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variational quantum algorithm for designing quantum information maskers

Communications in Theoretical Physics 2025年第3期77卷 66-74页

作者： Jin-Ze Li Ming-Hao Wang Bin Zhou School of Physics Hubei UniversityWuhan 430062China

Since the concept of quantum information masking was proposed by Modi et al(2018 ***.120,230501),many interesting and significant results have been reported,both theoretically and ***,designing a quantum information masker is not an easy task,especially for larger *** this paper,we propose a variational quantum algorithm to resolve this ***,our algorithm is a hybrid quantum-classical model,where the quantum device with adjustable parameters tries to mask quantum information and the classical device evaluates the performance of the quantum device and optimizes its *** optimization,the quantum device behaves as an optimal *** loss value during optimization can be used to characterize the performance of the *** particular,if the loss value converges to zero,we obtain a perfect masker that completely masks the quantum information generated by the quantum information source,otherwise,the perfect masker does not exist and the subsystems always contain the original ***,these resulting maskers are still *** parallelism is utilized to reduce quantum state preparations and *** study paves the way for wide application of quantum information masking,and some of the techniques used in this study may have potential applications in quantum information processing.

关键词： variational quantum algorithm quantum information masking quantum parallelism

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A variational quantum algorithm for the Poisson equation based on the banded Toeplitz systems

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Communications in Theoretical Physics 2025年第4期77卷 23-33页

作者： Xiaoqi Liu Yuedi Qu Ming Li Shu-Qian Shen College of Science China University of PetroleumQingdao 266580China

To solve the Poisson equation it is usually possible to discretize it into solving the corresponding linear system Ax=*** quantum algorithms(VQAs)for the discretized Poisson equation have been studied *** present a VQA based on the banded Toeplitz systems for solving the Poisson equation with respect to the structural features of matrix *** detail,we decompose the matrices A and A^(2)into a linear combination of the corresponding banded Toeplitz matrix and sparse matrices with only a few non-zero *** the one-dimensional Poisson equation with different boundary conditions and the d-dimensional Poisson equation with Dirichlet boundary conditions,the number of decomposition terms is less than that reported in[***.A 2023108,032418].Based on the decomposition of the matrix,we design quantum circuits that efficiently evaluate the cost ***,numerical simulation verifies the feasibility of the proposed ***,the VQAs for linear systems of equations and matrix-vector multiplications with the K-banded Toeplitz matrix T_(n)^(K)are given,where T_(n)^(K)∈R^(n×n)and K∈O(ploylogn).

关键词： variational quantum algorithm Poisson equation quantum circuit

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Resource-Efficient Adaptive variational quantum algorithm for Combinatorial Optimization Problems

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ADVANCED quantum TECHNOLOGIES 2025年第0期

作者： Wu, Sheng-Yao Song, Yan-Qi Li, Run-Ze Qin, Su-Juan Wen, Qiao-Yan Gao, Fei Beijing Univ Posts & Telecommun State Key Lab Networking & Switching Technol Beijing 100876 Peoples R China Beijing Univ Posts & Telecommun Sch Cyberspace Secur Beijing 100876 Peoples R China China Acad Informat & Commun Technol Beijing 100191 Peoples R China China Elect Technol Grp Corp Res Inst 15 Beijing 100083 Peoples R China Beijing Univ Posts & Telecommun Natl Engn Res Ctr Disaster Backup & Recovery Beijing 100876 Peoples R China

variational quantum algorithms (VQAs) are quantum-classical hybrid algorithms that are promising for the near future. The quantum Approximate Optimization algorithm (QAOA) is a representative VQA for solving combinatorial optimization problems. However, the parameterized quantum circuit (PQC) of QAOA still has room for improvement. The existing method, called ADAPT-QAOA, has improved the PQC of QAOA, but the circuit depth remains deep. A Resource-Efficient Adaptive VQA (RE-ADAPT-VQA) that utilizes gates from a new gate pool is proposed to construct a PQC. RE-ADAPT-VQA incrementally integrates parameterized quantum gates based on the gradient until the predefined stopping criteria are satisfied, and a rollback mechanism is proposed to ensure that the circuit remains shallow. The algorithm is experimentally simulated to solve Max-Cut problem and the maximum independent set problem. The results show that RE-ADAPT-VQA significantly reduces circuit depth, single-qubit gates, and CNOT gates compared to existing methods, while maintaining the same level of energy error.

关键词： max-cut maximum independent set parameterized quantum circuit variational quantum algorithm

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variational quantum algorithm for node embedding

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Fundamental Research 2024年第4期4卷 845-850页

作者： Zeng-rong Zhou Hang Li Gui-Lu Long Research Center for Quantum Sensing Zhejiang LabHangzhou 311121China Bejing Academy of Quantum Information Sciences Beijing 100193China State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics Tsinghua UniversityBeijing 100084China

quantum machine learning has made remarkable progress in many important ***,the gate complexity of the initial state preparation is seldom considered in lots of quantum machine learning algorithms,making them ***,we propose a quantum algorithm for the node embedding problem that maps a node graph's topological structure to embedding *** resulting quantum embedding state can be used as an input for other quantum machine learning *** O(log(N))qubits to store the information of N nodes,our algorithm will not lose quantum advantage for the subsequent quantum information ***,owing to the use of a parameterized quantum circuit with O(poly(log(N)))depth,the resulting state can serve as an efficient quantum *** addition,we explored the measurement complexity of the quantum node embedding algorithm,which is the main issue in training parameters,and extended the algorithm to capture high-order neighborhood information between ***,we experimentally demonstrated our algorithm on an nuclear magnetic resonance quantum processor to solve a graph model.

关键词： quantum machine learning quantum computation Node embedding variational quantum algorithm Nuclear magnetic resonance

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Simulator Demonstration of Large Scale variational quantum algorithm on HPC Cluster

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IEEE ACCESS 2024年 12卷 85219-85230页

作者： Morita, Mikio Tomita, Yoshinori Koyama, Junpei Kimura, Koichi Fujitsu Ltd Quantum Lab Kawasaki 2118588 Japan

Advances in quantum simulator technology are increasingly required because research on quantum algorithms is becoming more sophisticated and complex. State vector simulation utilizes CPU and memory resources in computing nodes exponentially with respect to the number of qubits;furthermore, in a variational quantum algorithm, the large number of repeated runs by classical optimization is also a heavy load. This problem has been addressed by preparing numerous computing nodes or simulation frameworks that operate effectively. This study aimed to accelerate quantum simulation using two newly proposed methods: to efficiently utilize limited computational resources by adjusting the ratio of the MPI and distributed processing parallelism corresponding to the target problem settings and to slim down the Hamiltonian by considering the effect of accuracy on the calculation result. Ground-state energy calculations of a fermionic model were performed using a variational quantum eigensolver (VQE) on an HPC cluster with up to 1024 FUJITSU Processor A64FX connected to each other by InfiniBand;the processor is also used on supercomputer Fugaku. We achieved 200 times higher speed over VQE simulations and demonstrated 32 qubits ground-state energy calculations in acceptable time. This result indicates that > 30 qubit state vector simulations can be realistically utilized for further research on variational quantum algorithms.

关键词： Distribute computing quantum computing quantum simulation variational quantum algorithm variational quantum eigensolver

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Towards an efficient variational quantum algorithm for solving linear equations

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Communications in Theoretical Physics 2024年第11期76卷 54-65页

作者： WenShan Xu Ri-Gui Zhou YaoChong Li XiaoXue Zhang College of Information Engineering Shanghai Maritime UniversityShanghai 201306China Research Center of Intelligent Information Processing and Quantum Intelligent Computing Shanghai 201306China

variational quantum algorithms are promising methods with the greatest potential to achieve quantum advantage,widely employed in the era of noisy intermediate-scale quantum *** study presents an advanced variational hybrid algorithm(EVQLSE)that leverages both quantum and classical computing paradigms to address the solution of linear equation ***,an innovative loss function is proposed,drawing inspiration from the similarity measure between two quantum *** function exhibits a substantial improvement in computational complexity when benchmarked against the variational quantum linear ***,a specialized parameterized quantum circuit structure is presented for small-scale linear systems,which exhibits powerful expressive *** rigorous numerical analysis,the expressiveness of this circuit structure is quantitatively assessed using a variational quantum regression algorithm,and it obtained the best score compared to the ***,the expansion in system size is accompanied by an increase in the number of parameters,placing considerable strain on the training process for the *** address this challenge,an optimization strategy known as quantum parameter sharing is introduced,which proficiently minimizes parameter volume while adhering to exacting precision ***,EVQLSE is successfully implemented on a quantum computing platform provided by IBM for the resolution of large-scale problems characterized by a dimensionality of 220.

关键词： quantum computing variational quantum algorithm systems of linear equations parameterized quantum circuit

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Lithium-ion battery state of health estimation method based on variational quantum algorithm optimized stacking strategy

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ENERGY REPORTS 2024年 11卷 2877-2891页

作者： Wang, Longze Jiang, Siyu Mao, Yuteng Li, Zhehan Zhang, Yan Li, Meicheng North China Elect Power Univ Sch Renewable Energy Sources State Key Lab Alternate Elect Power Syst Renewble Beijing 102206 Peoples R China Univ Macau State Key Lab Internet Things Smart City Taipa 999078 Macao Peoples R China North China Elect Power Univ Sch Econ & Management Beijing 102206 Peoples R China Beijing Key Lab New Energy & Low Carbon Dev Beijing 102206 Peoples R China

Accurate state -of -health (SOH) estimation is critical for the performance and safety of lithium -ion batteries. An innovative method for SOH estimation is proposed by employing a variational quantum algorithm to optimize a stacking integrated learning strategy. The strategy effectively combines multiple model advantages, enhancing the estimation accuracy and generalizability. Using this method, eight sets of health factors are extracted, focusing on the relationship between battery capacity degradation and electrothermal parameters. A stacking integrated learning framework is developed by utilizing diverse primary learners to effectively capture the dynamic changes in health factors. A ridge regression meta -learner is incorporated to address overfitting problems found in primary learners. A significant innovation is the integration of a variational quantum circuit module as the primary learner. This module plays a crucial role in optimizing the hyperparameters for the analysis of complex and high -dimensional battery data. The effectiveness of the method is validated using four different types of batteries, showing a 77.4% improvement in prediction accuracy compared with traditional methods, with the SOH estimation error maintained within a tight margin of 0.67%. The mean absolute error, mean absolute percentage error, and root mean square error with maximum reduction rates are 76.7%, 77.4%, and 62.7%, respectively. The maximum increase in the R -squared coefficient is 5.3%. This study demonstrates the potential of variational quantum algorithms in enhancing the SOH estimation accuracy and opens new possibilities for the advanced health status management of lithium -ion batteries.

关键词： Lithium -ion battery State of health estimation Stacking strategy variational quantum algorithm Hyperparameter optimization

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A variational quantum algorithm for Ordered SVD

A Variational Quantum Algorithm for Ordered SVD

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IEEE Global Communications Conference (GLOBECOM)

作者： Ryu, Ju-Young Jung, Jiwon Lee, Jaeyoung Gwon, Youngjune Rhee, June-Koo Kevin Korea Adv Inst Sci & Technol Sch Elect Engn Daejeon South Korea Samsung SDS AI Res Ctr Seoul South Korea KAIST Inst IT Convergence & QuNova Comp Daejeon South Korea

ISBN: (纸本)9781728181042

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： singular value decomposition variational quantum algorithm parametric quantum circuit

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A variational quantum algorithm for Hamiltonian diagonalization

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quantum SCIENCE AND TECHNOLOGY 2021年第4期6卷

作者： Zeng, Jinfeng Cao, Chenfeng Zhang, Chao Xu, Pengxiang Zeng, Bei Hong Kong Univ Sci & Technol Dept Phys Kowloon Clear Water Bay Hong Kong Peoples R China Peng Cheng Lab Shenzhen 518055 Peoples R China

Hamiltonian diagonalization is at the heart of understanding physical properties and practical applications of quantum systems. It is highly desired to design quantum algorithms that can speedup Hamiltonian diagonalization, especially those can be implemented on near-term quantum devices. In this work, we propose a variational quantum algorithm for Hamiltonian diagonalization (VQHD) of quantum systems, which explores the important physical properties, such as temperature, locality, and correlation, of the system. The key idea is that the thermal states of the system encode the information of eigenvalues and eigenstates of the system Hamiltonian. To obtain the full spectrum of the Hamiltonian, we use a quantum imaginary time evolution algorithm with high temperature, which prepares a thermal state with a small correlation length. With Trotterization, this then allows us to implement each step of imaginary time evolution by a local unitary transformation on only a small number of sites. Diagonalizing these thermal states hence leads to a full knowledge of the Hamiltonian eigensystem. We apply our algorithm to diagonalize local Hamiltonians and return results with high precision. Our VQHD algorithm sheds new light on the applications of near-term quantum computers.

关键词： Hamiltonian diagonalization variational quantum algorithm thermal state

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A variational quantum algorithm FOR APPROXIMATING CONVEX ROOFS

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quantum INFORMATION & COMPUTATION 2022年第13-14期22卷 1081-1109页

作者： Androulakis, George McGaha, Ryan Univ South Carolina Dept Math 1523 Greene St Columbia SC 29208 USA

Many entanglement measures are first defined for pure states of a bipartite Hilbert space, and then extended to mixed states via the convex roof extension. In this article we alter the convex roof extension of an entanglement measure, to produce a sequence of extensions that we call f-d extensions, for d is an element of N, where f : [0,1] -> [0, infinity) is a fixed continuous function which vanishes only at zero. We prove that for any such function f, and any continuous, faithful, non-negative function, (such as an entanglement measure), mu on the set of pure states of a finite dimensional bipartite Hilbert space, the collection of f-d extensions of mu detects entanglement, i.e. a mixed state rho on a finite dimensional bipartite Hilbert space is separable, if and only if there exists d is an element of N such that the f -d extension of mu applied to rho is equal to zero. We introduce a quantum variational algorithm which aims to approximate the f-d extensions of entanglement measures defined on pure states. However, the algorithm does have its drawbacks. We show that this algorithm exhibits barren plateaus when used to approximate the family of f-d extensions of the Tsallis entanglement entropy for a certain function f and unitary ansatz U(theta) of sufficient depth. In practice, if additional information about the state is known, then one needs to avoid using the suggested ansatz for long depth of circuits.

关键词： Entangelement measure barren plateau variational quantum algorithm

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