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
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
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
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
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
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
In the noisy intermediate-scale quantum era,emerging classical-quantum hybrid optimization algorithms,such as variational quantum algorithms(VQAs),can leverage the unique characteristics of quantum devices to accelera...In the noisy intermediate-scale quantum era,emerging classical-quantum hybrid optimization algorithms,such as variational quantum algorithms(VQAs),can leverage the unique characteristics of quantum devices to accelerate computations tailored to specific problems with shallow circuits.However,these algorithms encounter biases and iteration difficulties due to significant noise in quantum processors.These difficulties can only be partially addressed without error correction by optimizing hardware,reducing circuit complexity,or fitting and extrapolating.A compelling solution is applying probabilistic error cancellation(PEC),a quantum error mitigation technique that enables unbiased results without full error correction.Traditional PEC is challenging to apply in VQAs due to its variance amplification,contradicting iterative process assumptions.This paper proposes a novel noise-adaptable strategy that combines PEC with the quantum approximate optimization algorithm(QAOA).It is implemented through invariant sampling circuits(invariant-PEC,or IPEC)and substantially reduces iteration variance.This strategy marks the first successful integration of PEC and QAOA,resulting in efficient convergence.Moreover,we introduce adaptive partial PEC(APPEC),which modulates the error cancellation proportion of IPEC during iteration.We experimentally validate this technique on a superconducting quantum processor,cutting sampling cost by 90.1%.Notably,we find that dynamic adjustments of error levels via APPEC can enhance the ability to escape from local minima and reduce sampling costs.These results open promising avenues for executing VQAs with large-scale,low-noise quantum circuits,paving the way for practical quantum computing advancements.展开更多
Solving the ground state of quantum many-body systems remains a fundamental challenge in physics and chemistry.Recent advancements in quantum hardware have opened new avenues for addressing this challenge.Inspired by ...Solving the ground state of quantum many-body systems remains a fundamental challenge in physics and chemistry.Recent advancements in quantum hardware have opened new avenues for addressing this challenge.Inspired by the quantum-enhanced Markov chain Monte Carlo(QeMCMC)algorithm,which was originally designed for sampling the Boltzmann distribution of classical spin models using quantum computers,we introduce a quantum-assisted variational Monte Carlo(QA-VMC)algorithm for solving the ground state of quantum many-body systems by adapting QeMCMC to sample the distribution of a(neural-network)wave function in VMC.The central question is whether such a quantum-assisted proposal can potentially offer a computational advantage over classical methods.Through numerical investigations for the Fermi−Hubbard model and molecular systems,we demonstrate that the quantum-assisted proposal exhibits larger absolute spectral gaps and reduced autocorrelation times compared to conventional classical proposals,leading to more efficient sampling and faster convergence to the ground state in VMC as well as a more accurate and precise estimation of physical observables.This advantage is especially pronounced for specific parameter ranges,where the ground-state configurations are more concentrated in some configurations separated by large Hamming distances.Our results underscore the potential of quantum-assisted algorithms to enhance classical variational methods for solving the ground state of quantum many-body systems.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
Quantum machine learning has made remarkable progress in many important tasks.However,the gate complexity of the initial state preparation is seldom considered in lots of quantum machine learning algorithms,making the...Quantum machine learning has made remarkable progress in many important tasks.However,the gate complexity of the initial state preparation is seldom considered in lots of quantum machine learning algorithms,making them non-end-to-end.Herein,we propose a quantum algorithm for the node embedding problem that maps a node graph's topological structure to embedding vectors.The resulting quantum embedding state can be used as an input for other quantum machine learning algorithms.With O(log(N))qubits to store the information of N nodes,our algorithm will not lose quantum advantage for the subsequent quantum information processing.Moreover,owing to the use of a parameterized quantum circuit with O(poly(log(N)))depth,the resulting state can serve as an efficient quantum database.In 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 nodes.Finally,we experimentally demonstrated our algorithm on an nuclear magnetic resonance quantum processor to solve a graph model.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
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
The problem of social workers visiting their patients at home is a class of combinatorial optimization problems and belongs to the class of problems known as NP-Hard. These problems require heuristic techniques to pro...The problem of social workers visiting their patients at home is a class of combinatorial optimization problems and belongs to the class of problems known as NP-Hard. These problems require heuristic techniques to provide an efficient solution in the best of cases. In this article, in addition to providing a detailed resolution of the social workers’ problem using the Quadratic Unconstrained Binary Optimization Problems (QUBO) formulation, an approach to mapping the inequality constraints in the QUBO form is given. Finally, we map it in the Hamiltonian of the Ising model to solve it with the Quantum Exact Solver and Variational Quantum Eigensolvers (VQE). The quantum feasibility of the algorithm will be tested on IBMQ computers.展开更多
In scenarios where a large amount of data needs to be learned,incremental learning can make full use of old knowledge,signif-icantly reduce the computational cost of the overall learning process,and maintain high perf...In scenarios where a large amount of data needs to be learned,incremental learning can make full use of old knowledge,signif-icantly reduce the computational cost of the overall learning process,and maintain high performance.In this paper,taking the MaxCut problem as our example,we introduce the idea of incremental learning into quantum computing,and propose a Quantum Proactive Incremental Learning algorithm(QPIL).Instead of a one-off training of quantum circuit,QPIL contains a multi-phase training on gradually-increased subgraphs of all vertices,proactively reducing large-scale problems to smaller ones to solve in steps,providing an efficient solution for MaxCut.Specifically,some vertices and corresponding edges are randomly selected for training to obtain optimized parameters of the quantum circuit at first.Then,in each incremental phase,the remaining vertices and corresponding edges are gradually added and the parameters obtained from the previous phase are reused in the parameter initialization of the current phase.We perform experiments on 120 different small-scale graphs,and it shows that QPIL performs superior to prevalent quantum and classical baselines in terms of approximation ratio(AR),time cost,anti-forgetting,and solv-ing stability.In particular,QPIL’s AR surpasses 20%of mainstream quantum baselines,and the time cost is less than 1/5 of them.The idea of QPIL is expected to inspire efficient and high-quality solutions in large-scale MaxCut and other combinatorial optimization problems.展开更多
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.
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(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.
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.
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 Innovation Program for Quantum Science and Technology(Grant Nos.2021ZD0301702,and 2024ZD0302000)the Natural Science Foundation of Jiangsu Province(Grant No.BK20232002)+1 种基金the National Natural Science Foundation of China(Grant Nos.U21A20436,and 12074179)the Natural Science Foundation of Shandong Province(Grant No.ZR2023LZH002)。
文摘In the noisy intermediate-scale quantum era,emerging classical-quantum hybrid optimization algorithms,such as variational quantum algorithms(VQAs),can leverage the unique characteristics of quantum devices to accelerate computations tailored to specific problems with shallow circuits.However,these algorithms encounter biases and iteration difficulties due to significant noise in quantum processors.These difficulties can only be partially addressed without error correction by optimizing hardware,reducing circuit complexity,or fitting and extrapolating.A compelling solution is applying probabilistic error cancellation(PEC),a quantum error mitigation technique that enables unbiased results without full error correction.Traditional PEC is challenging to apply in VQAs due to its variance amplification,contradicting iterative process assumptions.This paper proposes a novel noise-adaptable strategy that combines PEC with the quantum approximate optimization algorithm(QAOA).It is implemented through invariant sampling circuits(invariant-PEC,or IPEC)and substantially reduces iteration variance.This strategy marks the first successful integration of PEC and QAOA,resulting in efficient convergence.Moreover,we introduce adaptive partial PEC(APPEC),which modulates the error cancellation proportion of IPEC during iteration.We experimentally validate this technique on a superconducting quantum processor,cutting sampling cost by 90.1%.Notably,we find that dynamic adjustments of error levels via APPEC can enhance the ability to escape from local minima and reduce sampling costs.These results open promising avenues for executing VQAs with large-scale,low-noise quantum circuits,paving the way for practical quantum computing advancements.
基金supported by the Innovation Program for Quantum Science and Technology(Grant No.2023ZD0300200)the Fundamental Research Funds for the Central Universities.
文摘Solving the ground state of quantum many-body systems remains a fundamental challenge in physics and chemistry.Recent advancements in quantum hardware have opened new avenues for addressing this challenge.Inspired by the quantum-enhanced Markov chain Monte Carlo(QeMCMC)algorithm,which was originally designed for sampling the Boltzmann distribution of classical spin models using quantum computers,we introduce a quantum-assisted variational Monte Carlo(QA-VMC)algorithm for solving the ground state of quantum many-body systems by adapting QeMCMC to sample the distribution of a(neural-network)wave function in VMC.The central question is whether such a quantum-assisted proposal can potentially offer a computational advantage over classical methods.Through numerical investigations for the Fermi−Hubbard model and molecular systems,we demonstrate that the quantum-assisted proposal exhibits larger absolute spectral gaps and reduced autocorrelation times compared to conventional classical proposals,leading to more efficient sampling and faster convergence to the ground state in VMC as well as a more accurate and precise estimation of physical observables.This advantage is especially pronounced for specific parameter ranges,where the ground-state configurations are more concentrated in some configurations separated by large Hamming distances.Our results underscore the potential of quantum-assisted algorithms to enhance classical variational methods for solving the ground state of quantum many-body systems.
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the National Natural Science Foundation of China(11974205 and 11774197)the National Key Research and Development Program of China(2017YFA0303700)+1 种基金the Key Research and Development Program of Guangdong Province(2018B030325002)the Beijing Nova Program(20230484345).
文摘Quantum machine learning has made remarkable progress in many important tasks.However,the gate complexity of the initial state preparation is seldom considered in lots of quantum machine learning algorithms,making them non-end-to-end.Herein,we propose a quantum algorithm for the node embedding problem that maps a node graph's topological structure to embedding vectors.The resulting quantum embedding state can be used as an input for other quantum machine learning algorithms.With O(log(N))qubits to store the information of N nodes,our algorithm will not lose quantum advantage for the subsequent quantum information processing.Moreover,owing to the use of a parameterized quantum circuit with O(poly(log(N)))depth,the resulting state can serve as an efficient quantum database.In 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 nodes.Finally,we experimentally demonstrated our algorithm on an nuclear magnetic resonance quantum processor to solve a graph model.
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.
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.
文摘The problem of social workers visiting their patients at home is a class of combinatorial optimization problems and belongs to the class of problems known as NP-Hard. These problems require heuristic techniques to provide an efficient solution in the best of cases. In this article, in addition to providing a detailed resolution of the social workers’ problem using the Quadratic Unconstrained Binary Optimization Problems (QUBO) formulation, an approach to mapping the inequality constraints in the QUBO form is given. Finally, we map it in the Hamiltonian of the Ising model to solve it with the Quantum Exact Solver and Variational Quantum Eigensolvers (VQE). The quantum feasibility of the algorithm will be tested on IBMQ computers.
基金supported by the National Natural Science Foundation of China(Grant Nos.62272048,61976056,and 62371069)BUPT Excellent Ph.D.Students Foundation(Grant No.CX20241055)。
文摘In scenarios where a large amount of data needs to be learned,incremental learning can make full use of old knowledge,signif-icantly reduce the computational cost of the overall learning process,and maintain high performance.In this paper,taking the MaxCut problem as our example,we introduce the idea of incremental learning into quantum computing,and propose a Quantum Proactive Incremental Learning algorithm(QPIL).Instead of a one-off training of quantum circuit,QPIL contains a multi-phase training on gradually-increased subgraphs of all vertices,proactively reducing large-scale problems to smaller ones to solve in steps,providing an efficient solution for MaxCut.Specifically,some vertices and corresponding edges are randomly selected for training to obtain optimized parameters of the quantum circuit at first.Then,in each incremental phase,the remaining vertices and corresponding edges are gradually added and the parameters obtained from the previous phase are reused in the parameter initialization of the current phase.We perform experiments on 120 different small-scale graphs,and it shows that QPIL performs superior to prevalent quantum and classical baselines in terms of approximation ratio(AR),time cost,anti-forgetting,and solv-ing stability.In particular,QPIL’s AR surpasses 20%of mainstream quantum baselines,and the time cost is less than 1/5 of them.The idea of QPIL is expected to inspire efficient and high-quality solutions in large-scale MaxCut and other combinatorial optimization problems.
