Quantum computing offers unprecedented computational power, enabling simultaneous computations beyond traditional computers. Quantum computers differ significantly from classical computers, necessitating a distinct ap...Quantum computing offers unprecedented computational power, enabling simultaneous computations beyond traditional computers. Quantum computers differ significantly from classical computers, necessitating a distinct approach to algorithm design, which involves taming quantum mechanical phenomena. This paper extends the numbering of computable programs to be applied in the quantum computing context. Numbering computable programs is a theoretical computer science concept that assigns unique numbers to individual programs or algorithms. Common methods include Gödel numbering which encodes programs as strings of symbols or characters, often used in formal systems and mathematical logic. Based on the proposed numbering approach, this paper presents a mechanism to explore the set of possible quantum algorithms. The proposed approach is able to construct useful circuits such as Quantum Key Distribution BB84 protocol, which enables sender and receiver to establish a secure cryptographic key via a quantum channel. The proposed approach facilitates the process of exploring and constructing quantum algorithms.展开更多
Quantum computing is a promising technology that has the potential to revolutionize many areas of science and technology,including communication.In this review,we discuss the current state of quantum computing in comm...Quantum computing is a promising technology that has the potential to revolutionize many areas of science and technology,including communication.In this review,we discuss the current state of quantum computing in communication and its potential applications in various areas such as network optimization,signal processing,and machine learning for communication.First,the basic principle of quantum computing,quantum physics systems,and quantum algorithms are analyzed.Then,based on the classification of quantum algorithms,several important basic quantum algorithms,quantum optimization algorithms,and quantum machine learning algorithms are discussed in detail.Finally,the basic ideas and feasibility of introducing quantum algorithms into communications are emphatically analyzed,which provides a reference to address computational bottlenecks in communication networks.展开更多
Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations.Using the‘sender-receiver’model,we propose quantum algorithms for matrix operations such as matrix-ve...Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations.Using the‘sender-receiver’model,we propose quantum algorithms for matrix operations such as matrix-vector product,matrix-matrix product,the sum of two matrices,and the calculation of determinant and inverse matrix.We encode the matrix entries into the probability amplitudes of the pure initial states of senders.After applying proper unitary transformation to the complete quantum system,the desired result can be found in certain blocks of the receiver’s density matrix.These quantum protocols can be used as subroutines in other quantum schemes.Furthermore,we present an alternative quantum algorithm for solving linear systems of equations.展开更多
It is known that quantum computer is more powerful than classical computer.In this paper we present quantum algorithms for some famous NP problems in graph theory and combination theory,these quantum algorithms are at...It is known that quantum computer is more powerful than classical computer.In this paper we present quantum algorithms for some famous NP problems in graph theory and combination theory,these quantum algorithms are at least quadratically faster than the classical ones.展开更多
With the rapid development of quantum theory and technology in recent years,especially the emergence of some quantum cloud computing platforms,more and more researchers are not satisfied with the theoretical derivatio...With the rapid development of quantum theory and technology in recent years,especially the emergence of some quantum cloud computing platforms,more and more researchers are not satisfied with the theoretical derivation and simulation verification of quantum computation(especially quantum algorithms),experimental verification on real quantum devices has become a new trend.In this paper,three representative quantum algorithms,namely Deutsch-Jozsa,Grover,and Shor algorithms,are briefly depicted,and then their implementation circuits are presented,respectively.We program these circuits on python with QISKit to connect the remote real quantum devices(i.e.,ibmqx4,ibmqx5)on IBM Q to verify these algorithms.The experimental results not only show the feasibility of these algorithms,but also serve to evaluate the functionality of these devices.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
This paper proposes a method to measure directly the concurrence of an arbitrary two-qubit pure state based on a generalized Grover quantum iteration algorithm and a phase estimation algorithm. The concurrence can be ...This paper proposes a method to measure directly the concurrence of an arbitrary two-qubit pure state based on a generalized Grover quantum iteration algorithm and a phase estimation algorithm. The concurrence can be calculated by applying quantum algorithms to two available copies of the bipartite system, and a final measurement on the auxiliary working qubits gives a better estimation of the concurrence. This method opens new prospects of entanglement measure by the application of quantum algorithms. The implementation of the protocol would be an important step toward quantum information processing and more complex entanglement measure of the finite-dimensional quantum system with an arbitrary number of qubits.展开更多
Most problems in uncertainty quantification,despite their ubiquitousness in scientific computing,applied mathematics and data science,remain formidable on a classical computer.For uncertainties that arise in partial d...Most problems in uncertainty quantification,despite their ubiquitousness in scientific computing,applied mathematics and data science,remain formidable on a classical computer.For uncertainties that arise in partial differential equations(PDEs),large numbers M>>1 of samples are required to obtain accurate ensemble averages.This usually involves solving the PDE M times.In addition,to characterise the stochasticity in a PDE,the dimension L of the random input variables is high in most cases,and classical algorithms suffer from the curse-of-dimensionality.We propose new quantum algorithms for PDEs with uncertain coefficients that are more efficient in M and L in various important regimes,compared to their classical counterparts.We introduce transformations that convert the original d-dimensional equation(with uncertain coefficients)into d+L(for dissipative equations)or d+2L(for wave type equations)dimensional equations(with certain coefficients)in which the uncertainties appear only in the initial data.These transformations also allow one to superimpose the M different initial data,so the computational cost for the quantum algorithm to obtain the ensemble average from M different samples is independent of M,while also showing potential advantage in d,L and precisionεin computing ensemble averaged solutions or physical observables.展开更多
Solving non-Hermitian quantum many-body systems on a quantum computer by minimizing the variational energy is challenging as the energy can be complex.Here,we propose a variational quantum algorithm for solving the no...Solving non-Hermitian quantum many-body systems on a quantum computer by minimizing the variational energy is challenging as the energy can be complex.Here,we propose a variational quantum algorithm for solving the non-Hermitian Hamiltonian by minimizing a type of energy variance,where zero variance can naturally determine the eigenvalues and the associated left and right eigenstates.Moreover,the energy is set as a parameter in the cost function and can be tuned to scan the whole spectrum efficiently by using a two-step optimization scheme.Through numerical simulations,we demonstrate the algorithm for preparing the left and right eigenstates,verifying the biorthogonal relations,as well as evaluating the observables.We also investigate the impact of quantum noise on our algorithm and show that its performance can be largely improved using error mitigation techniques.Therefore,our work suggests an avenue for solving non-Hermitian quantum many-body systems with variational quantum algorithms on near-term noisy quantum computers.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
Quantum algorithms offer more enhanced computational efficiency in comparison to their classical counterparts when solving specific tasks.In this study,we implement the quantum permutation algorithm utilizing a polar ...Quantum algorithms offer more enhanced computational efficiency in comparison to their classical counterparts when solving specific tasks.In this study,we implement the quantum permutation algorithm utilizing a polar molecule within an external electric field.The selection of the molecular qutrit involves the utilization of field-dressed states generated through the pendular modes of SrO.Through the application of multi-target optimal control theory,we strategically design microwave pulses to execute logical operations,including Fourier transform,oracle U_(f)operation,and inverse Fourier transform within a three-level molecular qutrit structure.The observed high fidelity of our outcomes is intricately linked to the concept of the quantum speed limit,which quantifies the maximum speed of quantum state manipulation.Subsequently,we design the optimized pulse sequence to successfully simulate the quantum permutation algorithm on a single SrO molecule,achieving remarkable fidelity.Consequently,a quantum circuit comprising a single qutrit suffices to determine permutation parity with just a single function evaluation.Therefore,our results indicate that the optimal control theory can be well applied to the quantum computation of polar molecular systems.展开更多
In the field of Internet, an image is of great significance to information transmission. Meanwhile, how to ensure and improve its security has become the focus of international research. We combine DNA codec with quan...In the field of Internet, an image is of great significance to information transmission. Meanwhile, how to ensure and improve its security has become the focus of international research. We combine DNA codec with quantum Arnold transform(QAr T) to propose a new double encryption algorithm for quantum color images to improve the security and robustness of image encryption. First, we utilize the biological characteristics of DNA codecs to perform encoding and decoding operations on pixel color information in quantum color images, and achieve pixel-level diffusion. Second, we use QAr T to scramble the position information of quantum images and use the operated image as the key matrix for quantum XOR operations. All quantum operations in this paper are reversible, so the decryption operation of the ciphertext image can be realized by the reverse operation of the encryption process. We conduct simulation experiments on encryption and decryption using three color images of “Monkey”, “Flower”, and “House”. The experimental results show that the peak value and correlation of the encrypted images on the histogram have good similarity, and the average normalized pixel change rate(NPCR) of RGB three-channel is 99.61%, the average uniform average change intensity(UACI) is 33.41%,and the average information entropy is about 7.9992. In addition, the robustness of the proposed algorithm is verified by the simulation of noise interference in the actual scenario.展开更多
The quantum alternating operator ansatz algorithm(QAOA+)is widely used for constrained combinatorial optimization problems(CCOPs)due to its ability to construct feasible solution spaces.In this paper,we propose a prog...The quantum alternating operator ansatz algorithm(QAOA+)is widely used for constrained combinatorial optimization problems(CCOPs)due to its ability to construct feasible solution spaces.In this paper,we propose a progressive quantum algorithm(PQA)to reduce qubit requirements for QAOA+in solving the maximum independent set(MIS)problem.PQA iteratively constructs a subgraph likely to include the MIS solution of the original graph and solves the problem on it to approximate the global solution.Specifically,PQA starts with a small-scale subgraph and progressively expands its graph size utilizing heuristic expansion strategies.After each expansion,PQA solves the MIS problem on the newly generated subgraph using QAOA+.In each run,PQA repeats the expansion and solving process until a predefined stopping condition is reached.Simulation results show that PQA achieves an approximation ratio of 0.95 using only 5.57%(2.17%)of the qubits and 17.59%(6.43%)of the runtime compared with directly solving the original problem with QAOA+on Erd?s-Rényi(3-regular)graphs,highlighting the efficiency and scalability of PQA.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 recent experiments [Nature 449, 438 （2007） and Nature Physics 6, 777 （2010）], a new approach for realizing quantum gates for the design of quantum algorithms was developed. Accordingly, the operation time...Based on recent experiments [Nature 449, 438 （2007） and Nature Physics 6, 777 （2010）], a new approach for realizing quantum gates for the design of quantum algorithms was developed. Accordingly, the operation times of such gates while functioning in algorithm applications depend on the number of photons present in their resonant cavities. Multi-qubit algorithms can be realized in systems in which the photon number is increased slightly over the qubit number. In addition, the time required for operation is considerably less than the dephasing and relaxation times of the systems. The contextual use of the photon number as a main control in the realization of any algorithm was demonstrated. The results indicate the possibility of a full integration into the realization of multi-qubit multiphoton states and its application in algorithm designs. Yhrthermore, this approach will lead to a successful implementation of these designs in future experiments.展开更多
As quantum computing transitions from a theoretical domain to a practical technology, many aspects of established practice in software engineering are being faced with new challenges. Quantum Software Engineering has ...As quantum computing transitions from a theoretical domain to a practical technology, many aspects of established practice in software engineering are being faced with new challenges. Quantum Software Engineering has been developed to address the peculiar needs that arise with quantum systems’ dependable, scalable, and fault-tolerant software development. The present paper critically reviews how traditional software engineering methodologies can be reshaped to fit into the quantum field. This also entails providing some critical contributions: frameworks to integrate classical and quantum systems, new error mitigation techniques, and the development of quantum-specific testing and debugging tools. In this respect, best practices have been recommended to ensure that future quantum software can harness the evolving capabilities of quantum hardware with continued performance, reliability, and scalability. The work is supposed to act as a foundational guide for the researcher and developer as quantum computing approaches widespread scientific and industrial adoption.展开更多
The query model(or black-box model)has attracted much attention from the communities of both classical and quantum computing.Usually,quantum advantages are revealed by presenting a quantum algorithm that has a better ...The query model(or black-box model)has attracted much attention from the communities of both classical and quantum computing.Usually,quantum advantages are revealed by presenting a quantum algorithm that has a better query complexity than its classical counterpart.In the history of quantum algorithms,the Deutsch algorithm and the Deutsch-Jozsa algorithm play a fundamental role and both are exact one-query quantum algorithms.This leads us to con-sider the problem:what functions can be computed by exact one-query quantum algorithms?This problem has been ad-dressed in the literature for total Boolean functions and symmetric partial Boolean functions,but is still open for general partial Boolean functions.Thus,in this paper,we continue to characterize the computational power of exact one-query quantum algorithms for general partial Boolean functions.First,we present several necessary and sufficient conditions for a partial Boolean function to be computed by exact one-query quantum algorithms.Second,inspired by these conditions,we discover some new representative functions that can be computed by exact one-query quantum algorithms but have an essential difference from the already known ones.Specially,it is worth pointing out that before our work,the known func-tions that can be computed by exact one-query quantum algorithms are all symmetric functions and the quantum algo-rithm used is essentially the Deutsch-Jozsa algorithm,whereas the functions discovered in this paper are generally asym-metric and new algorithms to compute these functions are required.Thus,this expands the class of functions that can be computed by exact one-query quantum algorithms.展开更多
We present two efficient quantum adiabatic algorithms for Bernstein–Vazirani problem and Simon’s problem.We show that the time complexities of the algorithms for Bernstein–Vazirani problem and Simon’s problem are ...We present two efficient quantum adiabatic algorithms for Bernstein–Vazirani problem and Simon’s problem.We show that the time complexities of the algorithms for Bernstein–Vazirani problem and Simon’s problem are O(1)and O(n),respectively,which are the same complexities as the corresponding algorithms in quantum circuit model.In these two algorithms,the adiabatic Hamiltonians are realized by unitary interpolation instead of standard linear interpolation.Comparing with the adiabatic algorithms using linear interpolation,the energy gaps of our algorithms keep constant.Therefore,the complexities are much easier to analyze using this method.展开更多
文摘Quantum computing offers unprecedented computational power, enabling simultaneous computations beyond traditional computers. Quantum computers differ significantly from classical computers, necessitating a distinct approach to algorithm design, which involves taming quantum mechanical phenomena. This paper extends the numbering of computable programs to be applied in the quantum computing context. Numbering computable programs is a theoretical computer science concept that assigns unique numbers to individual programs or algorithms. Common methods include Gödel numbering which encodes programs as strings of symbols or characters, often used in formal systems and mathematical logic. Based on the proposed numbering approach, this paper presents a mechanism to explore the set of possible quantum algorithms. The proposed approach is able to construct useful circuits such as Quantum Key Distribution BB84 protocol, which enables sender and receiver to establish a secure cryptographic key via a quantum channel. The proposed approach facilitates the process of exploring and constructing quantum algorithms.
文摘Quantum computing is a promising technology that has the potential to revolutionize many areas of science and technology,including communication.In this review,we discuss the current state of quantum computing in communication and its potential applications in various areas such as network optimization,signal processing,and machine learning for communication.First,the basic principle of quantum computing,quantum physics systems,and quantum algorithms are analyzed.Then,based on the classification of quantum algorithms,several important basic quantum algorithms,quantum optimization algorithms,and quantum machine learning algorithms are discussed in detail.Finally,the basic ideas and feasibility of introducing quantum algorithms into communications are emphatically analyzed,which provides a reference to address computational bottlenecks in communication networks.
基金supported by the National Natural Science Foundation of China(Grant No.12031004 and Grant No.12271474,61877054)the Fundamental Research Foundation for the Central Universities(Project No.K20210337)+1 种基金the Zhejiang University Global Partnership Fund,188170+194452119/003partially funded by a state task of Russian Fundamental Investigations(State Registration No.FFSG-2024-0002)。
文摘Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations.Using the‘sender-receiver’model,we propose quantum algorithms for matrix operations such as matrix-vector product,matrix-matrix product,the sum of two matrices,and the calculation of determinant and inverse matrix.We encode the matrix entries into the probability amplitudes of the pure initial states of senders.After applying proper unitary transformation to the complete quantum system,the desired result can be found in certain blocks of the receiver’s density matrix.These quantum protocols can be used as subroutines in other quantum schemes.Furthermore,we present an alternative quantum algorithm for solving linear systems of equations.
文摘It is known that quantum computer is more powerful than classical computer.In this paper we present quantum algorithms for some famous NP problems in graph theory and combination theory,these quantum algorithms are at least quadratically faster than the classical ones.
基金This work was supported by the Natural Science Foundation of Jiangsu Province under Grant BK20171458in part by the Natural Science Foundation of China under Grant Nos.61672290 and 61802002+2 种基金the Natural Science Foundation of Jiangsu Higher Education Institutions of China under Grant No.19KJB520028Jiangsu Graduate Scientific Research Innovation Program under Grant No.KYCX20_0978the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD).
文摘With the rapid development of quantum theory and technology in recent years,especially the emergence of some quantum cloud computing platforms,more and more researchers are not satisfied with the theoretical derivation and simulation verification of quantum computation(especially quantum algorithms),experimental verification on real quantum devices has become a new trend.In this paper,three representative quantum algorithms,namely Deutsch-Jozsa,Grover,and Shor algorithms,are briefly depicted,and then their implementation circuits are presented,respectively.We program these circuits on python with QISKit to connect the remote real quantum devices(i.e.,ibmqx4,ibmqx5)on IBM Q to verify these algorithms.The experimental results not only show the feasibility of these algorithms,but also serve to evaluate the functionality of these devices.
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Project supported by the National Natural Science Foundation of China (Grant No 60667001)
文摘This paper proposes a method to measure directly the concurrence of an arbitrary two-qubit pure state based on a generalized Grover quantum iteration algorithm and a phase estimation algorithm. The concurrence can be calculated by applying quantum algorithms to two available copies of the bipartite system, and a final measurement on the auxiliary working qubits gives a better estimation of the concurrence. This method opens new prospects of entanglement measure by the application of quantum algorithms. The implementation of the protocol would be an important step toward quantum information processing and more complex entanglement measure of the finite-dimensional quantum system with an arbitrary number of qubits.
基金supported by the National Natural Science Foundation of China(Grant Nos.12031013,12341104,and 12050410230)the National Natural Science Foundation of China International Young Scientists Project(Grant No.12050410230)+6 种基金the Shanghai Municipal Science and Technology Major Project(Grant No.2021SHZDZX0102)the Innovation Program of Shanghai Municipal Education Commission(Grant No.2021-01-07-00-02-E00087)the Science and Technology Program of ShanghaiChina(Grant No.21JC1402900)the Shanghai Pujiang Talent Grant(Grant No.20PJ1408400)the Shanghai Jiao Tong University 2030 Initiativethe Fundamental Research Funds for the Central Universities。
文摘Most problems in uncertainty quantification,despite their ubiquitousness in scientific computing,applied mathematics and data science,remain formidable on a classical computer.For uncertainties that arise in partial differential equations(PDEs),large numbers M>>1 of samples are required to obtain accurate ensemble averages.This usually involves solving the PDE M times.In addition,to characterise the stochasticity in a PDE,the dimension L of the random input variables is high in most cases,and classical algorithms suffer from the curse-of-dimensionality.We propose new quantum algorithms for PDEs with uncertain coefficients that are more efficient in M and L in various important regimes,compared to their classical counterparts.We introduce transformations that convert the original d-dimensional equation(with uncertain coefficients)into d+L(for dissipative equations)or d+2L(for wave type equations)dimensional equations(with certain coefficients)in which the uncertainties appear only in the initial data.These transformations also allow one to superimpose the M different initial data,so the computational cost for the quantum algorithm to obtain the ensemble average from M different samples is independent of M,while also showing potential advantage in d,L and precisionεin computing ensemble averaged solutions or physical observables.
基金This work was 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)the Guangdong Provincial Key Laboratory(Grant No.2020B1212060066).
文摘Solving non-Hermitian quantum many-body systems on a quantum computer by minimizing the variational energy is challenging as the energy can be complex.Here,we propose a variational quantum algorithm for solving the non-Hermitian Hamiltonian by minimizing a type of energy variance,where zero variance can naturally determine the eigenvalues and the associated left and right eigenstates.Moreover,the energy is set as a parameter in the cost function and can be tuned to scan the whole spectrum efficiently by using a two-step optimization scheme.Through numerical simulations,we demonstrate the algorithm for preparing the left and right eigenstates,verifying the biorthogonal relations,as well as evaluating the observables.We also investigate the impact of quantum noise on our algorithm and show that its performance can be largely improved using error mitigation techniques.Therefore,our work suggests an avenue for solving non-Hermitian quantum many-body systems with variational quantum algorithms on near-term noisy quantum computers.
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.
基金supported by the National Natural Science Foundation of China under Grant Nos.92265209,11174081 and 62305285the Natural Science Foundation of Chongqing under Grant No.CSTB2024NSCQ-MSX0643the Shanghai Municipal Science and Technology Major Project under Grant No.2019SHZDZX01。
文摘Quantum algorithms offer more enhanced computational efficiency in comparison to their classical counterparts when solving specific tasks.In this study,we implement the quantum permutation algorithm utilizing a polar molecule within an external electric field.The selection of the molecular qutrit involves the utilization of field-dressed states generated through the pendular modes of SrO.Through the application of multi-target optimal control theory,we strategically design microwave pulses to execute logical operations,including Fourier transform,oracle U_(f)operation,and inverse Fourier transform within a three-level molecular qutrit structure.The observed high fidelity of our outcomes is intricately linked to the concept of the quantum speed limit,which quantifies the maximum speed of quantum state manipulation.Subsequently,we design the optimized pulse sequence to successfully simulate the quantum permutation algorithm on a single SrO molecule,achieving remarkable fidelity.Consequently,a quantum circuit comprising a single qutrit suffices to determine permutation parity with just a single function evaluation.Therefore,our results indicate that the optimal control theory can be well applied to the quantum computation of polar molecular systems.
基金Project supported by the Natural Science Foundation of Shandong Province, China (Grant No. ZR2021MF049)Joint Fund of Natural Science Foundation of Shandong Province (Grant Nos. ZR2022LLZ012 and ZR2021LLZ001)the Key R&D Program of Shandong Province, China (Grant No. 2023CXGC010901)。
文摘In the field of Internet, an image is of great significance to information transmission. Meanwhile, how to ensure and improve its security has become the focus of international research. We combine DNA codec with quantum Arnold transform(QAr T) to propose a new double encryption algorithm for quantum color images to improve the security and robustness of image encryption. First, we utilize the biological characteristics of DNA codecs to perform encoding and decoding operations on pixel color information in quantum color images, and achieve pixel-level diffusion. Second, we use QAr T to scramble the position information of quantum images and use the operated image as the key matrix for quantum XOR operations. All quantum operations in this paper are reversible, so the decryption operation of the ciphertext image can be realized by the reverse operation of the encryption process. We conduct simulation experiments on encryption and decryption using three color images of “Monkey”, “Flower”, and “House”. The experimental results show that the peak value and correlation of the encrypted images on the histogram have good similarity, and the average normalized pixel change rate(NPCR) of RGB three-channel is 99.61%, the average uniform average change intensity(UACI) is 33.41%,and the average information entropy is about 7.9992. In addition, the robustness of the proposed algorithm is verified by the simulation of noise interference in the actual scenario.
基金supported by the National Natural Science Foundation of China(Grant Nos.62371069,62372048,and 62272056)BUPT Excellent Ph.D.Students Foundation(Grant No.CX2023123)。
文摘The quantum alternating operator ansatz algorithm(QAOA+)is widely used for constrained combinatorial optimization problems(CCOPs)due to its ability to construct feasible solution spaces.In this paper,we propose a progressive quantum algorithm(PQA)to reduce qubit requirements for QAOA+in solving the maximum independent set(MIS)problem.PQA iteratively constructs a subgraph likely to include the MIS solution of the original graph and solves the problem on it to approximate the global solution.Specifically,PQA starts with a small-scale subgraph and progressively expands its graph size utilizing heuristic expansion strategies.After each expansion,PQA solves the MIS problem on the newly generated subgraph using QAOA+.In each run,PQA repeats the expansion and solving process until a predefined stopping condition is reached.Simulation results show that PQA achieves an approximation ratio of 0.95 using only 5.57%(2.17%)of the qubits and 17.59%(6.43%)of the runtime compared with directly solving the original problem with QAOA+on Erd?s-Rényi(3-regular)graphs,highlighting the efficiency and scalability of PQA.
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.
文摘Based on recent experiments [Nature 449, 438 （2007） and Nature Physics 6, 777 （2010）], a new approach for realizing quantum gates for the design of quantum algorithms was developed. Accordingly, the operation times of such gates while functioning in algorithm applications depend on the number of photons present in their resonant cavities. Multi-qubit algorithms can be realized in systems in which the photon number is increased slightly over the qubit number. In addition, the time required for operation is considerably less than the dephasing and relaxation times of the systems. The contextual use of the photon number as a main control in the realization of any algorithm was demonstrated. The results indicate the possibility of a full integration into the realization of multi-qubit multiphoton states and its application in algorithm designs. Yhrthermore, this approach will lead to a successful implementation of these designs in future experiments.
文摘As quantum computing transitions from a theoretical domain to a practical technology, many aspects of established practice in software engineering are being faced with new challenges. Quantum Software Engineering has been developed to address the peculiar needs that arise with quantum systems’ dependable, scalable, and fault-tolerant software development. The present paper critically reviews how traditional software engineering methodologies can be reshaped to fit into the quantum field. This also entails providing some critical contributions: frameworks to integrate classical and quantum systems, new error mitigation techniques, and the development of quantum-specific testing and debugging tools. In this respect, best practices have been recommended to ensure that future quantum software can harness the evolving capabilities of quantum hardware with continued performance, reliability, and scalability. The work is supposed to act as a foundational guide for the researcher and developer as quantum computing approaches widespread scientific and industrial adoption.
基金supported by the National Natural Science Foundation of China under Grant Nos.61772565 and 62272492the Guangdong Basic and Applied Basic Research Foundation under Grant No.2020B1515020050the Key Research and Development Program of Guangdong Province of China under Grant No.2018B030325001.
文摘The query model(or black-box model)has attracted much attention from the communities of both classical and quantum computing.Usually,quantum advantages are revealed by presenting a quantum algorithm that has a better query complexity than its classical counterpart.In the history of quantum algorithms,the Deutsch algorithm and the Deutsch-Jozsa algorithm play a fundamental role and both are exact one-query quantum algorithms.This leads us to con-sider the problem:what functions can be computed by exact one-query quantum algorithms?This problem has been ad-dressed in the literature for total Boolean functions and symmetric partial Boolean functions,but is still open for general partial Boolean functions.Thus,in this paper,we continue to characterize the computational power of exact one-query quantum algorithms for general partial Boolean functions.First,we present several necessary and sufficient conditions for a partial Boolean function to be computed by exact one-query quantum algorithms.Second,inspired by these conditions,we discover some new representative functions that can be computed by exact one-query quantum algorithms but have an essential difference from the already known ones.Specially,it is worth pointing out that before our work,the known func-tions that can be computed by exact one-query quantum algorithms are all symmetric functions and the quantum algo-rithm used is essentially the Deutsch-Jozsa algorithm,whereas the functions discovered in this paper are generally asym-metric and new algorithms to compute these functions are required.Thus,this expands the class of functions that can be computed by exact one-query quantum algorithms.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11504430,11805279,61501514,and 61502526)
文摘We present two efficient quantum adiabatic algorithms for Bernstein–Vazirani problem and Simon’s problem.We show that the time complexities of the algorithms for Bernstein–Vazirani problem and Simon’s problem are O(1)and O(n),respectively,which are the same complexities as the corresponding algorithms in quantum circuit model.In these two algorithms,the adiabatic Hamiltonians are realized by unitary interpolation instead of standard linear interpolation.Comparing with the adiabatic algorithms using linear interpolation,the energy gaps of our algorithms keep constant.Therefore,the complexities are much easier to analyze using this method.
