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An improved quantum algorithm for data fitting

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2023年 613卷

作者： Lei, Jiancheng Song, Tingting Liu, Ling Zhang, Kejia Jinan Univ Coll Cyber Secur Guangzhou 510632 Peoples R China State Key Lab Cryptol POB 5159 Beijing 100878 Peoples R China Jinan Univ Coll Informat Sci & Technol Guangzhou 510632 Peoples R China Heilongjiang Univ Sch Math Sci Harbin 150080 Peoples R China

As researchers focus on the field of quantum machine learning, there are more and more quantum algorithms for data fitting. However, the majority of quantum algorithms for data fitting are only applicable to sparse matrices, which bring a large number of limitations to their application. In this paper, to solve this problem, we propose a quantum algorithm for data fitting for general matrices, not only sparse and dense matrices. The quantum algorithm is mainly composed of three subroutines which are generating target state, quantum state tomography and estimating fit quality. The time complexity of the quantum algorithm is O (kappa 4 parallel to A parallel to Fpolylog(MN)(M ' 2 log(M ')2/epsilon 3+ 1/(epsilon epsilon 2))), where A is an element of RMxN, kappa is the conditional number of matrix A dagger A is an element of RNxN, ||A||F is the Frobenius norm of A, M ' is the maxima number of fit functions in allowing fit, epsilon is the fitting error, and epsilon is the error of fit quality estimation. Moreover, our quantum algorithm is independent of the sparsity of the matrix, so our algorithm has wide application in dense matrices and poses a new state of the art for solving dense data fitting. (c) 2023 Elsevier B.V. All rights reserved.

关键词： quantum algorithm quantum machine learning Data fitting

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Windowed quantum Phase Estimation: Signal Processing Approach to a quantum algorithm

Windowed Quantum Phase Estimation: Signal Processing Approac...

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International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Xue Wen Samsung Research China Beijing

ISBN: (数字)9798350368741

ISBN: (纸本)9798350368758

quantum phase estimation (QPE) is a key ingredient to some of the most important results of quantum computing. In this paper we examine the QPE algorithm through the looking glass of signal processing. This perspective helps to reveal a relation between the distribution of quantum phase estimates and the shape of the discrete Fourier transform (DFT) of a pure complex sinusoid. Guided by spectral shaping theory, we design a class of quantum circuits that are the quantum equivalents to classical windowing operators, for a family of window functions that have compact support in the DFT. These circuits have complexity linear in the number of target qubits, strictly lower than QPE itself. Using these circuits we are able to reshape QPE's performance characteristics. In particular, the asymptotic marginal cost for 2x reduction in fail rate (2x improvement in reliability) is reduced from one qubit to 1/3 qubit or lower, which can help reduce the qubit budget for a preset accuracy-reliability target, especially in high-reliability scenarios. This makes a demonstration of the value of signal processing principles in designing quantum algorithms.

关键词： quantum algorithm Shape Qubit Discrete Fourier transforms Phase estimation Signal processing algorithms quantum mechanics Signal processing Windows Speech processing

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Efficient Earth Observation Satellites Mission Planning with quantum algorithm

Efficient Earth Observation Satellites Mission Planning with...

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Trends in quantum Computing and Emerging Business Technologies (TQCEBT), International Conference on

作者： Jitesh Lalwani Dana Linnet Babita Jajodia Mandaar B. Pande Amit Patel Kshitij Dave B R Nikilesh Artificial Brain Tech Inc Sheridan Wyoming USA Artificial Brain Tech B.V. Amsterdam Netherlands Artificial Brain Technology (OPC) Private Limited Pune India Department of Electronics and Communication Engineering Indian Institute of Information Technology Guwahati India Symbiosis Centre for Information Technology (SCIT) Symbiosis International (Deemed University) (SIU) Pune Maharashtra India

ISBN: (数字)9798350384277

ISBN: (纸本)9798350384284

Earth observation satellites (EOS) play a crucial role in collecting data for applications like weather forecasting and disaster management. Optimizing EOS missions to capture high-priority targets within constraints such as storage, energy, and weather is challenging for traditional computing methods. quantum computing shows promise in enhancing efficiency by exploring vast solution spaces for optimal schedules, even with complex constraints. This paper demonstrates the potential of a quantum algorithm to improve real-time EOS mission planning, maximizing high-priority target acquisition under resource limitations. Compared to classical algorithms like simulated annealing and Gurobi optimizer, the proposed quantum algorithm outperformed in selecting high-priority targets by 23.46%, executed faster than Gurobi by 39.09%, and successfully satisfied all constraints for all data.

关键词： Earth Satellites quantum algorithm Annealing Earth Observing System Weather forecasting Simulated annealing

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Recursive Generation of Multi-Qubits Control Gate to Facilitate the Grover's quantum algorithm in Large Scale Database Search

Recursive Generation of Multi-Qubits Control Gate to Facilit...

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IEEE International Conference on Software Quality, Reliability and Security Companion (QRS-C)

作者： Wen-Li Wang Shahid Hussain Nathaniel V. Rondinelli Mei-Huei Tang Saif Ur Rehman Khan Department of Computer Science and Software Engineering Penn State University Behrend Erie PA USA Department of Computer Information Science Gannon University Erie PA USA Department of Computing Shifa Tameer-e-Millat University Islamabad Pakistan

ISBN: (数字)9798350365658

ISBN: (纸本)9798350365665

Context: Grover's algorithm is a powerful tool in the realm of quantum computing because it offers exponential speedup over classical linear searching for unstructured / unsorted search problems. However, it is challenging to construct efficient and scalable circuits for a multi-input control gate in the algorithm, particularly with a huge number of qubit inputs. Problem: Traditional circuit construction methods often require manual composition for the multi-input gate from basic quantum gates, which can be time consuming and error prone, thus hindering practical implementation. Moreover, the number of simple gates in the composition grows exponentially with the addition of each qubit. Method: This research provides an approach to recursively generate the oracle using Toffoli gates as the fundamental units to enhance scalability and reusability while maintaining effectiveness. The methodology leverages IBM Qiskit and quantum Lab to simulate quantum computation to prove the practicality and feasibility. Result: The findings from the experiments between recursively and non-recursively generated circuits suggest that our recursive approach can offer comparable accuracy and computational complexity compared to the non-recursive approach. However, it tends to require a larger number of basic quantum gates due to a lack of circuit optimization. Conclusion: The results showcase the applicability of utilizing recursion as a speedy and economical alternative to generate circuits when implementing the Grover's algorithm. It not only presents potential scalability benefits, but also creates an avenue for further research on test verification and performance improvement to the computing community when running in actual quantum hardware.

关键词： quantum algorithm Scalability Circuits Qubit Software algorithms Software quality Logic gates Search problems Software reliability Security

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A Comparative Technique with Credit card based Fraud detection with Machine Learning and quantum algorithm

A Comparative Technique with Credit card based Fraud detecti...

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Self Sustainable Artificial Intelligence Systems (ICSSAS), International Conference on

作者： Meenalosini Vimal Cruz G. Usha N. A. S. Vinoth A. Anbarasi R. Thamizhamuthu Kumar Gautam Georgia Southern University USA Department of Computing Technologies SRMInstitute of Science and Technology Kattanlulathur Kanchipuram Dt TamilNadu Quantum Compting Lab Quantum Research And Centre of Excellence New Delhi India

ISBN: (数字)9798350368413

ISBN: (纸本)9798350368420

quantum computing greatly benefit a wide range of fields, including the detection of credit card fraud, through its twin characteristics of improved computational power and efficiency. quantum algorithms are used to enhance data analysis, pattern recognition and optimization properly with increased speed and efficiency. In the proposed model, we investigate how quantum machine learnings algorithms (QML) are used to spot credit card fraud using a data set that includes transactions from European cardholders. Various models such as neural network activation functions, epochs, and other factors employed in a hybrid quantum-classical method. The results from the best model employing a quantum hybrid technique, a conventional neural network, and an ML approach are compared. For equivalent prediction performance, we find that the quantum models train substantially more effectively than the conventional models. In order to implement quantum algorithms, penny lane is used for enabling differentiable scripting of quantum computers that is cross-platform. Similar to how a neural network is trained, a quantum computer is trained. Overall, this in-depth investigation of the application of hybrid QML in credit card fraud detection shows significant promise.

关键词： Computers Training Machine learning algorithms quantum algorithm Computational modeling Neural networks Predictive models Credit cards Fraud Pattern recognition

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A Novel quantum algorithm for Solving Optimization Problems in Electrical Engineering

A Novel Quantum Algorithm for Solving Optimization Problems ...

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Innovative Practices in Technology and Management (ICIPTM), International Conference on

作者： Ajay Sharma Kuldeep Sharma Kanchan Yadav A L N Rao Amit Srivastava Shivani Pant Chitkara Centre for Research and Development Chitkara University Himachal Pradesh India Centre of Research Impact and Outreach Chitkara University Institute of Engineering and Technology Chitkara University Rajpura Punjab India Department of Electrical Engineering GLA University Mathura Lloyd Institute of Engineering & Technology Greater Noida Lloyd Law College Greater Noida Uttaranchal Institute of Technology Uttaranchal University Uttarakhand India

ISBN: (数字)9798350307757

ISBN: (纸本)9798350307764

The ability of theoretical and monadic quantum models against number comparison to conventional quantum Genetic algorithm (QGA), quantitative particle swarm optimization, ant colony groups with simulated annealing types is analyzed in the context of electrical engineering. Several experiments were done, involving a collection of multiple data sets standard for the proposed circuit layout within power distribution and signal processing applications. In regard to comparative analysis, each algorithm presents its particular strengths for QGA-competitive convergence speed; ͟QPSO – quick conversion of individuals into a global optimum during evolution’s course and robust solutions quality in an unstable environment without tuning. The related works of the proposed algorithms include evaluating it against metaheuristics for power systems, nature-inspired hybrid heuristic approaches as well as physics motivated optimization schemes. The paper emphasizes the superiority of quantum algorithms over their classical counterparts, which is a major innovation in optimization space. This detailed analysis contributes to further comprehending the potentials of quantum computing in overcoming tough optimization challenges faced by electrical engineers.

关键词： Electrical engineering Electric potential quantum algorithm Signal processing algorithms quantum mechanics Simulated annealing Writing

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Variational quantum algorithm as an Efficient Tool for Data Fitting

Variational Quantum Algorithm as an Efficient Tool for Data ...

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quantum Computing and Engineering (QCE), IEEE International Conference on

作者： Mohammadreza Saghafi Lamine Mili Ravi Raghunathan Bradley Dept. of Electrical and Computer Engineering Northern Virginia Center Virginia Tech Falls Church VA Bradley Dept. of Electrical and Computer Engineering Virginia Tech Research Center Arlington VA

ISBN: (数字)9798331541378

ISBN: (纸本)9798331541385

This study explores the suitability of the variational quantum data fitting method as an enabling tool to better understand and characterize power system analytics. A recently proposed algorithm, the Variational quantum Linear Solver (VQLS) is investigated as an efficient approach to analyze power systems. In most studies so far, the VQLS technique has been primarily applied to square matrices. However, many problems in the analysis of power systems are represented by tall matrices. In this paper, we study the transformation of tall matrices into a form suitable for the VQLS algorithm. Two computing methodologies are explored: Internal Multiplication and Hermitian Expansion. Preliminary results show that for a sample matrix of size 64×16, Hermitian expansion requires a minimum of 7 qubits and a significantly longer computational time to prepare unitaries, as compared to Internal Multiplication which requires just 4 qubits and a significantly shorter computational time to prepare unitaries. Preliminary results also show that under the condition that matrix A has orthonormal column vectors, the Euclidean distance between vectors of answers from quantum and classical methods exhibits a slight discrepancy beyond 6 qubits. Furthermore, the technique has a polynomial scaling (in terms of qubits), which is an improvement compared to classical algorithms of UP to eight qubits.

关键词： quantum algorithm Qubit Fitting Euclidean distance Vectors Polynomials Power systems Matrix decomposition

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quantum algorithm based on the ε-random linear disequations for the continuous hidden shift problem

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quantum INFORMATION PROCESSING 2021年第10期20卷 347-347页

作者： Bae, Eunok Lee, Soojoon Kyung Hee Univ Dept Math Seoul 02447 South Korea Kyung Hee Univ Res Inst Basic Sci Seoul 02447 South Korea

There have been several research works on the hidden shift problem, quantum algorithms for the problem, and their applications. However, all the results have focused on discrete groups with discrete oracle functions. In this paper, we define the continuous hidden shift problem on R-n with a continuous oracle function as an extension of the hidden shift problem, and also define the epsilon-random linear disequations which is a generalization of the random linear disequations. By employing the newly defined concepts, we show that there exists a quantum computational algorithm which solves this problem in time polynomial in n.

关键词： quantum algorithm Continuous hidden shift problem epsilon-Random linear disequations

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AMARETTO: Enabling Efficient quantum algorithm Emulation on Low-Tier FPGAs

AMARETTO: Enabling Efficient Quantum Algorithm Emulation on ...

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IEEE International Conference on Electronics, Circuits and Systems (ICECS)

作者： Christian Conti Deborah Volpe Mariagrazia Graziano Maurizio Zamboni Giovanna Turvani Politecnico di Torino Italy

ISBN: (数字)9798350377200

ISBN: (纸本)9798350377217

Researchers and industries are increasingly drawn to quantum computing for its computational potential. However, validating new quantum algorithms is challenging due to the limitations of current quantum devices. Software simulators are time and memory-consuming, making hardware emulators an attractive alternative. This article introduces AMARETTO (quantum ARchitecture EmulaTion TechnOlogy), designed for quantum computing emulation on low-tier Field-Programmable gate arrays (FPGAs), supporting Clifford+T and rotational gate sets. It simplifies and accelerates the verification of quantum algorithms using a Reduced-Instruction-Set-Computer (RISC)-like structure and efficient handling of sparse quantum gates. A dedicated compiler translates OpenQASM 2.0 into RISC-like instructions. AMARETTO is validated against the Qiskit simulators. Our results show successful emulation of sixteen qubits on a AMD Kria KV260 SoM. This approach rivals other works in emulated qubit capacity on a smaller, more affordable FPGA.

关键词： Industries quantum algorithm Emulation Qubit Computer architecture Logic gates Vectors Software Hardware Field programmable gate arrays

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Towards a quantum algorithm for the Incompressible Nonlinear Navier-Stokes Equations

Towards a Quantum Algorithm for the Incompressible Nonlinear...

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quantum Computing and Engineering (QCE), IEEE International Conference on

作者： Muralikrishnan Gopalakrishnan Meena Yu Zhang Weiwen Jiang Youzuo Lin Stefanie Günther Xinfeng Gao National Center for Computational Sciences Oak Ridge National Laboratory Oak Ridge TN USA Theoretical Division Los Alamos National Laboratory Los Alamos NM USA Department of Electrical and Computer Engineering George Mason University Fairfax VA USA School of Data Science and Society University of North Carolina at Chapel Hill Chapel Hill NC USA Center for Applied Scientific Computing Lawrence Livermore National Laboratory Livermore CA USA Department of Mechanical and Aerospace Engineering University of Virginia Charlottesville VA USA

ISBN: (数字)9798331541378

ISBN: (纸本)9798331541385

In this work, we present novel concepts for quantum algorithms to solve transient, nonlinear partial differential equations (PDEs). The challenge lies in how to effectively represent, encode, process, and evolve the nonlinear system of PDEs on quantum computers. We will discuss the new techniques using the incompressible Navier-Stokes equations as an example, because it represents the fundamental nonlinear feature and yet removes certain complexity in physics, allowing us to focus on the design of quantum algorithms. Previous attempts solving nonlinear PDEs in quantum computation have often involved storing multiple copies of solutions or employing linearizations. Neither is practical due to exponential scaling with evolution time or insufficient solution accuracy. We propose a new framework based on matrix product states (MPSs) and matrix product operators (MPOs), in addition to the Krylov subspace methods. For example, the solution variables of the Navier-Stokes equations are represented by MPSs, and the linear and nonlinear terms are processed by MPOs. The time evolution of the operators is attained by a fast-forwarding algorithm using Krylov subspace methods. Furthermore, we discuss various techniques for efficient encoding of MPSs, measurement reduction for MPOs, and use of tensor operations to treat multi-variate, multi-physics characteristics of Navier-Stokes.

关键词： Computers quantum algorithm Tensors Fluids Partial differential equations Encoding Transient analysis Nonlinear systems Physics Navier-Stokes equations

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