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quantum Search algorithm for Exceptional Vertexes in Regular Graphs and its Circuit Implementation

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS 2021年第8期60卷 2723-2732页

作者： Dong, Yumin Liu, Zhixin Zhang, Jinlei Chongqing Normal Univ Coll Comp & Informat Sci Chongqing 401331 Peoples R China

There are some interesting properties in quantum mechanics, such as quantum superposition and entanglement. We can use these features to solve some specific problems. quantum computer has more advantages than classical computer in many problems. In this paper, we are interested in regular graph. A special case of graph structure destroyed is given. We present a search algorithm to find exceptional vertexes in the graph in this case. The algorithm uses the trick of amplitude amplification in quantum search algorithm. In the corresponding classical algorithm, the adjacency matrix may be used to store the information of vertex and edge of graph. It takes one time for the best and N times for the worst to find the target. Which means that N/2 times on average need to be conducted. In our quantum algorithm, nodes and vertexes are stored in quantum states, using quantum search to design algorithm. The search process can be accelerated in our quantum algorithm.

关键词： quantum algorithm quantum circuit Regular graph Graph theory

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Special Functions and HHL quantum algorithm for Solving Moving Boundary Value Problems Occurring in Electric Contact Phenomena

Special Functions and HHL Quantum Algorithm for Solving Movi...

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IEEE Holm Conference on Electrical Contacts

作者： Merey M. Sarsengeldin M. Zuhair Nashed University of Central Florida Orlando Florida US

ISBN: (纸本)9781665421089

This series of studies is devoted to developing and employing mathematical methods along with quantum algorithms for solving moving boundary value problems which occur in heat and mass transfer problems. In this particular study we develop mathematical framework where we utilize special functions and Harrow-Hassidim-Lloyd (HHL) quantum algorithm for finding exact and approximate solutions of Generalized Heat Equation with moving boundaries and as examples we consider plane and spherical cases. In spherical case the Generalized Heat Equation is reduced to linear moving boundary value problem with discontinuous coefficients and solved exactly. In plane case we use collocation method for approximate solution of Inverse Two-Phase Stefan problem. Experimental verification of suggested mathematical framework has been tested for modeling arcing phenomena in composite electrical contacts with AgCdO (90%) and Ni (10%). HHL algorithm was applied and run on IBM Q with Qiskit and the code is openly available on https://***/users/Schrodinger-cat-kz/projects/2.

关键词： Boundary value problems quantum algorithm Codes Contacts Conferences Approximation algorithms Mathematical models

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A Variational quantum algorithm for Ordered SVD

A Variational Quantum Algorithm for Ordered SVD

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2021 IEEE Global Communications Conference (GLOBECOM)

作者： Ju–Young Ryu Jiwon Jung Jaeyoung Lee Youngjune Gwon June–Koo Kevin Rhee School of Electrical Engineering KAIST Daejeon South Korea AI Research Center Samsung SDS Seoul South Korea KAIST Institute for IT Convergence & QuNova Computing Daejeon South Korea

ISBN: (纸本)9781728181059

Singular value decomposition (SVD) is fundamentally important and broadly useful in both quantum and classical computing. There are several quantum algorithms known for SVD. Variational quantum algorithms with parametric quantum circuits (PQC) are the most promising approach to find SVD with near-term quantum computers. This paper reports a new method for quantum SVD (QSVD) that finds the singular vectors ordered by the magnitude of singular values by adding extra CNOT gates and a new local cost function design. This ordering is important because the singular vectors with the larger singular values is more representative for the given information. The ordering property of this approach is investigated with the standard Iris dataset by numerical simulations of 4-qubit states. Methods for choosing appropriate choices for the cost function hyperparameter and cost function terms as well as an application example of a quantum encoder are also discussed.

关键词： Training Iris quantum algorithm Logic gates Numerical simulation Cost function quantum circuit

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Adaptation of Grover's quantum algorithm to Multiuser Detection in an OCDMA System

Adaptation of Grover's Quantum Algorithm to Multiuser Detect...

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Future Telecommunication Technologies (SOFTT), Symposium on

作者： Muhammad Idham Habibie Jihad Hamie Claire Goursaud INSA Lyon INRIA Université de Lyon Villeurbanne France

ISBN: (纸本)9781665405713

To support multiple transmissions in an optical fiber, several techniques have been studied such as Optical Code Division Multiple Access (OCDMA). In particular, the incoherent OCDMA systems are appreciated for their sim-plicity and reduced cost. However, they suffer from Multiple Access Interference (MAI), which degrades the performances. In order to cope with this MAI, several detectors have been studied. Among them, the Maximum Likelihood (ML) detector is the optimal one but it suffers from high complexity as all possibilities have to be tested prior to decision. However, thanks to the recent quantum computing advances, the complexity problem can be circumvented. As a matter of fact, quantum algorithms, such as Grover, exploit the superposition states in the quantum domain to accelerate the computation. Thus, in this paper, we propose to adapt the quantum Grover's algorithm in the context of Multi-User Detection (MUD), in an OCDMA system using non-orthogonal codes. We propose a way to adapt the received noisy signal to the constraints defined by Grover's algorithm. We further evaluate the probability of success in detecting the active users for different noise levels. Aside from the complexity reduction, simulations show that our proposal has a high probability of detection when the received signal is not highly altered. We show the benefits of our proposal compared to the classical and the optimal ML detector.

关键词： Multiuser detection Optical fibers quantum algorithm Detectors Optical detectors Complexity theory Proposals

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Loading is the Key: A Novel Genetic quantum algorithm for SDVRP

Loading is the Key: A Novel Genetic Quantum Algorithm for SD...

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Congress on Evolutionary Computation

作者： Weijian Ma Xinyuan Zhang Yichen Xu Fei Gao School of Computer Science Beijing University of Posts and Telecommunications Beijing China School of Economics and Management Tsinghua University Beijing China State Key Laboratary of Networking and Switching Technology Beijing University of Posts and Telecommunications Beijing China

This paper solves Split Demand Vehicle Routing Problem with minimal vehicles and controlled task splits. Our algorithm encodes the mapping between task splits and vehicles into a binary matrix and uses Genetic quantum algorithm to control the evolvement process. To convert the binary matrix solution into task loading schemes, we design a novel cost function and successfully convert task assignment problem to Transportation Problem which can be solved by Transportation Simplex Method. Our algorithm uses a simple nearest-neighborhood based heuristic to generate vehicle routes and adopts a local search method tailored for SDVRP to improve solution quality. The experimental results show that our algorithm splits few tasks and can obtain many solutions better than CVRP best-known in TSPLIB 95. Further analysis reveals that savings of SDVRP mostly come from CVRP’s failure to combine tasks geographically close into one route, when the number of vehicles are restricted to minimum.

关键词： quantum algorithm Loading Vehicle routing Transportation Transforms Genetics Search problems

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quantum algorithm for Finding the Negative Curvature Direction

Quantum Algorithm for Finding the Negative Curvature Directi...

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作者： Zhang, Kaining University of Sydney

学位级别：硕士

Non-convex optimization is an essential problem in the field of machine learning. Optimization methods for non-convex problems can be roughly di- vided into first-order methods and second-order methods, depending on the or- der of the derivative to the objective function they used. Generally, to find the local minima, the second-order methods are applied to find the effective direc- tion to escape the saddle point. Specifically, finding the Negative Curvature is considered as the subroutine to analyze the characteristic of the saddle point. However, the calculation of the Negative Curvature is expensive, which prevents the practical usage of second-order algorithms. In this thesis, we present an efficient quantum algorithm aiming to find the negative curvature direction for escaping the saddle point, which is a critical subroutine for many second-order non-convex optimization algorithms. We prove that our algorithm could produce the target state corresponding to the negative curvature direction with query complexity ˜ O(polylog(d)ϵ −1 ), where d is the dimension of the optimization function. The quantum negative curva- ture finding algorithm is exponentially faster than any known classical method, which takes time at least O(dϵ −1/2 ). Moreover, we propose an efficient quan- tum algorithm to achieve the classical read-out of the target state. Our classical read-out algorithm runs exponentially faster on the degree of d than existing counterparts.

关键词： quantum algorithm optimization state readout

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quantum hybrid algorithm for solving SAT problem

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ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE 2023年第1期121卷

作者： Varmantchaonala, Charles Moudina Fendji, Jean Louis Kedieng Ebongue Njafa, Jean Pierre Tchapet Atemkeng, Marcellin Univ Ngaoundere Fac Sci Dept Math & Comp Sci POB 454 Ngaoundere Cameroon Univ Ngaoundere Univ Inst Technol Dept Comp Engn POB 455 Ngaoundere Cameroon Univ Ngaoundere Natl Sch Chem Engn & Mineral Ind Dept Fundamental Sci & Engn Tech POB 454 Ngaoundere Cameroon Univ Maroua Fac Sci Dept Phys POB 46 Maroua Cameroon Rhodes Univ Dept Math POB 6140 Grahamstown South Africa Univ Ngaoundere Natl Sch Chem Engn & Mineral Ind Dept Fundamental Sci & Engn Tech POB 454 Ngaoundere Cameroon

Combinatorial problems usually have a large search space, and almost all classical algorithms for solving this class of problems are inefficient for real-life input sizes. quantum algorithms have been introduced with the aim of reducing computational time. In addition, to speed up the computation while solving combinatorial problems, another approach is to reduce the search space and focus on a restricted area. In this work, we study a parameter that helps reduce the search space for the solution to the satisfiability problem (SAT). We propose an approach based on Grover's algorithm that considers the defined parameter to reduce the ./ search space for the solution of the SAT problem. Our algorithm has a complexity of the order O( ./N/S), or O(N/lS) if there are l good solutions among the initial solutions, with N the number of potential solutions and S the reduction or subdivision factor of the space.

关键词： quantum algorithm Grover algorithm Combinatorial problem SAT problem

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Hybrid quantum Search algorithm for Solving the Multi-Dimensional Knapsack Problem

Hybrid Quantum Search Algorithm for Solving the Multi-Dimens...

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

作者： Gordon Cui Rei Sato Kazuhiro Saito Rodney Van Meter Hideyuki Kawashima Faculty of Environment and Information Studies Keio University Fujisawa Kanagawa Japan Quantum Computing Group KDDI Research Inc. Fujimino Saitama Japan

ISBN: (数字)9798331541378

ISBN: (纸本)9798331541385

The Multi-Dimensional Knapsack Problem (MDKP) is a strongly NP-Hard combinatorial optimization problem that extends the Knapsack Problem (KP) to multiple constraints. While effective heuristic classical MDKP algorithms have been studied, there remains no optimal exact classical algorithm and only few contributions using quantum algorithms exist. In this study, we leverage Grover's search and pre-processing techniques to propose an iterative quantum search algorithm and circuit design that integrates classical adjustments to the oracle, progressively refining solutions until optimal. Evaluations show that our method reduces depth, width, iterations, and runtime.

关键词： Runtime quantum algorithm Circuit optimization Heuristic algorithms Scalability Refining Search problems Iterative algorithms Circuit synthesis Optimization

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Design of a Post-quantum Signature algorithm

Design of a Post-Quantum Signature Algorithm

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Image Processing and Computer Applications (ICIPCA), IEEE International Conference on

作者： Yang Liu Yantai Penglai District Party Committee Office Yantai Shandong China

ISBN: (数字)9798350360240

ISBN: (纸本)9798350384161

The security of digital signatures has always been a closely watched issue in the field of cryptography. With the introduction of quantum algorithms and the development of quantum computers, traditional digital signature algorithms are threatened by being cracked. The best solution currently is to replace traditional digital signature algorithms with anti-quantum attack digital signature algorithms. Although existing anti quantum signature algorithms can effectively resist targeted attacks such as ISD and GBA, with the increasing demand for the security level of signature algorithms, the efficiency of algorithms gradually cannot meet the requirements of practical applications. In response to this issue, this article introduces a plaintext random splitting method based on Goppa codes in parallel CFS, designs and implements a fast CFS signature algorithm. Through performance analysis and comparison, it can be seen that the fast CFS signature algorithm solves the problem of multiple decoding times and low signature efficiency at higher security levels, and has smaller decoding times at the same security level, thereby improving the efficiency of signature.

关键词： Resistance Codes quantum algorithm Image processing Design methodology Resists Decoding Performance analysis Security Digital signatures

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Maximum Likelihood Detection Based on Warm-start quantum Optimization algorithm

Maximum Likelihood Detection Based on Warm-start Quantum Opt...

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Information Communication Technologies Conference (ICTC)

作者： Xinlin He Han Zeng Xutao Yu National Mobile Communications Research Laboratory Southeast University Nanjing China Purple Mountain Laboratories Nanjing China

ISBN: (数字)9798350373523

ISBN: (纸本)9798350373530

quantum computing, with its powerful parallel computing capabilities, is considered one of the promising candidates for solving complex communication problems. This paper proposes a new detection scheme by combining quantum approximation optimization algorithms (QAOA) with maximum likelihood (ML) detection. The scheme addresses the computational complexity problem faced by ML detection in large-scale multiple-input multiple-output (MIMO) channels. The primary focus lies in the warm-start optimization based on the QAOA-ML detection. We use semi-definite relaxation (SDR) to calculate the temporary solution of ML for initializing quantum circuits. The feasibility of the scheme is verified through simulation. The proposed detection scheme is evaluated and compared with classical computer-based ML detection and Minimum Mean Square Error (MMSE) detection, demonstrating similar bit error rate (BER) performance. The enormous potential of quantum algorithms in computing power solving the drawbacks of traditional ML detection algorithms provides new possibilities for improving detection efficiency.

关键词： Maximum likelihood detection quantum algorithm Simulation Bit error rate Stationary state Symbols Detectors

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