recent methods too. Moreover, in downscaling cases with an odd scale factor, we give an estimate of the mean squared error produced by our method and prove it is theoretically null (hence PSNR equals to infinite and SSIM equals to one) in absence of noise or initial artifacts on the input image. © 2021, CC BY.

关键词： Lagrange multipliers

Electrostatic Discovery Atomic Force Microscopy

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arXiv 2021年

作者： Oinonen, Niko Xu, Chen Alldritt, Benjamin Canova, Filippo Federici Urtev, Fedor Cai, Shuning Krejčí, Ondřej Kannala, Juho Liljeroth, Peter Foster, Adam S. Department of Applied Physics Aalto University Aalto Helsinki00076 Finland Nanolayers Research Computing Ltd LondonN12 0HL United Kingdom Department of Computer Science Aalto University Aalto Helsinki00076 Finland Kanazawa University Kakuma-machi Kanazawa920-1192 Japan

While offering high resolution of atomic and electronic structure, Scanning Probe Microscopy techniques have found greater challenges in providing reliable electrostatic characterization at the same scale. In this work, we offer Electrostatic Discovery Atomic Force Microscopy, a machine learning based method which provides immediate maps of the electrostatic potential directly from Atomic Force Microscopy images with functionalized tips. We apply this to characterize the electrostatic properties of a variety of molecular systems and compare directly to reference simulations, demonstrating good agreement. This approach offers reliable atomic scale electrostatic maps on any system with minimal computational overhead. Copyright © 2021, The Authors. All rights reserved.

关键词： Electrostatics

Multi-graph Graph matching for coronary artery semantic labeling in invasive coronary angiograms

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Pattern Recognition 2026年 169卷

作者： Chen Zhao Zhihui Xu Pukar Baral Michel Esposito Weihua Zhou Department of Computer Science Kennesaw State University Marietta GA USA Department of Cardiology The First Affiliated Hospital of Nanjing Medical University Nanjing China Department of Applied Computing Michigan Technological University Houghton MI USA Department of Cardiology Medical University of South Carolina Charleston SC USA Center for Biocomputing and Digital Health Institute of Computing and Cyber-systems and Health Research Institute Michigan Technological University Houghton MI USA

Coronary artery disease (CAD) stands as the leading cause of death worldwide, and invasive coronary angiography (ICA) remains the gold standard for assessing vascular anatomical information. However, deep learning-based methods encounter challenges in generating semantic labels for arterial segments, primarily due to the morphological similarity between arterial branches and varying anatomy of arterial system between different projection view angles and patients. To address this challenge, we model the vascular tree as a graph and propose a multi-graph matching (MGM) algorithm for coronary artery semantic labeling. The MGM algorithm assesses the similarity between arterials in multiple vascular tree graphs, considering the cycle consistency between each pair of graphs. As a result, the unannotated arterial segments are appropriately labeled by matching them with annotated segments. Through the incorporation of anatomical graph structure, radiomics features, and semantic mapping, the proposed MGM model achieves an impressive accuracy of 0.9471 for coronary artery semantic labeling using our multi-site dataset with 718 ICAs. With the semantic labeled arteries, an overall accuracy of 0.9155 was achieved for stenosis detection. The proposed MGM presents a novel tool for coronary artery analysis using multiple ICA-derived graphs, offering valuable insights into vascular health and pathology.

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Variational quantum algorithm for generalized eigenvalue problems and its application to the finite-element method

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Physical Review A 2023年第2期108卷 022429-022429页

作者： Yuki Sato Hiroshi C. Watanabe Rudy Raymond Ruho Kondo Kaito Wada Katsuhiro Endo Michihiko Sugawara Naoki Yamamoto Toyota Central R&D Labs. Inc. 41-1 Yokomichi Nagakute Aichi 480-1192 Japan Quantum Computing Center Keio University 3-14-1 Hiyoshi Kohoku-ku Yokohama Kanagawa 223-8522 Japan Department of Chemistry Graduate School of Science Kyushu University 744 Motooka Nishi-ku Fukuoka 819-0395 Japan IBM Quantum IBM Japan 19-21 Nihonbashi Hakozaki-cho Chuo-ku Tokyo 103-8510 Japan Department of Computer Science The University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo 113-0033 Japan Department of Applied Physics and Physico-Informatics Keio University Hiyoshi 3-14-1 Kohoku-ku Yokohama 223-8522 Japan Research Center for Computational Design of Advanced Functional Materials National Institute of Advanced Industrial Science and Technology (AIST) 1-1-1 Umezono Tsukuba Ibaraki 305-8568 Japan

Generalized eigenvalue problems (GEPs) play an important role in the variety of fields including engineering, machine learning, and quantum chemistry. Especially, many problems in these fields can be reduced to finding the minimum or maximum eigenvalue of GEPs. One of the key problems to handle GEPs is that the memory usage and computational complexity explode as the size of the system of interest grows. This paper aims at extending sequential quantum optimizers for GEPs. Sequential quantum optimizers are a family of algorithms that iteratively solve the analytical optimization of single-qubit gates in a coordinate descent manner. The contribution of this paper is as follows. First, we formulate the GEP as the minimization or maximization problem of the fractional form of the expectations of two Hermitians. We then show that the fractional objective function can be analytically minimized or maximized with respect to a single-qubit gate by solving a GEP of a 4×4 matrix. Second, we show that a system of linear equations characterized by a positive-definite Hermitian can be formulated as a GEP and thus be attacked using the proposed method. Finally, we demonstrate two applications to important engineering problems formulated with the finite-element method. Through the demonstration, we have the following bonus finding; a problem having a real-valued solution can be solved more effectively using quantum gates generating a complex-valued state vector, which demonstrates the effectiveness of the proposed method.

关键词： Quantum algorithms

Employing derivatives for creating texture masks for digital images

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AIP Conference Proceedings 2024年第1期2898卷

作者： Taha Basheer Taha Ruzelita Ngadiran Dujan B. Taha IT Department Faculty of Applied Science Tishk International University Erbil Kurdistan Region Iraq Faculty of Electronic Engineering Technology Universiti Malaysia Perlis 02600 Arau Perlis Malaysia Centre of Excellence Advanced Computing (AdvComp) Universiti Malaysia Perlis 02600 Arau Perlis Malaysia Software Engineering Department College of Computer Science and Mathematics Mosul University Mosul Iraq

Texture masking has been used as a significant factor in creating perceptual maps that simulates human vision system in observing noise in digital images. In this paper, the possibility of creating texture masks using first and second derivatives is investigated and tested. Results shows that after applying the derivatives, areas of higher texture were highlighted and recognized, which will lead to simple implementation of texture masks using numerical analysis.

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Which algorithm to select in sports timetabling?

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arXiv 2023年

作者： Van Bulck, David Goossens, Dries Clarner, Jan-Patrick Dimitsas, Angelos Fonseca, George H.G. Lamas-Fernandez, Carlos Lester, Martin Mariusz Pedersen, Jaap Phillips, Antony E. Rosati, Roberto Maria Faculty of Economics and Business Administration Ghent University Tweekerkenstraat 2 Ghent9000 Belgium Core lab CVAMO FlandersMake@UGent Belgium Applied Algorithmic Intelligence Methods Department Zuse Institute Berlin Takustrase 7 Berlin14195 Germany Department of Informatics University of Ioannina University of Ioannina Greece Computing and Systems Department Federal University of Ouro Preto R. Diogo de Vasconcelos 122 Ouro Preto Brazil Southampton Business School University of Southampton United Kingdom Department of Computer Science University of Reading Reading United Kingdom 7bridges *** 23 Meard St London United Kingdom DPIA University of Udine via delle Scienze 206 Udine33100 Italy

Any sports competition needs a timetable, specifying when and where teams meet each other. The recent International Timetabling Competition (ITC2021) on sports timetabling showed that, although it is possible to develop general algorithms, the performance of each algorithm varies considerably over the problem instances. This paper provides a problem type analysis for sports timetabling, resulting in powerful insights into the strengths and weaknesses of eight state-of-the-art algorithms. Based on machine learning techniques, we propose an algorithm selection system that predicts which algorithm is likely to perform best based on the type of competition and constraints being used (i.e., the problem type) in a given sports timetabling problem instance. Furthermore, we visualize how the problem type relates to algorithm performance, providing insights and possibilities to further enhance several algorithms. Finally, we assess the empirical hardness of the instances. Our results are based on large computational experiments involving about 50 years of CPU time on more than 500 newly generated problem instances. © 2023, CC BY-NC-ND.

关键词： Scheduling algorithms