The variational data assimilation scheme (VAR) is applied to investigating the advective effect and the evolution of the control variables in time splitting semi-Lagrangian framework. Two variational algorithms are us...The variational data assimilation scheme (VAR) is applied to investigating the advective effect and the evolution of the control variables in time splitting semi-Lagrangian framework. Two variational algorithms are used. One is the conjugate code method-direct approach, and another is the numerical backward integration of analytical adjoint equation—indirect approach. Theoretical derivation and sensitivity tests are conducted in order to verify the consistency and inconsistency of the two algorithms under the semi-Lagrangian framework. On the other hand, the sensitivity of the perfect and imperfect initial condition is also tested in both direct and indirect approaches. Our research has shown that the two algorithms are not only identical in theory, but also identical in numerical calculation. Furthermore, the algorithms of the indirect approach are much more feasible and efficient than that of the direct one when both are employed in the semi-Lagrangian framework. Taking advantage of semi-Lagrangian framework, one purpose of this paper is to illustrate when the variational assimilation algorithm is concerned in the computational method of the backward integration, the algorithm is extremely facilitated. Such simplicity in indirect approach should be meaningful for the VAR design in passive model. Indeed, if one can successfully split the diabatic and adiabatic process, the algorithms represented in this paper might be easily used in a more general vision of atmospheric model.展开更多
In open quantum systems,the Liouvillian gap characterizes the relaxation time toward the steady state.However,accurately computing this quantity is notoriously difficult due to the exponential growth of the Hilbert sp...In open quantum systems,the Liouvillian gap characterizes the relaxation time toward the steady state.However,accurately computing this quantity is notoriously difficult due to the exponential growth of the Hilbert space and the non-Hermitian nature of the Liouvillian superoperator.In this work,we propose a variational quantum algorithm for efficiently estimating the Liouvillian gap.By utilizing the Choi-Jamio lkowski isomorphism,we reformulate the problem as finding the first excitation energy of an effective non-Hermitian Hamiltonian.Our method employs variance minimization with an orthogonality constraint to locate the first excited state and adopts a two-stage optimization scheme to enhance convergence.Moreover,to address scenarios with degenerate steady states,we introduce an iterative energy-offset scanning technique.Numerical simulations on the dissipative XXZ model confirm the accuracy and robustness of our algorithm across a range of system sizes and dissipation strengths.These results demonstrate the promise of variational quantum algorithms for simulating open quantum many-body systems on near-term quantum hardware.展开更多
To solve the Poisson equation it is usually possible to discretize it into solving the corresponding linear system Ax=b.Variational quantum algorithms(VQAs)for the discretized Poisson equation have been studied before...To solve the Poisson equation it is usually possible to discretize it into solving the corresponding linear system Ax=b.Variational quantum algorithms(VQAs)for the discretized Poisson equation have been studied before.We present a VQA based on the banded Toeplitz systems for solving the Poisson equation with respect to the structural features of matrix A.In 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 elements.For 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[Phys.Rev.A 2023108,032418].Based on the decomposition of the matrix,we design quantum circuits that efficiently evaluate the cost function.Additionally,numerical simulation verifies the feasibility of the proposed algorithm.Finally,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).展开更多
Since the concept of quantum information masking was proposed by Modi et al(2018 Phys.Rev.Lett.120,230501),many interesting and significant results have been reported,both theoretically and experimentally.However,desi...Since the concept of quantum information masking was proposed by Modi et al(2018 Phys.Rev.Lett.120,230501),many interesting and significant results have been reported,both theoretically and experimentally.However,designing a quantum information masker is not an easy task,especially for larger systems.In this paper,we propose a variational quantum algorithm to resolve this problem.Specifically,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 parameters.After optimization,the quantum device behaves as an optimal masker.The loss value during optimization can be used to characterize the performance of the masker.In 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 information.Nevertheless,these resulting maskers are still optimal.Quantum parallelism is utilized to reduce quantum state preparations and measurements.Our 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.展开更多
The trace norm of matrices plays an important role in quantum information and quantum computing. How to quantify it in today’s noisy intermediate scale quantum(NISQ) devices is a crucial task for information processi...The trace norm of matrices plays an important role in quantum information and quantum computing. How to quantify it in today’s noisy intermediate scale quantum(NISQ) devices is a crucial task for information processing. In this paper, we present three variational quantum algorithms on NISQ devices to estimate the trace norms corresponding to different situations.Compared with the previous methods, our means greatly reduce the requirement for quantum resources. Numerical experiments are provided to illustrate the effectiveness of our algorithms.展开更多
In this paper we use the auxiliary principle technique to suggest and analyze novel and innovative iterative algorithms for a class of nonlinear variational inequalities. Several special cases, which can be obtained f...In this paper we use the auxiliary principle technique to suggest and analyze novel and innovative iterative algorithms for a class of nonlinear variational inequalities. Several special cases, which can be obtained from our main results, are also discussed.展开更多
Variational quantum algorithms are promising methods with the greatest potential to achieve quantum advantage,widely employed in the era of noisy intermediate-scale quantum computing.This study presents an advanced va...Variational quantum algorithms are promising methods with the greatest potential to achieve quantum advantage,widely employed in the era of noisy intermediate-scale quantum computing.This study presents an advanced variational hybrid algorithm(EVQLSE)that leverages both quantum and classical computing paradigms to address the solution of linear equation systems.Initially,an innovative loss function is proposed,drawing inspiration from the similarity measure between two quantum states.This function exhibits a substantial improvement in computational complexity when benchmarked against the variational quantum linear solver.Subsequently,a specialized parameterized quantum circuit structure is presented for small-scale linear systems,which exhibits powerful expressive capabilities.Through 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 others.Moreover,the expansion in system size is accompanied by an increase in the number of parameters,placing considerable strain on the training process for the algorithm.To address this challenge,an optimization strategy known as quantum parameter sharing is introduced,which proficiently minimizes parameter volume while adhering to exacting precision standards.Finally,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.展开更多
Classical machine learning algorithms seem to be totally incapable of processing tremendous amounts of data,while quantum machine learning algorithms could deal with big data with ease and provide exponential accelera...Classical machine learning algorithms seem to be totally incapable of processing tremendous amounts of data,while quantum machine learning algorithms could deal with big data with ease and provide exponential acceleration over classical counterparts.Meanwhile,variational quantum algorithms are widely proposed to solve relevant computational problems on noisy,intermediate-scale quantum devices.In this paper,we apply variational quantum algorithms to quantum support vector machines and demonstrate a proof-of-principle numerical experiment of this algorithm.In addition,in the classification stage,fewer qubits,shorter circuit depth,and simpler measurement requirements show its superiority over the former algorithms.展开更多
Quantum computers promise to solve finite-temperature properties of quantum many-body systems,which is generally challenging for classical computers due to high computational complexities.Here,we report experimental p...Quantum computers promise to solve finite-temperature properties of quantum many-body systems,which is generally challenging for classical computers due to high computational complexities.Here,we report experimental preparations of Gibbs states and excited states of Heisenberg X X and X X Z models by using a 5-qubit programmable superconducting processor.In the experiments,we apply a hybrid quantum–classical algorithm to generate finite temperature states with classical probability models and variational quantum circuits.We reveal that the Hamiltonians can be fully diagonalized with optimized quantum circuits,which enable us to prepare excited states at arbitrary energy density.We demonstrate that the approach has a self-verifying feature and can estimate fundamental thermal observables with a small statistical error.Based on numerical results,we further show that the time complexity of our approach scales polynomially in the number of qubits,revealing its potential in solving large-scale problems.展开更多
As a typical physical retrieval algorithm for retrieving atmospheric parameters,one-dimensional variational(1 DVAR)algorithm is widely used in various climate and meteorological communities and enjoys an important pos...As a typical physical retrieval algorithm for retrieving atmospheric parameters,one-dimensional variational(1 DVAR)algorithm is widely used in various climate and meteorological communities and enjoys an important position in the field of microwave remote sensing.Among algorithm parameters affecting the performance of the 1 DVAR algorithm,the accuracy of the microwave radiative transfer model for calculating the simulated brightness temperature is the fundamental constraint on the retrieval accuracies of the 1 DVAR algorithm for retrieving atmospheric parameters.In this study,a deep neural network(DNN)is used to describe the nonlinear relationship between atmospheric parameters and satellite-based microwave radiometer observations,and a DNN-based radiative transfer model is developed and applied to the 1 DVAR algorithm to carry out retrieval experiments of the atmospheric temperature and humidity profiles.The retrieval results of the temperature and humidity profiles from the Microwave Humidity and Temperature Sounder(MWHTS)onboard the Feng-Yun-3(FY-3)satellite show that the DNN-based radiative transfer model can obtain higher accuracy for simulating MWHTS observations than that of the operational radiative transfer model RTTOV,and also enables the 1 DVAR algorithm to obtain higher retrieval accuracies of the temperature and humidity profiles.In this study,the DNN-based radiative transfer model applied to the 1 DVAR algorithm can fundamentally improve the retrieval accuracies of atmospheric parameters,which may provide important reference for various applied studies in atmospheric sciences.展开更多
Label propagation is an essential semi-supervised learning method based on graphs,which has a broad spectrum of applications in pattern recognition and data mining.This paper proposes a quantum semi-supervised classif...Label propagation is an essential semi-supervised learning method based on graphs,which has a broad spectrum of applications in pattern recognition and data mining.This paper proposes a quantum semi-supervised classifier based on label propagation.Considering the difficulty of graph construction,we develop a variational quantum label propagation(VQLP)method.In this method,a locally parameterized quantum circuit is created to reduce the parameters required in the optimization.Furthermore,we design a quantum semi-supervised binary classifier based on hybrid Bell and Z bases measurement,which has a shallower circuit depth and is more suitable for implementation on near-term quantum devices.We demonstrate the performance of the quantum semi-supervised classifier on the Iris data set,and the simulation results show that the quantum semi-supervised classifier has higher classification accuracy than the swap test classifier.This work opens a new path to quantum machine learning based on graphs.展开更多
A new system of set-valued variational inclusions involving generalized H（·, ·）-accretive mapping in real q-uniformly smooth Banach spaces is introduced, and then based on the generalized resolvent operato...A new system of set-valued variational inclusions involving generalized H（·, ·）-accretive mapping in real q-uniformly smooth Banach spaces is introduced, and then based on the generalized resolvent operator technique associated with H（·, ·）-accretivity, the existence and approximation solvability of solutions using an iterative algorithm is investigated.展开更多
Quantum computing is a game-changing technology for global academia,research centers and industries including computational science,mathematics,finance,pharmaceutical,materials science,chemistry and cryptography.Altho...Quantum computing is a game-changing technology for global academia,research centers and industries including computational science,mathematics,finance,pharmaceutical,materials science,chemistry and cryptography.Although it has seen a major boost in the last decade,we are still a long way from reaching the maturity of a full-fledged quantum computer.That said,we will be in the noisy-intermediate scale quantum(NISQ)era for a long time,working on dozens or even thousands of qubits quantum computing systems.An outstanding challenge,then,is to come up with an application that can reliably carry out a nontrivial task of interest on the near-term quantum devices with non-negligible quantum noise.To address this challenge,several near-term quantum computing techniques,including variational quantum algorithms,error mitigation,quantum circuit compilation and benchmarking protocols,have been proposed to characterize and mitigate errors,and to implement algorithms with a certain resistance to noise,so as to enhance the capabilities of near-term quantum devices and explore the boundaries of their ability to realize useful applications.Besides,the development of near-term quantum devices is inseparable from the efficient classical sim-ulation,which plays a vital role in quantum algorithm design and verification,error-tolerant verification and other applications.This review will provide a thorough introduction of these near-term quantum computing techniques,report on their progress,and finally discuss the future prospect of these techniques,which we hope will motivate researchers to undertake additional studies in this field.展开更多
Based on the observation by a Regional Air Quality Monitoring Network including 16 monitoring stations, temporal and spatial variations of ozone （O3）, NO2 and total oxidant （Ox） were analyzed by both linear regres...Based on the observation by a Regional Air Quality Monitoring Network including 16 monitoring stations, temporal and spatial variations of ozone （O3）, NO2 and total oxidant （Ox） were analyzed by both linear regression and cluster analysis. A fast increase of regional O3 concentrations of 0.86 ppbWyr was found for the annual averaged values from 2006 to 2011 in Guangdong, China. Such fast O3 increase is accompanied by a correspondingly fast NOx reduction as indicated by a fast NO2 reduction rate of 0,61 ppbV/yr. Based on a cluster analysis, the monitoring stations were classified into two major categories - rural stations （non-urban） and suburban/urban stations. The 03 concentrations at rural stations were relatively conserved while those at suburban/urban stations showed a fast increase rate of 2.0 ppbV/yr accompanied by a NO2 reduction rate of 1.2 ppbV/yr. Moreover, a rapid increase of the averaged O3 concentrations in springtime （13%/yr referred to 2006 level） was observed, which may result from the increase of solar duration, reduction of precipitation in Guangdong and transport from Eastern Central China. Application of smog production algorithm showed that the photochemical O3 production is mainly volatile organic compounds （VOC）-controlled. However, the photochemical O3 production is sensitive to both NOx and VOC for O3 pollution episode. Accordingly, it is expected that a combined NOx and VOC reduction will be helpful for the reduction of the O3 pollution episodes in Pearl River Delta while stringent VOC emission control is in general required for the regional O3 pollution control.展开更多
The Microwave Temperature Sounder-Ⅱ(MWTS-Ⅱ) and Microwave Humidity and Temperature Sounder(MWHTS) onboard the Fengyun-3 C(FY-3 C) satellite can be used to detect atmospheric temperature profiles. The MWTS-II has 13 ...The Microwave Temperature Sounder-Ⅱ(MWTS-Ⅱ) and Microwave Humidity and Temperature Sounder(MWHTS) onboard the Fengyun-3 C(FY-3 C) satellite can be used to detect atmospheric temperature profiles. The MWTS-II has 13 temperature sounding channels around the 60 GHz oxygen absorption band and the MWHTS has 8 temperature sounding channels around the 118.75 GHz oxygen absorption line. The data quality of the observed brightness temperatures can be evaluated using atmospheric temperature retrievals from the MWTS-Ⅱ and MWHTS observations. Here, the bias characteristics and corrections of the observed brightness temperatures are described. The information contents of observations are calculated, and the retrieved atmospheric temperature profiles are compared using a neural network(NN) retrieval algorithm and a one-dimensional variational inversion(1 D-var) retrieval algorithm. The retrieval results from the NN algorithm show that the accuracy of the MWTS-Ⅱ retrieval is higher than that of the MWHTS retrieval, which is consistent with the results of the radiometric information analysis. The retrieval results from the 1 D-var algorithm show that the accuracy of MWTS-Ⅱ retrieval is similar to that of the MWHTS retrieval at the levels from 850-1,000 h Pa, is lower than that of the MWHTS retrieval at the levels from 650-850 h Pa and 125-300 h Pa, and is higher than that of MWHTS at the other levels. A comparison of the retrieved atmospheric temperature using these satellite observations provides a reference value for assessing the accuracy of atmospheric temperature detection at the 60 GHz oxygen band and 118.75 GHz oxygen line. In addition, based on the comparison of the retrieval results, an optimized combination method is proposed using a branch and bound algorithm for the NN retrieval algorithm, which combines the observations from both the MWTS-Ⅱand MWHTS instruments to retrieve the atmospheric temperature profiles. The results show that the optimal combination can further improve the accuracy of MWTS-Ⅱ retrieval and enhance the detection accuracy of atmospheric temperatures near the surface.展开更多
This paper introduces a novel transform method to produce the newly generated programs through code transform model called the second generation of Generative Pre-trained Transformer(GPT-2)reasonably,improving the pro...This paper introduces a novel transform method to produce the newly generated programs through code transform model called the second generation of Generative Pre-trained Transformer(GPT-2)reasonably,improving the program execution performance significantly.Besides,a theoretical estimation in statistics has given the minimum number of generated programs as required,which guarantees to find the best one within them.The proposed approach can help the voice assistant machine resolve the problem of inefficient execution of application code.In addition to GPT-2,this study develops the variational Simhash algorithm to check the code similarity between sample program and newly generated program,and conceives the piecewise longest common subsequence algorithm to examine the execution’s conformity from the two programs mentioned above.The code similarity check deducts the redundant generated programs,and the output conformity check finds the best-performing generative program.In addition to texts,the proposed approach can also prove the other media,including images,sounds,and movies.As a result,the newly generated program outperforms the sample program significantly because the number of code lines reduces 27.21%,and the program execution time shortens 24.62%.展开更多
Electric power systems provide the backbone of modern industrial societies.Enabling scalable grid analytics is the keystone to successfully operating large transmission and distribution systems.However,today’s power ...Electric power systems provide the backbone of modern industrial societies.Enabling scalable grid analytics is the keystone to successfully operating large transmission and distribution systems.However,today’s power systems are suffering from ever-increasing computational burdens in sustaining the expanding communities and deep integration of renewable energy resources,as well as managing huge volumes of data accordingly.These unprecedented challenges call for transformative analytics to support the resilient operations of power systems.Recently,the explosive growth of quantum computing techniques has ignited new hopes of revolutionizing power system computations.Quantum computing harnesses quantum mechanisms to solve traditionally intractable computational problems,which may lead to ultra-scalable and efficient power grid analytics.This paper reviews the newly emerging application of quantum computing techniques in power systems.We present a comprehensive overview of existing quantum-engineered power analytics from different operation perspectives,including static analysis,transient analysis,stochastic analysis,optimization,stability,and control.We thoroughly discuss the related quantum algorithms,their benefits and limitations,hardware implementations,and recommended practices.We also review the quantum networking techniques to ensure secure communication of power systems in the quantum era.Finally,we discuss challenges and future research directions.This paper will hopefully stimulate increasing attention to the development of quantum-engineered smart grids.展开更多
In this paper, we investigate the adjoint equation in photoacoustic tomography with variable sound speed, and propose three variational iterative algorithms. The basic idea of these algorithms is to compute the origin...In this paper, we investigate the adjoint equation in photoacoustic tomography with variable sound speed, and propose three variational iterative algorithms. The basic idea of these algorithms is to compute the original equation and the adjoint equation iteratively. We present numerical examples and show the well performance of these variational iterative algorithms.展开更多
This paper presents a condensed method for linear complementary equations of elasto-plastic problems derived from the variational inequations The present method cuts down computing time enormously and greatly promote...This paper presents a condensed method for linear complementary equations of elasto-plastic problems derived from the variational inequations The present method cuts down computing time enormously and greatly promotes the efficiency of the elasto-plastic analvsis for large scale structures展开更多
Optimization problems are prevalent in various fields,and the gradient-based gradient descent algorithm is a widely adopted optimization method.However,in classical computing,computing the numerical gradient for a fun...Optimization problems are prevalent in various fields,and the gradient-based gradient descent algorithm is a widely adopted optimization method.However,in classical computing,computing the numerical gradient for a function with variables necessitates at least d+1 function evaluations,resulting in a computational complexity of O(d).As the number of variables increases,the classical gradient estimation methods require substantial resources,ultimately surpassing the capabilities of classical computers.Fortunately,leveraging the principles of superposition and entanglement in quantum mechanics,quantum computers can achieve genuine parallel computing,leading to exponential acceleration over classical algorithms in some cases.In this paper,we propose a novel quantum-based gradient calculation method that requires only a single oracle calculation to obtain the numerical gradient result for a multivariate function.The complexity of this algorithm is just O(1).Building upon this approach,we successfully implemented the quantum gradient descent algorithm and applied it to the variational quantum eigensolver(VQE),creating a pure quantum variational optimization algorithm.Compared with classical gradient-based optimization algorithm,this quantum optimization algorithm has remarkable complexity advantages,providing an efficient solution to optimization problems.The proposed quantum-based method shows promise in enhancing the performance of optimization algorithms,highlighting the potential of quantum computing in this field.展开更多
文摘The variational data assimilation scheme (VAR) is applied to investigating the advective effect and the evolution of the control variables in time splitting semi-Lagrangian framework. Two variational algorithms are used. One is the conjugate code method-direct approach, and another is the numerical backward integration of analytical adjoint equation—indirect approach. Theoretical derivation and sensitivity tests are conducted in order to verify the consistency and inconsistency of the two algorithms under the semi-Lagrangian framework. On the other hand, the sensitivity of the perfect and imperfect initial condition is also tested in both direct and indirect approaches. Our research has shown that the two algorithms are not only identical in theory, but also identical in numerical calculation. Furthermore, the algorithms of the indirect approach are much more feasible and efficient than that of the direct one when both are employed in the semi-Lagrangian framework. Taking advantage of semi-Lagrangian framework, one purpose of this paper is to illustrate when the variational assimilation algorithm is concerned in the computational method of the backward integration, the algorithm is extremely facilitated. Such simplicity in indirect approach should be meaningful for the VAR design in passive model. Indeed, if one can successfully split the diabatic and adiabatic process, the algorithms represented in this paper might be easily used in a more general vision of atmospheric model.
基金supported by the National Natural Science Foundation of China(Grant Nos.12375013 and 12275090)the Guangdong Basic and Applied Basic Research Fund(Grant No.2023A1515011460)Guangdong Provincial Quantum Science Strategic Initiative(Grant No.GDZX2200001)。
文摘In open quantum systems,the Liouvillian gap characterizes the relaxation time toward the steady state.However,accurately computing this quantity is notoriously difficult due to the exponential growth of the Hilbert space and the non-Hermitian nature of the Liouvillian superoperator.In this work,we propose a variational quantum algorithm for efficiently estimating the Liouvillian gap.By utilizing the Choi-Jamio lkowski isomorphism,we reformulate the problem as finding the first excitation energy of an effective non-Hermitian Hamiltonian.Our method employs variance minimization with an orthogonality constraint to locate the first excited state and adopts a two-stage optimization scheme to enhance convergence.Moreover,to address scenarios with degenerate steady states,we introduce an iterative energy-offset scanning technique.Numerical simulations on the dissipative XXZ model confirm the accuracy and robustness of our algorithm across a range of system sizes and dissipation strengths.These results demonstrate the promise of variational quantum algorithms for simulating open quantum many-body systems on near-term quantum hardware.
基金supported by the Shandong Provincial Natural Science Foundation for Quantum Science under Grant No.ZR2021LLZ002the Fundamental Research Funds for the Central Universities under Grant No.22CX03005A。
文摘To solve the Poisson equation it is usually possible to discretize it into solving the corresponding linear system Ax=b.Variational quantum algorithms(VQAs)for the discretized Poisson equation have been studied before.We present a VQA based on the banded Toeplitz systems for solving the Poisson equation with respect to the structural features of matrix A.In 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 elements.For 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[Phys.Rev.A 2023108,032418].Based on the decomposition of the matrix,we design quantum circuits that efficiently evaluate the cost function.Additionally,numerical simulation verifies the feasibility of the proposed algorithm.Finally,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).
基金Supported by the National Natural Science Foundation of China(under Grant Nos.12105090 and 12074107)the Program of Outstanding Young and Middle-aged Scientific and Technological Innovation Team of Colleges and Universities in Hubei Province of China(under Grant No.T2020001)the Innovation Group Project of the Natural Science Foundation of Hubei Province of China(under Grant No.2022CFA012)。
文摘Since the concept of quantum information masking was proposed by Modi et al(2018 Phys.Rev.Lett.120,230501),many interesting and significant results have been reported,both theoretically and experimentally.However,designing a quantum information masker is not an easy task,especially for larger systems.In this paper,we propose a variational quantum algorithm to resolve this problem.Specifically,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 parameters.After optimization,the quantum device behaves as an optimal masker.The loss value during optimization can be used to characterize the performance of the masker.In 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 information.Nevertheless,these resulting maskers are still optimal.Quantum parallelism is utilized to reduce quantum state preparations and measurements.Our 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.
文摘The trace norm of matrices plays an important role in quantum information and quantum computing. How to quantify it in today’s noisy intermediate scale quantum(NISQ) devices is a crucial task for information processing. In this paper, we present three variational quantum algorithms on NISQ devices to estimate the trace norms corresponding to different situations.Compared with the previous methods, our means greatly reduce the requirement for quantum resources. Numerical experiments are provided to illustrate the effectiveness of our algorithms.
文摘In this paper we use the auxiliary principle technique to suggest and analyze novel and innovative iterative algorithms for a class of nonlinear variational inequalities. Several special cases, which can be obtained from our main results, are also discussed.
基金supported by the National Natural Science Foundation of China under Grant Nos.62172268 and 62302289the Shanghai Science and Technology Project under Grant Nos.21JC1402800 and 23YF1416200。
文摘Variational quantum algorithms are promising methods with the greatest potential to achieve quantum advantage,widely employed in the era of noisy intermediate-scale quantum computing.This study presents an advanced variational hybrid algorithm(EVQLSE)that leverages both quantum and classical computing paradigms to address the solution of linear equation systems.Initially,an innovative loss function is proposed,drawing inspiration from the similarity measure between two quantum states.This function exhibits a substantial improvement in computational complexity when benchmarked against the variational quantum linear solver.Subsequently,a specialized parameterized quantum circuit structure is presented for small-scale linear systems,which exhibits powerful expressive capabilities.Through 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 others.Moreover,the expansion in system size is accompanied by an increase in the number of parameters,placing considerable strain on the training process for the algorithm.To address this challenge,an optimization strategy known as quantum parameter sharing is introduced,which proficiently minimizes parameter volume while adhering to exacting precision standards.Finally,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.
基金supported by the Shandong Provincial Natural Science Foundation for Quantum Science No.ZR2020LLZ003,ZR2021LLZ002。
文摘Classical machine learning algorithms seem to be totally incapable of processing tremendous amounts of data,while quantum machine learning algorithms could deal with big data with ease and provide exponential acceleration over classical counterparts.Meanwhile,variational quantum algorithms are widely proposed to solve relevant computational problems on noisy,intermediate-scale quantum devices.In this paper,we apply variational quantum algorithms to quantum support vector machines and demonstrate a proof-of-principle numerical experiment of this algorithm.In addition,in the classification stage,fewer qubits,shorter circuit depth,and simpler measurement requirements show its superiority over the former algorithms.
基金Project supported by the State Key Development Program for Basic Research of China(Grant No.2017YFA0304300)the National Natural Science Foundation of China(Grant Nos.11934018,11747601,and 11975294)+4 种基金Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDB28000000)Scientific Instrument Developing Project of Chinese Academy of Sciences(Grant No.YJKYYQ20200041)Beijing Natural Science Foundation(Grant No.Z200009)the Key-Area Research and Development Program of Guangdong Province,China(Grant No.2020B0303030001)Chinese Academy of Sciences(Grant No.QYZDB-SSW-SYS032)。
文摘Quantum computers promise to solve finite-temperature properties of quantum many-body systems,which is generally challenging for classical computers due to high computational complexities.Here,we report experimental preparations of Gibbs states and excited states of Heisenberg X X and X X Z models by using a 5-qubit programmable superconducting processor.In the experiments,we apply a hybrid quantum–classical algorithm to generate finite temperature states with classical probability models and variational quantum circuits.We reveal that the Hamiltonians can be fully diagonalized with optimized quantum circuits,which enable us to prepare excited states at arbitrary energy density.We demonstrate that the approach has a self-verifying feature and can estimate fundamental thermal observables with a small statistical error.Based on numerical results,we further show that the time complexity of our approach scales polynomially in the number of qubits,revealing its potential in solving large-scale problems.
基金National Natural Science Foundation of China(41901297,41806209)Science and Technology Key Project of Henan Province(202102310017)+1 种基金Key Research Projects for the Universities of Henan Province(20A170013)China Postdoctoral Science Foundation(2021M693201)。
文摘As a typical physical retrieval algorithm for retrieving atmospheric parameters,one-dimensional variational(1 DVAR)algorithm is widely used in various climate and meteorological communities and enjoys an important position in the field of microwave remote sensing.Among algorithm parameters affecting the performance of the 1 DVAR algorithm,the accuracy of the microwave radiative transfer model for calculating the simulated brightness temperature is the fundamental constraint on the retrieval accuracies of the 1 DVAR algorithm for retrieving atmospheric parameters.In this study,a deep neural network(DNN)is used to describe the nonlinear relationship between atmospheric parameters and satellite-based microwave radiometer observations,and a DNN-based radiative transfer model is developed and applied to the 1 DVAR algorithm to carry out retrieval experiments of the atmospheric temperature and humidity profiles.The retrieval results of the temperature and humidity profiles from the Microwave Humidity and Temperature Sounder(MWHTS)onboard the Feng-Yun-3(FY-3)satellite show that the DNN-based radiative transfer model can obtain higher accuracy for simulating MWHTS observations than that of the operational radiative transfer model RTTOV,and also enables the 1 DVAR algorithm to obtain higher retrieval accuracies of the temperature and humidity profiles.In this study,the DNN-based radiative transfer model applied to the 1 DVAR algorithm can fundamentally improve the retrieval accuracies of atmospheric parameters,which may provide important reference for various applied studies in atmospheric sciences.
基金Project supported by the Open Fund of Advanced Cryptography and System Security Key Laboratory of Sichuan Province(Grant No.SKLACSS-202108)the National Natural Science Foundation of China(Grant No.U162271070)Scientific Research Fund of Zaozhuang University(Grant No.102061901).
文摘Label propagation is an essential semi-supervised learning method based on graphs,which has a broad spectrum of applications in pattern recognition and data mining.This paper proposes a quantum semi-supervised classifier based on label propagation.Considering the difficulty of graph construction,we develop a variational quantum label propagation(VQLP)method.In this method,a locally parameterized quantum circuit is created to reduce the parameters required in the optimization.Furthermore,we design a quantum semi-supervised binary classifier based on hybrid Bell and Z bases measurement,which has a shallower circuit depth and is more suitable for implementation on near-term quantum devices.We demonstrate the performance of the quantum semi-supervised classifier on the Iris data set,and the simulation results show that the quantum semi-supervised classifier has higher classification accuracy than the swap test classifier.This work opens a new path to quantum machine learning based on graphs.
基金Supported by the National Natural Science Foundation of China(Grant No.11371015)the Key Project of Chinese Ministry of Education(Grant No.211163)+3 种基金Sichuan Youth Science and Technology Foundation(GrantNo.2012JQ0032)the Foundation of China West Normal University(Grant No.11A028,11A029)the Fundamental Research Funds of China West Normal University(Grant No.13D016)the Natural Science Foundation ofSichuan Provincial Education Department(Grant No.14ZB0142)
文摘A new system of set-valued variational inclusions involving generalized H（·, ·）-accretive mapping in real q-uniformly smooth Banach spaces is introduced, and then based on the generalized resolvent operator technique associated with H（·, ·）-accretivity, the existence and approximation solvability of solutions using an iterative algorithm is investigated.
基金support from the Youth Talent Lifting Project(Grant No.2020-JCJQ-QT-030)the National Natural Science Foundation of China(Grant Nos.11905294,and 12274464)+7 种基金the China Postdoctoral Science Foundation,and the Open Research Fund from State Key Laboratory of High Performance Computing of China(Grant No.201901-01)support from the National Natural Science Foundation of China(Grant Nos.11805279,12074117,61833010,and 12061131011)support from the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDB28000000)the National Natural Science Foundation of China(Grant Nos.61832003,61872334,and 61801459)the National Natural Science Foundation of China(Grant No.12005015)the National Natural Science Foundation of China(Grant Nos.11974205,and 11774197)the National Key Research and Development Program of China(Grant No.2017YFA0303700)the Key Research and Development Program of Guangdong Province(Grant No.2018B030325002).
文摘Quantum computing is a game-changing technology for global academia,research centers and industries including computational science,mathematics,finance,pharmaceutical,materials science,chemistry and cryptography.Although it has seen a major boost in the last decade,we are still a long way from reaching the maturity of a full-fledged quantum computer.That said,we will be in the noisy-intermediate scale quantum(NISQ)era for a long time,working on dozens or even thousands of qubits quantum computing systems.An outstanding challenge,then,is to come up with an application that can reliably carry out a nontrivial task of interest on the near-term quantum devices with non-negligible quantum noise.To address this challenge,several near-term quantum computing techniques,including variational quantum algorithms,error mitigation,quantum circuit compilation and benchmarking protocols,have been proposed to characterize and mitigate errors,and to implement algorithms with a certain resistance to noise,so as to enhance the capabilities of near-term quantum devices and explore the boundaries of their ability to realize useful applications.Besides,the development of near-term quantum devices is inseparable from the efficient classical sim-ulation,which plays a vital role in quantum algorithm design and verification,error-tolerant verification and other applications.This review will provide a thorough introduction of these near-term quantum computing techniques,report on their progress,and finally discuss the future prospect of these techniques,which we hope will motivate researchers to undertake additional studies in this field.
基金supported by the National Natural Science Foundation of China(No.21190052,41121004)the Strategic Priority Research Program of the Chinese Academy of Sciences(No.XDB05010500)+1 种基金the National Public Benefit Special Fund for Environmental Protection Research(No.201009001-4)the Special Fund of State Key Joint Laboratory of Environment Simulation and Pollution Control(No.13Z02ESPCP)
文摘Based on the observation by a Regional Air Quality Monitoring Network including 16 monitoring stations, temporal and spatial variations of ozone （O3）, NO2 and total oxidant （Ox） were analyzed by both linear regression and cluster analysis. A fast increase of regional O3 concentrations of 0.86 ppbWyr was found for the annual averaged values from 2006 to 2011 in Guangdong, China. Such fast O3 increase is accompanied by a correspondingly fast NOx reduction as indicated by a fast NO2 reduction rate of 0,61 ppbV/yr. Based on a cluster analysis, the monitoring stations were classified into two major categories - rural stations （non-urban） and suburban/urban stations. The 03 concentrations at rural stations were relatively conserved while those at suburban/urban stations showed a fast increase rate of 2.0 ppbV/yr accompanied by a NO2 reduction rate of 1.2 ppbV/yr. Moreover, a rapid increase of the averaged O3 concentrations in springtime （13%/yr referred to 2006 level） was observed, which may result from the increase of solar duration, reduction of precipitation in Guangdong and transport from Eastern Central China. Application of smog production algorithm showed that the photochemical O3 production is mainly volatile organic compounds （VOC）-controlled. However, the photochemical O3 production is sensitive to both NOx and VOC for O3 pollution episode. Accordingly, it is expected that a combined NOx and VOC reduction will be helpful for the reduction of the O3 pollution episodes in Pearl River Delta while stringent VOC emission control is in general required for the regional O3 pollution control.
基金Key Fostering Project of the National Space Science Center,Chinese Academy of Sciences(Y62112f37s)National 863 Project of China(2015AA8126027)
文摘The Microwave Temperature Sounder-Ⅱ(MWTS-Ⅱ) and Microwave Humidity and Temperature Sounder(MWHTS) onboard the Fengyun-3 C(FY-3 C) satellite can be used to detect atmospheric temperature profiles. The MWTS-II has 13 temperature sounding channels around the 60 GHz oxygen absorption band and the MWHTS has 8 temperature sounding channels around the 118.75 GHz oxygen absorption line. The data quality of the observed brightness temperatures can be evaluated using atmospheric temperature retrievals from the MWTS-Ⅱ and MWHTS observations. Here, the bias characteristics and corrections of the observed brightness temperatures are described. The information contents of observations are calculated, and the retrieved atmospheric temperature profiles are compared using a neural network(NN) retrieval algorithm and a one-dimensional variational inversion(1 D-var) retrieval algorithm. The retrieval results from the NN algorithm show that the accuracy of the MWTS-Ⅱ retrieval is higher than that of the MWHTS retrieval, which is consistent with the results of the radiometric information analysis. The retrieval results from the 1 D-var algorithm show that the accuracy of MWTS-Ⅱ retrieval is similar to that of the MWHTS retrieval at the levels from 850-1,000 h Pa, is lower than that of the MWHTS retrieval at the levels from 650-850 h Pa and 125-300 h Pa, and is higher than that of MWHTS at the other levels. A comparison of the retrieved atmospheric temperature using these satellite observations provides a reference value for assessing the accuracy of atmospheric temperature detection at the 60 GHz oxygen band and 118.75 GHz oxygen line. In addition, based on the comparison of the retrieval results, an optimized combination method is proposed using a branch and bound algorithm for the NN retrieval algorithm, which combines the observations from both the MWTS-Ⅱand MWHTS instruments to retrieve the atmospheric temperature profiles. The results show that the optimal combination can further improve the accuracy of MWTS-Ⅱ retrieval and enhance the detection accuracy of atmospheric temperatures near the surface.
基金This work is fully supported by the Ministry of Science and Technology,Taiwan,Republic of China,under Grant Nos.MOST 110-2622-E-390-001 and MOST 109-2622-E-390-002-CC3.
文摘This paper introduces a novel transform method to produce the newly generated programs through code transform model called the second generation of Generative Pre-trained Transformer(GPT-2)reasonably,improving the program execution performance significantly.Besides,a theoretical estimation in statistics has given the minimum number of generated programs as required,which guarantees to find the best one within them.The proposed approach can help the voice assistant machine resolve the problem of inefficient execution of application code.In addition to GPT-2,this study develops the variational Simhash algorithm to check the code similarity between sample program and newly generated program,and conceives the piecewise longest common subsequence algorithm to examine the execution’s conformity from the two programs mentioned above.The code similarity check deducts the redundant generated programs,and the output conformity check finds the best-performing generative program.In addition to texts,the proposed approach can also prove the other media,including images,sounds,and movies.As a result,the newly generated program outperforms the sample program significantly because the number of code lines reduces 27.21%,and the program execution time shortens 24.62%.
基金supported in part by the Advanced Grid Modeling Program under U.S.Department of Energy’s Office of Electricity under Agreement No.37533(P.Z.)in part by Stony Brook Uni-versity’s Office of the Vice President for Research through a Quantum Information Science and Technology Seed Grant(P.Z.)in part by the National Science Foundation under Grant No.PHY 1915165(T.-C.W.).
文摘Electric power systems provide the backbone of modern industrial societies.Enabling scalable grid analytics is the keystone to successfully operating large transmission and distribution systems.However,today’s power systems are suffering from ever-increasing computational burdens in sustaining the expanding communities and deep integration of renewable energy resources,as well as managing huge volumes of data accordingly.These unprecedented challenges call for transformative analytics to support the resilient operations of power systems.Recently,the explosive growth of quantum computing techniques has ignited new hopes of revolutionizing power system computations.Quantum computing harnesses quantum mechanisms to solve traditionally intractable computational problems,which may lead to ultra-scalable and efficient power grid analytics.This paper reviews the newly emerging application of quantum computing techniques in power systems.We present a comprehensive overview of existing quantum-engineered power analytics from different operation perspectives,including static analysis,transient analysis,stochastic analysis,optimization,stability,and control.We thoroughly discuss the related quantum algorithms,their benefits and limitations,hardware implementations,and recommended practices.We also review the quantum networking techniques to ensure secure communication of power systems in the quantum era.Finally,we discuss challenges and future research directions.This paper will hopefully stimulate increasing attention to the development of quantum-engineered smart grids.
文摘In this paper, we investigate the adjoint equation in photoacoustic tomography with variable sound speed, and propose three variational iterative algorithms. The basic idea of these algorithms is to compute the original equation and the adjoint equation iteratively. We present numerical examples and show the well performance of these variational iterative algorithms.
文摘This paper presents a condensed method for linear complementary equations of elasto-plastic problems derived from the variational inequations The present method cuts down computing time enormously and greatly promotes the efficiency of the elasto-plastic analvsis for large scale structures
基金supported by the National Natural Science Foundation of China under Grant No.12105195.
文摘Optimization problems are prevalent in various fields,and the gradient-based gradient descent algorithm is a widely adopted optimization method.However,in classical computing,computing the numerical gradient for a function with variables necessitates at least d+1 function evaluations,resulting in a computational complexity of O(d).As the number of variables increases,the classical gradient estimation methods require substantial resources,ultimately surpassing the capabilities of classical computers.Fortunately,leveraging the principles of superposition and entanglement in quantum mechanics,quantum computers can achieve genuine parallel computing,leading to exponential acceleration over classical algorithms in some cases.In this paper,we propose a novel quantum-based gradient calculation method that requires only a single oracle calculation to obtain the numerical gradient result for a multivariate function.The complexity of this algorithm is just O(1).Building upon this approach,we successfully implemented the quantum gradient descent algorithm and applied it to the variational quantum eigensolver(VQE),creating a pure quantum variational optimization algorithm.Compared with classical gradient-based optimization algorithm,this quantum optimization algorithm has remarkable complexity advantages,providing an efficient solution to optimization problems.The proposed quantum-based method shows promise in enhancing the performance of optimization algorithms,highlighting the potential of quantum computing in this field.
