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Decomposing large unitaries into multimode devices of arbitrary size

Physical Review Research 2024年第1期6卷 L012043-L012043页

作者： Christian Arends Lasse Wolf Jasmin Meinecke Sonja Barkhofen Tobias Weich Tim J. Bartley Department of Mathematics Aarhus University Ny Munkegade 118 8000 Aarhus C Denmark PhoQS Universität Paderborn Warburger Strasse 100 33098 Paderborn Germany Institute of Mathematics Universität Paderborn Warburger Strasse 100 33098 Paderborn Germany Max-Planck-Institut für Quantenoptik 85748 Garching Germany Department für Physik Ludwig-Maximilians-Universität 80539 München Germany Munich Center for Quantum Science and Technology (MCQST) 80799 München Germany Institute of Solid State Physics Technische Universität Berlin 10623 Berlin Germany Department of Physics Universität Paderborn Warburger Strasse 100 33098 Paderborn Germany

Decomposing complex unitary evolution into a series of constituent components is a cornerstone of practical quantum information processing. While the decomposition of an n×n unitary into a product of 2×2 subunitaries (which can for example be realized by beam splitters and phase shifters in linear optics) is well established, we show how for any m>2 this decomposition can be generalized into a product of m×m subunitaries (which can then be realized by a more complex device acting on m modes). If the cost associated with building each m×m multimode device is less than constructing with m(m−1)2 individual 2×2 devices, we show that the decomposition of large unitaries into m×m submatrices is more resource efficient and exhibits a higher tolerance to errors, than its 2×2 counterpart. This allows larger-scale unitaries to be constructed with lower errors, which is necessary for various tasks, not least boson sampling, the quantum Fourier transform, and quantum simulations.

关键词： quantum algorithms & computation quantum circuits quantum computation quantum information processing quantum protocols quantum simulation

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A generalisation of the Phase Kick-Back

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quantum information processing 2023年第3期22卷 1-20页

作者： Ossorio-Castillo, Joaquin Pastor-Diaz, Ulises Tornero, Jose M. Univ Seville Fac Matemat Dept Algebra Avda Reina Mercedes S-N Seville 41012 Spain

In this paper, we present a generalisation of the Phase Kick-Back technique, which is central to some of the classical algorithms in quantum computing. We will begin by recalling the Phase Kick-Back technique to then introduce the new generalised version for f : {0, 1}(n) ->{0, 1}(m) functions using the eigenvalues of the oracle function U (f). After that, we will present a new generalised version of the Deutsch-Jozsa problem and how it can be solved using the previously defined technique. We will also deal with a generalised version of the Bernstein-Vazirani problem and solve it using the generalised Phase Kick-Back. Finally, we show how we can use this technique to obtain an algorithm for Simon's problem that improves the classical one.

关键词： quantum algorithms Phase Kick-Back Deutsch-Jozsa Bernstein-Vazirani Boolean functions

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Online Parameter Estimation for Continuously Monitored quantum Systems

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IEEE CONTROL SYSTEMS LETTERS 2024年 8卷 1247-1252页

作者： Clausen, Henrik Glavind Rouchon, Pierre Wisniewski, Rafal Aalborg Univ Dept Elect Syst Sect Automat & Control DK-9220 Aalborg Denmark Univ PSL Lab Phys Ecole Normale Super Mines Paris PSLInriaENS PSLCNRS F-75272 Paris France

In this letter, we consider the problem of online (real-time, single-shot) estimation of static or slow-varying parameters along quantum trajectories in quantum dynamical systems. Based on the measurement signal of a continuously monitored quantum system, we propose a recursive algorithm for computing the maximum likelihood (ML) estimate of unknown parameters using an approach based on stochastic gradient ascent on the log-likelihood function. We formulate the algorithm in both discrete-time and continuous-time and illustrate the performance of the algorithm through simulations of a simple two-level system undergoing homodyne measurement from which we are able to track multiple parameters simultaneously.

关键词： Maximum likelihood estimation Mathematical models Sensitivity quantum system quantum computing Time measurement Signal processing algorithms quantum information and control estimation stochastic systems

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Scheduling algorithm for fidelity of quantum gate circuits 3

Scheduling algorithm for fidelity of quantum gate circuits

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3rd International Conference on Electronic information Engineering and Data processing, EIEDP 2024

作者： Liu, Xudong Xu, Jinchen Lian, Hang Information Engineering University Zhengzhou450001 China

ISBN: (纸本)9781510680531

As quantum computing technology matures, the availability and performance of quantum devices are steadily improving. However, in the NISQ (Noisy Intermediate-Scale quantum) era, the quantum bit error rate caused by quantum noise remains a significant constraint on computational accuracy and reliability. In quantum operating systems, quantum task scheduling is a core technology crucial for fully leveraging the performance potential of quantum processors. Currently, most multi-processor scheduling algorithms focus on task load balancing and do not directly consider the characteristics of quantum circuits and the differentiated error rates of quantum computing backends. In quantum computing, the impact of noise errors in single-qubit gates, two-qubit gates, and measurement gates on the fidelity of quantum gate circuits is crucial. Therefore, intelligently matching quantum tasks with the characteristics of backend processors to optimize computational accuracy is an urgent problem to be addressed. This paper proposes a new quantum task scheduling algorithm, which matches tasks with backends based on the weight of single-qubit gates, two-qubit gates, and measurement gates in quantum circuits, as well as the error rate characteristics of each quantum computing backend. Experimental results show that the proposed scheduling algorithm for improving the fidelity of quantum gate circuits outperforms static load balancing scheduling algorithms, resulting in a 4.39% increase in the fidelity of quantum tasks. © 2024 SPIE.

关键词： Scheduling algorithms

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A user-centric quantum benchmarking test suite and evaluation framework

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quantum information processing 2023年第11期22卷 1-24页

作者： Liu, Wenbo Wang, Fei Lin, Han Shang, Jiandong Zhengzhou Univ Natl Supercomp Ctr Zhengzhou Zhengzhou 450001 Peoples R China Zhengzhou Univ Sch Comp & Artificial Intelligence Zhengzhou 450001 Peoples R China Zhengzhou Univ Sch Mech & Safety Engn Zhengzhou 450001 Peoples R China

This article proposes a benchmark testing set and evaluation system for quantum computers. Our tests do not focus on the topology of quantum computers or the specific implementation details of preparing quantum bits. Instead, we examine the overall performance of quantum computers from the perspective of users. Inspired by traditional computer benchmark tests such as SPECCPU2017, we integrate existing scalable quantum applications and algorithms to generate a testing set that covers algorithms such as search, machine learning, factorization, portfolio optimization, and entanglement state preparation, effectively simulating real workloads. By running the testing set, we can understand the performance of current quantum computers and generate a comprehensive score by combining our evaluation system, which consists of sub-scores of various backend features, including quantum gate error rate, entanglement between quantum bits, cross talk, and connectivity. These sub-scores are calculated based on the program features of the testing cases combined with their running results, where the program features are analyzed through the logical circuits of the testing cases. We incorporate Hellinger fidelity and polarization rescaling into each benchmark to calculate the fidelity of the running results. Through our evaluation system, researchers can be guided toward research directions and understand how far quantum computers are from solving practical problems.

关键词： quantum computing Benchmarking quantum algorithm library Application level

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quantum-Inspired Data processing for Big Data Analytics 4

Quantum-Inspired Data Processing for Big Data Analytics

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4th International Conference on Advancement in Electronics and Communication Engineering, AECE 2024

作者： Thota, Sunil Raj Arora, Saransh Gupta, Sandeep Engineering Andhra University Technology AP Visakhapatnam India Jaypee Institute of Information Technology U.P. Noida India Techieshubhdeep It Solutions Pvt. Ltd M.P. Gwalior India

ISBN: (纸本)9798350364729

Technological advancements in the 21st century have led to the rise of "big data,"characterized by datasets so vast and complex that traditional database systems struggle to manage them. This term denotes datasets that are too vast and complex to be processed by traditional database systems. As big data continues to evolve, it introduces significant challenges related to data processing, storage, and analysis. In response, quantum-inspired algorithms have emerged as a promising solution to these challenges. quantum-inspired algorithms, which draw on principles from quantum computing, present a promising solution to the challenges of big data processing, storage, and analysis. Techniques such as quantum Annealing, quantum Circuits and Gates, and quantum Parallelism leverage quantum principles like superposition and entanglement to enhance data processing efficiency and speed. These methods offer significant improvements over traditional tools like Hadoop, MapReduce, RapidMiner, and R Programming, which are used for distributed storage, processing, and analytics of large datasets. By integrating quantum-inspired algorithms with existing data processing techniques, this study aims to address the limitations of classical methods and advance the field of big data analytics. © 2024 IEEE.

关键词： quantum entanglement

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New quantum color image watermarking technique (NQCIWT)

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Soft Computing 2024年第17-18期28卷 10177-10186页

作者： Aly, Rasha F. Department of Computer and Systems Engineering Faculty of Engineering Helwan University Cairo Egypt

The crazy, unconscious use of the Internet, and the increase in cybercrime and hacking, which resulted in the loss of a large number of sensitive data, the risk of piracy, etc. were the motivation for protecting rights, securing and hiding essential information such as images, audio, etc. Watermarking was a popular security, copyright and privacy approach and one of the problems in modern quantum digital computing that produced more powerful quantum protection techniques than the classical one that used classical techniques such as digital wavelet transformation and Hungarian algorithms. Recent advances in quantum image representation and processing help to manipulate data hidden. This paper proposes a new watermark technique in which a color watermark image is hidden within another color-carrying image after transformation into the quantum domain using the recently completed quantum color image representation technique. Finally, a comparison is made between the proposed method and the most recent watermarking techniques is establish in terms of PSNR (peak signal-to-noise ratio), which shows the high precision of the proposed technique and improves the imperceptibility compared to the related schemes. © The Author(s) 2024.

关键词： Color

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Reduction of the semigroup-action problem on a module to the hidden-subgroup problem

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quantum information processing 2024年第8期23卷 1-16页

作者： Huang, Huawei Peng, Changgen Deng, Lunzhi Guizhou Normal Univ Sch Math Sci Guiyang 550025 Peoples R China Guizhou Univ Coll Comp Sci & Technol State Key Lab Publ Big Data Guiyang 550025 Peoples R China

The discrete-logarithm problem and related problems are important in public-key cryptography;however, these problems can be reduced to the hidden-subgroup problem (HSP) of an abelian group, for which efficient quantum algorithms exist. This paper more broadly regards these problems as semigroup-action problems (SAPs) on different modules. The results prove that if the action on a module is injective or the cardinality of the hidden subgroup's least generating set is less than or equal to that of the ring's least generating set, the corresponding SAP on the module can be reduced to the HSP of an abelian group in polynomial time;therefore, most cryptosystems based on the SAP on a module cannot resist quantum cryptanalysis. The results are applicable to the discrete-logarithm problem and matrix-action problem on a group, along with other SAPs on a module. Such reduction is not be found for the SAP on the semi-module. The cryptographic systems based on SAPs on some semi-modules are likely to resist quantum attacks.

关键词： Shor's algorithm Hidden-subgroup problem Semigroup-action problem Public-key cryptography Resistance to quantum cryptanalysis

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quantum Neural Network Classification-Based Cyber Threat Detection in Virtual Environment

Quantum Neural Network Classification-Based Cyber Threat Det...

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International Conference on Computational Science and Computational Intelligence (CSCI)

作者： Tripathi, Sarvapriya M. Upadhyay, Himanshu Soni, Jayesh Florida Int Univ Elect & Comp Engn Miami FL 33199 USA

ISBN: (纸本)9798350361513;9798350372304

quantum computing is an upcoming research area that applies quantum properties of the materials, e.g., superposition and Entanglement, to information processing. The probabilistic nature of this computation allows some unique capabilities that are not available in classical computing. quantum information processing (QIP), the area of computation using quantum devices, promises to speed up computing significantly compared to classical processing. QIP has been extended to Artificial Intelligence / Machine learning (AI/ML.) in what is referred to as quantum Artificial Intelligence (QAI) / quantum Machine Learning (QML). Whereas the classical ML algorithms efficiently identify patterns from datasets, QML tries to implement algorithms that utilize classical computing in handling the datasets and quantum computing for quantum-specific algorithms. In this paper, we attempt to implement QML in Cyber Security. We will demonstrate an advanced method of attack vector recognition using virtual machine memory introspection using quantum neural networks.

关键词： quantum Machine Learning quantum Neural Networks Variational quantum Circuits

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Simulating non-completely positive actions via exponentiation of Hermitian-preserving maps

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NPJ quantum information 2024年第1期10卷 1-10页

作者： Wei, Fuchuan Liu, Zhenhuan Liu, Guoding Han, Zizhao Deng, Dong-Ling Liu, Zhengwei Tsinghua Univ Yau Math Sci Ctr Beijing 100084 Peoples R China Tsinghua Univ Dept Math Beijing 100084 Peoples R China Tsinghua Univ Inst Interdisciplinary Informat Sci Ctr Quantum Informat Beijing 100084 Peoples R China Shanghai Qi Zhi Inst 41th FloorAI Tower701 Yunjin Rd Shanghai 200232 Peoples R China Hefei Natl Lab Hefei 230088 Peoples R China Yanqi Lake Beijing Inst Math Sci & Applicat Beijing 100407 Peoples R China

Legitimate quantum operations must adhere to principles of quantum mechanics, particularly the requirements of complete positivity and trace preservation. Yet, non-completely positive maps, especially Hermitian-preserving maps, play a crucial role in quantum information science. Here, we introduce the Hermitian-preserving map exponentiation algorithm, which can effectively simulate the action of an arbitrary Hermitian-preserving map by exponentiating its output, N(rho)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{N}}(\rho )$$\end{document}, into a quantum process, e-iN(rho)t\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${e}<^>{-i{\mathcal{N}}(\rho )t}$$\end{document}. We analyze the sample complexity of this algorithm and prove its optimality in certain cases. Utilizing positive but not completely positive maps, this algorithm provides exponential speedups in entanglement detection and quantification compared to protocols based on single-copy operations. In addition, it facilitates the encoding-free recovery of noiseless quantum states from multiple noisy ones by simulating the inverse map of the corresponding noise channel, providing a new approach to handling quantum noises. This algorithm acts as a building block of large-scale quantum algorithms and presents a pathway for exploring potential quantum speedups across a wide range of information-processing tasks.

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