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quantum algorithms for the Physical Layer: Potential Applications to Physical Layer Security

IEEE ACCESS 2025年 13卷 13988-14009页

作者： Matsumine, Toshiki Ochiai, Hideki Shikata, Junji Yokohama Natl Univ Inst Adv Sci Yokohama 2408501 Japan Osaka Univ Grad Sch Engn Osaka 5650871 Japan Yokohama Natl Univ Grad Sch Environm & Informat Sci Yokohama 2408501 Japan

The field of quantum technologies has garnered considerable interest and witnessed noteworthy progress in recent years. It is also anticipated that these technologies will continue to flourish and exert a considerable influence on society, i.e., a plethora of real-world problems that cannot be solved by classical algorithms are believed to benefit from the implementation of quantum algorithms. Meanwhile, as an alternative to cryptographic methods, physical layer security (PLS) has been extensively studied as a means to realize secure wireless communication that is resistant to attacks by both classical and quantum computers, i.e., quantum-safe. While the prevailing approach to PLS has been based on classical algorithms, this could potentially be accelerated by the application of quantum algorithms. This paper examines the potential applications of various quantum algorithms, including quantum annealing, hybrid quantum-classical algorithms, and Grover-based algorithms, to the the PLS problems. In particular, we begin with a concise overview of their applications to physical layer techniques and then proceed to discuss their use in addressing the challenges of secret message transmission and secret key generation from wireless channels.

关键词： Logic gates quantum computing quantum algorithm Optimization Annealing Qubit quantum annealing Cryptography Computers Approximation algorithms hybrid quantum-classical algorithms multi-input multi-output (MIMO) physical layer security (PLS) quantum algorithms quantum annealing (QA) quantum approximate optimization algorithm (QAOA) reconfigurable intelligent surface (RIS) secret key generation (SKG)

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An implementation of the finite element method in hybrid classical/quantum computers

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FINITE ELEMENTS IN ANALYSIS AND DESIGN 2025年 248卷

作者： Arora, Abhishek Ward, Benjamin M. Oskay, Caglar Vanderbilt Univ Dept Civil & Environm Engn Nashville TN 37212 USA Vanderbilt Univ Dept Mech Engn Nashville TN 37212 USA

This manuscript presents the quantum Finite Element Method (Q-FEM) developed for use in noisy intermediate-scale quantum (NISQ) computers and employs the variational quantum linear solver (VQLS) algorithm. The proposed method leverages the classical FEM procedure to perform the unitary decomposition of the stiffness matrix and employs generator functions to design explicit quantum circuits corresponding to the unitaries. Q-FEM keeps the structure of the finite element discretization intact allowing for the use of variable element lengths and material coefficients in FEM discretization. The proposed method is tested on a steady-state heat equation discretized using linear and quadratic shape functions. Numerical verification studies are performed on the IBM QISKIT simulator and it is demonstrated that Q-FEM is effective in converging to the correct solution for a variety of problems and model discretizations, including with different element lengths, variable coefficients, and different boundary conditions. The formalism developed herein is general and can be extended to problems with higher dimensions. However, numerical examples also demonstrate that the number of parameters for the variational ansatz scale exponentially with the number of qubits, and increases the odds of convergence. Moreover, the deterioration of system conditioning with problem size results in barren plateaus and convergence difficulties.

关键词： quantum computing quantum-finite element method Variational quantum linear solver hybrid quantum-classical algorithms

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quantum metric learning with fuzzy-informed learning

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2024年 643卷

作者： Huang, Chenyi Zhang, Shibin Chang, Yan Yan, Lily Chengdu Univ Informat Technol Xin Gu Ind Coll Sch Cybersecur Chengdu 610225 Peoples R China Adv Cryptog & Syst Secur Key Lab Sichuan Prov Chengdu 610225 Peoples R China

By constructing a quantum circuit with adjustable parameters, variational quantum circuits are capable of embedding input data into Hilbert space and facilitating the execution of complex deep learning tasks. Recently, a method known as quantum metric learning has emerged. It adaptively adjusts quantum embedding circuits to enable clusters of classical data from different categories to form linear separations in Hilbert space. This approach combines the advantages of kernel methods and is implementable on near -term quantum devices. However, applying quantum metric learning to more complex data presents challenges, largely due to the inherent fuzziness, uncertainty, and noise in the data itself and in the classical neural network preprocessing. To address these challenges, this paper proposes a fuzzy information -driven framework for quantum metric learning. This framework leverages fuzzy learning to accurately describe the uncertainty of data characteristics and adaptively integrates features, fuzziness, and uncertainty. Numerical experiments demonstrate that, compared to standard quantum metric learning, this framework achieves competitive performance and promising results. Furthermore, the interpretability provided by fuzzy logic aids in understanding the intrinsic mechanisms of the selected features during the quantum feature mapping process, offering new perspectives and approaches for better utilization of current quantum information processors.

关键词： quantum metric learning quantum machine learning Fuzzy learning hybrid quantum-classical algorithms

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Integration of Simulated quantum Annealing in Parallel Tempering and Population Annealing for Heterogeneous-Profile QUBO Exploration

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IEEE ACCESS 2023年 11卷 30390-30441页

作者： Volpe, Deborah Cirillo, Giovanni Amedeo Zamboni, Maurizio Turvani, Giovanna Politecn Torino Dept Elect & Telecommun I-10129 Turin Italy

Simulated quantum Annealing (SQA) is a heuristic algorithm which can solve Quadratic Unconstrained Binary Optimization (QUBO) problems by emulating the exploration of the solution space done by a quantum annealer. It mimics the quantum superposition and tunnelling effects through a set of correlated replicas of the spins system representing the problem to be solved and performing Monte Carlo steps. However, the effectiveness of SQA over a classical algorithm strictly depends on the cost/energy profile of the target problem. In fact, quantum annealing only performs well in exploring functions with high and narrow peaks, while classical annealing is better in overcoming flat and wide energy-profile barriers. Unfortunately, real-world problems have a heterogeneous solution space and the probability of success of each solver depends on the size of the energy profile region compatible with its exploration mechanism. Therefore, significant advantages could be obtained by exploiting hybrid solvers, which combine SQA and classical algorithms. This work proposes four new quantum-classical algorithms: Simulated quantum Parallel Tempering (SQPT), Simulated quantum Population Annealing (SQPA), Simulated quantum Parallel Tempering - Population Annealing v1 (SQPTPA1) and Simulated quantum Parallel Tempering - Population Annealing v2 (SQPTPA2). They are obtained by combining SQA, Parallel Tempering (PT), and Population Annealing (PA). Their results are compared with those provided by SQA, considering benchmark QUBO problems, characterized by different profiles. Even though this work is preliminary, the obtained results are encouraging and prove hybrid solvers' potential in solving a generic optimization problem.

关键词： quantum annealing Simulated annealing Statistics Sociology Optimization Annealing MIMICs Simulated quantum annealing parallel tempering population annealing hybrid quantum-classical algorithms optimization problems quadratic unconstrained binary optimization Ising machine cost function energy profile

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Engineering Grover Adaptive Search: Exploring the Degrees of Freedom for Efficient QUBO Solving

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IEEE JOURNAL ON EMERGING AND SELECTED TOPICS IN CIRCUITS AND SYSTEMS 2022年第3期12卷 614-623页

作者： Giuffrida, Luigi Volpe, Deborah Cirillo, Giovanni Amedeo Zamboni, Maurizio Turvani, Giovanna Politecn Torino Dept Elect & Telecommun I-10129 Turin Italy STMicroelectronics I-20007 Cornaredo Italy

quantum computers have the potential to solve Quadratic Unconstrained Binary Optimization (QUBO) problems with lower computational complexity than classical ones. Considering the current limitations of quantum hardware, the joint use of classical and quantum paradigms could exploit both advantages. quantum routines can make some complex tasks for classical computers feasible. For example, in the Grover Adaptive Search (GAS) procedure, the problem cost function is classically shifted iteratively, whenever a negative value is found through the quantum Grover Search (GS) algorithm, until the minimum is achieved. This quantum-classical approach is characterized by many degrees of freedom, e.g. the number of GS iterations in each call and the stop condition of the algorithm, which should be appropriately tuned for an effective and fast convergence to the optimal solution. The availability of software routines could permit the best management of the GAS parameters. This work proposes new mechanisms for GAS parameters management and compares them with the existing ones, like one available in the Qiskit framework. The proposed mechanisms can automatically arrange the parameters according to the algorithm evolution and their previous experience, thus ensuring a more frequent and faster achievement of the optimal solution. Even though these strategies can be further improved, the results are encouraging. The analysis is done to identify the best policy for different problems. It lays the foundation for designing an automatic toolchain for QUBO solving, which can obtain the best possible implementation of the GAS algorithm for each submitted problem.

关键词： quantum computing Cost function Computers Search problems Task analysis quantum circuit Optimal scheduling Grover search Grover adaptive search hybrid quantum-classical algorithms optimization problems quadratic unconstrained binary optimization cost function quantum dictionary

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Learning adiabatic quantum algorithms over optimization problems

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quantum MACHINE INTELLIGENCE 2021年第1期3卷 1-19页

作者： Pastorello, Davide Blanzieri, Enrico Cavecchia, Valter Univ Trento Dept Informat Engn & Comp Sci Via Sommar 9 I-38123 Trento Italy Ist Nazl Fis Nucl Trento Inst Fundamental Phys & Applicat TIFPA Via Sommar 14 I-38123 Trento Italy CNR Inst Mat Elect & Magnetism Via Cascata 56-C I-38123 Trento Italy

An adiabatic quantum algorithm is essentially given by three elements: An initial Hamiltonian with known ground state, a problem Hamiltonian whose ground state corresponds to the solution of the given problem, and an evolution schedule such that the adiabatic condition is satisfied. A correct choice of these elements is crucial for an efficient adiabatic quantum computation. In this paper, we propose a hybrid quantum-classical algorithm that, by solving optimization problems with an adiabatic machine, determines a problem Hamiltonian assuming restrictions on the class of available problem Hamiltonians. The scheme is based on repeated calls to the quantum machine into a classical iterative structure. In particular, we suggest a technique to estimate the encoding of a given optimization problem into a problem Hamiltonian and we prove the convergence of the algorithm.

关键词： Adiabatic quantum computing hybrid quantum-classical algorithms Tabu search

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An Experimental Comparison of Qiskit and Pennylane for hybrid quantum-classical Support Vector Machines 1

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20th Conference of the Spanish Association for Artificial Intelligence (CAEPIA)

作者： Rodriguez-Diaz, Francesc Francisco Torres, Jose Gutierrez-Aviles, David Troncoso, Alicia Martinez-Alvarez, Francisco Pablo de Olavide Univ Data Sci & Big Data Lab Seville Spain Univ Seville Dept Comp Sci Seville Spain

ISBN: (数字)9783031627996

ISBN: (纸本)9783031627989;9783031627996

quantum computing holds great promise for enhancing machine learning algorithms, particularly by integrating classical and quantum techniques. This study compares two prominent quantum development frameworks, Qiskit and Pennylane, focusing on their suitability for hybrid quantum-classical support vector machines with quantum kernels. Our analysis reveals that Qiskit requires less theoretical information to be used, while Pennylane demonstrates superior performance in terms of execution time. Although both frameworks exhibit variances, our experiments reveal that Qiskit consistently yields superior classification accuracy compared to Pennylane when training classifiers with quantum kernels. Additionally, our results suggest that the performance of both frameworks remains stable for up to 20 qubits, indicating their suitability for practical applications. Overall, our findings provide valuable insights into the strengths and limitations of Qiskit and Pennylane for hybrid quantum-classical machine learning.

关键词： quantum Computing quantum Support Vector Machine quantum Kernel hybrid quantum-classical algorithms

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Recommending Solution Paths for Solving Optimization Problems with quantum Computing

Recommending Solution Paths for Solving Optimization Problem...

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2nd IEEE International Conference on quantum Software (IEEE QSW)

作者： Poggel, Benedikt Quetschlich, Nils Burgholzer, Lukas Wille, Robert Lorenz, Jeanette Miriam Fraunhofer Inst Cognit Syst IKS Munich Germany Tech Univ Munich Chair Design Automat Munich Germany Software Competence Ctr Hagenberg GmbH SCCH Hagenberg Austria Johannes Kepler Univ Linz Inst Integrated Circuits Linz Austria

ISBN: (纸本)9798350304794

Solving real-world optimization problems with quantum computing requires choosing between a large number of options concerning formulation, encoding, algorithm and hardware. Finding good solution paths is challenging for end users and researchers alike. We propose a framework designed to identify and recommend the best-suited solution paths in an automated way. This introduces a novel abstraction layer that is required to make quantum-computing-assisted solution techniques accessible to end users without requiring a deeper knowledge of quantum technologies. State-of-the-art hybrid algorithms, encoding and decomposition techniques can be integrated in a modular manner and evaluated using problem-specific performance metrics. Equally, tools for the graphical analysis of variational quantum algorithms are developed. classical, fault tolerant quantum and quantum-inspired methods can be included as well to ensure a fair comparison resulting in useful solution paths. We demonstrate and validate our approach on a selected set of options and illustrate its application on the capacitated vehicle routing problem (CVRP). We also identify crucial requirements and the major design challenges for the proposed abstraction layer within a quantum-assisted solution workflow for optimization problems.

关键词： quantum computing applied optimization hybrid quantum-classical algorithms variational quantum algorithms design automation abstraction layer

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Benchmarking Simulated and Physical quantum Processing Units Using quantum and hybrid algorithms

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ADVANCED quantum TECHNOLOGIES 2023年第8期6卷

作者： Kordzanganeh, Mohammad Buchberger, Markus Kyriacou, Basil Povolotskii, Maxim Fischer, Wilhelm Kurkin, Andrii Somogyi, Wilfrid Sagingalieva, Asel Pflitsch, Markus Melnikov, Alexey Terra Quantum AG CH-9000 St Gallen Switzerland QMware AG CH-9000 St Gallen Switzerland

Powerful hardware services and software libraries are vital tools for quickly and affordably designing, testing, and executing quantum algorithms. A robust large-scale study of how the performance of these platforms scales with the number of qubits is key to providing quantum solutions to challenging industry problems. This work benchmarks the runtime and accuracy for a representative sample of specialized high-performance simulated and physical quantum processing units. Results show the QMware simulator can reduce the runtime for executing a quantum circuit by up to 78% compared to the next fastest option for algorithms with fewer than 27 qubits. The Amazon Web Service State-Vector Simulator 1 offers a runtime advantage for larger circuits, up to the maximum 34 qubits. Beyond this limit, QMware can execute circuits as large as 40 qubits. Physical quantum devices, such as Rigetti's Aspen-M2, can provide an exponential runtime advantage for circuits with more than 30 qubits. However, the high financial cost of physical quantum processing units presents a serious barrier to practical use. Moreover, only IonQ's Harmony quantum device achieves high fidelity with more than four qubits. This study paves the way to understanding the optimal combination of available software and hardware for executing practical quantum algorithms.

关键词： hardware and software benchmarking hybrid quantum-classical algorithms quantum algorithms quantum processing units simulated quantum processing units

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qLEET: visualizing loss landscapes, expressibility, entangling power and training trajectories for parameterized quantum circuits

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quantum INFORMATION PROCESSING 2023年第6期22卷 256-256页

作者： Azad, Utkarsh Sinha, Animesh Int Inst Informat Technol Ctr Computat Nat Sci & Bioinformat Hyderabad India Int Inst Informat Technol Ctr Quantum Sci & Technol Hyderabad India

We present qLEET, an open-source Python package for studying parameterized quantum circuits (PQCs), which are widely used in various variational quantum algorithms (VQAs) and quantum machine learning (QML) algorithms. qLEET enables computation of properties such as expressibility and entangling power of a PQC by studying its entanglement spectrum and the distribution of parameterized states produced by it. Furthermore, it allows users to visualize the training trajectories of PQCs along with high-dimensional loss landscapes generated by them for different objective functions. It supports quantum circuits and noise models built using popular quantum computing libraries such as Qiskit, Cirq, and PyQuil. In our work, we demonstrate how qLEET provides opportunities to design and improve hybrid quantum-classical algorithms by utilizing intuitive insights from the ansatz capability and structure of the loss landscape.

关键词： quantum computing quantum software Parameterized quantum circuits hybrid quantum-classical algorithms

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