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
The quantum hybrid algorithm has recently become a very promising and speedy method for solving larger-scale optimization problems in the noisy intermediate-scale quantum(NISQ)era.The unit commitment(UC)problem is a f...The quantum hybrid algorithm has recently become a very promising and speedy method for solving larger-scale optimization problems in the noisy intermediate-scale quantum(NISQ)era.The unit commitment(UC)problem is a fundamental problem in the field of power systems that aims to satisfy the power balance constraint with minimal cost.In this paper,we focus on the implementation of the UC solution using exact quantum algorithms based on the quantum neural network(QNN).This method is tested with a ten-unit system under the power balance constraint.In order to improve computing precision and reduce network complexity,we propose a knowledge-based partially connected quantum neural network(PCQNN).The results show that exact solutions can be obtained by the improved algorithm and that the depth of the quantum circuit can be reduced simultaneously.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
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 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
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
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
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
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
Shor proposed a polynomial time algorithm for computing the order of one element in a multiplicative group using a quantum computer. Based on Miller’s randomization, he then gave a factorization algorithm. But the al...Shor proposed a polynomial time algorithm for computing the order of one element in a multiplicative group using a quantum computer. Based on Miller’s randomization, he then gave a factorization algorithm. But the algorithm has two shortcomings, the order must be even and the output might be a trivial factor. Actually, these drawbacks can be overcome if the number is an RSA modulus. Applying the special structure of the RSA modulus, an algorithm is presented to overcome the two shortcomings. The new algorithm improves Shor’s algorithm for factoring RSA modulus. The cost of the factorization algorithm almost depends on the calculation of the order of 2 in the multiplication group.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
A quantum algorithm for solving the classical NP-complete problem - the Hamilton circuit is presented. The algorithm employs the quantum SAT and the quantum search algorithms. The algorithm is square-root faster than ...A quantum algorithm for solving the classical NP-complete problem - the Hamilton circuit is presented. The algorithm employs the quantum SAT and the quantum search algorithms. The algorithm is square-root faster than classical algorithm, and becomes exponentially faster than classical algorithm if nonlinear quantum mechanical computer is used.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
Using quantum algorithms to solve various problems has attracted widespread attention with the development of quantum computing.Researchers are particularly interested in using the acceleration properties of quantum a...Using quantum algorithms to solve various problems has attracted widespread attention with the development of quantum computing.Researchers are particularly interested in using the acceleration properties of quantum algorithms to solve NP-complete problems.This paper focuses on the well-known NP-complete problem of finding the minimum dominating set in undirected graphs.To expedite the search process,a quantum algorithm employing Grover’s search is proposed.However,a challenge arises from the unknown number of solutions for the minimum dominating set,rendering direct usage of original Grover’s search impossible.Thus,a swap test method is introduced to ascertain the number of iterations required.The oracle,diffusion operators,and swap test are designed with achievable quantum gates.The query complexity is O(1.414^(n))and the space complexity is O(n).To validate the proposed approach,qiskit software package is employed to simulate the quantum circuit,yielding the anticipated results.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
Toeplitz matrix-vector multiplication is widely used in various fields,including optimal control,systolic finite field multipliers,multidimensional convolution,etc.In this paper,we first present a non-asymptotic quant...Toeplitz matrix-vector multiplication is widely used in various fields,including optimal control,systolic finite field multipliers,multidimensional convolution,etc.In this paper,we first present a non-asymptotic quantum algorithm for Toeplitz matrix-vector multiplication with time complexity O(κpolylogn),whereκand 2n are the condition number and the dimension of the circulant matrix extended from the Toeplitz matrix,respectively.For the case with an unknown generating function,we also give a corresponding non-asymptotic quantum version that eliminates the dependency on the L_(1)-normρof the displacement of the structured matrices.Due to the good use of the special properties of Toeplitz matrices,the proposed quantum algorithms are sufficiently accurate and efficient compared to the existing quantum algorithms under certain circumstances.展开更多
Neighborhood preserving embedding(NPE)is an important linear dimensionality reduction technique that aims at preserving the local manifold structure.NPE contains three steps,i.e.,finding the nearest neighbors of each ...Neighborhood preserving embedding(NPE)is an important linear dimensionality reduction technique that aims at preserving the local manifold structure.NPE contains three steps,i.e.,finding the nearest neighbors of each data point,constructing the weight matrix,and obtaining the transformation matrix.Liang et al.proposed a variational quantum algorithm(VQA)for NPE[Phys.Rev.A 101032323(2020)].The algorithm consists of three quantum sub-algorithms,corresponding to the three steps of NPE,and was expected to have an exponential speedup on the dimensionality n.However,the algorithm has two disadvantages:(i)It is not known how to efficiently obtain the input of the third sub-algorithm from the output of the second one.(ii)Its complexity cannot be rigorously analyzed because the third sub-algorithm in it is a VQA.In this paper,we propose a complete quantum algorithm for NPE,in which we redesign the three sub-algorithms and give a rigorous complexity analysis.It is shown that our algorithm can achieve a polynomial speedup on the number of data points m and an exponential speedup on the dimensionality n under certain conditions over the classical NPE algorithm,and achieve a significant speedup compared to Liang et al.’s algorithm even without considering the complexity of the VQA.展开更多
We present a novel quantum algorithm to evaluate the hamming distance between two unknown oracles via measuring the degree of entanglement between two ancillary qubits.In particular,we use the power of the entanglemen...We present a novel quantum algorithm to evaluate the hamming distance between two unknown oracles via measuring the degree of entanglement between two ancillary qubits.In particular,we use the power of the entanglement degree based quantum computing model that preserves at most the locality of interactions within the quantum model structure.This model uses one of two techniques to retrieve the solution of a quantum computing problem at hand.In the first technique,the solution of the problem is obtained based on whether there is an entanglement between the two ancillary qubits or not.In the second,the solution of the quantum computing problem is obtained as a function in the concurrence value,and the number of states that can be generated from the Boolean variables.The proposed algorithm receives two oracles,each oracle represents an unknown Boolean function,then it measures the hamming distance between these two oracles.The hamming distance is evaluated based on the second technique.It is shown that the proposed algorithm provides exponential speedup compared with the classical counterpart for Boolean functions that have large numbers of Boolean variables.The proposed algorithm is explained via a case study.Finally,employing recently developed experimental techniques,the proposed algorithm has been verified using IBM’s quantum computer simulator.展开更多
Suppose a practical scene that when two or more parties want to schedule anappointment, they need to share their calendars with each other in order to make itpossible. According to the present result the whole communi...Suppose a practical scene that when two or more parties want to schedule anappointment, they need to share their calendars with each other in order to make itpossible. According to the present result the whole communication cost to solve thisproblem should be their calendars’ length by using a classical algorithm. In this work, weinvestigate the appointment schedule issue made by N users and try to accomplish it inquantum information case. Our study shows that the total communication cost will bequadratic times smaller than the conventional case if we apply a quantum algorithm in theappointment-scheduling problem.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.
基金supported in part by the China Postdoctoral Science Foundation(Grant No.2023M740874)。
文摘The quantum hybrid algorithm has recently become a very promising and speedy method for solving larger-scale optimization problems in the noisy intermediate-scale quantum(NISQ)era.The unit commitment(UC)problem is a fundamental problem in the field of power systems that aims to satisfy the power balance constraint with minimal cost.In this paper,we focus on the implementation of the UC solution using exact quantum algorithms based on the quantum neural network(QNN).This method is tested with a ten-unit system under the power balance constraint.In order to improve computing precision and reduce network complexity,we propose a knowledge-based partially connected quantum neural network(PCQNN).The results show that exact solutions can be obtained by the improved algorithm and that the depth of the quantum circuit can be reduced simultaneously.
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.
基金Supported by the National Natural Science Foundation of China(under Grant Nos.12105090 and 12074107)the Program of Outstanding Young and Middle-aged Scientific and Technological Innovation Team of Colleges and Universities in Hubei Province of China(under Grant No.T2020001)the Innovation Group Project of the Natural Science Foundation of Hubei Province of China(under Grant No.2022CFA012)。
文摘Since the concept of quantum information masking was proposed by Modi et al(2018 Phys.Rev.Lett.120,230501),many interesting and significant results have been reported,both theoretically and experimentally.However,designing a quantum information masker is not an easy task,especially for larger systems.In this paper,we propose a variational quantum algorithm to resolve this problem.Specifically,our algorithm is a hybrid quantum-classical model,where the quantum device with adjustable parameters tries to mask quantum information and the classical device evaluates the performance of the quantum device and optimizes its parameters.After optimization,the quantum device behaves as an optimal masker.The loss value during optimization can be used to characterize the performance of the masker.In particular,if the loss value converges to zero,we obtain a perfect masker that completely masks the quantum information generated by the quantum information source,otherwise,the perfect masker does not exist and the subsystems always contain the original information.Nevertheless,these resulting maskers are still optimal.Quantum parallelism is utilized to reduce quantum state preparations and measurements.Our study paves the way for wide application of quantum information masking,and some of the techniques used in this study may have potential applications in quantum information processing.
文摘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 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.
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.
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(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Shor proposed a polynomial time algorithm for computing the order of one element in a multiplicative group using a quantum computer. Based on Miller’s randomization, he then gave a factorization algorithm. But the algorithm has two shortcomings, the order must be even and the output might be a trivial factor. Actually, these drawbacks can be overcome if the number is an RSA modulus. Applying the special structure of the RSA modulus, an algorithm is presented to overcome the two shortcomings. The new algorithm improves Shor’s algorithm for factoring RSA modulus. The cost of the factorization algorithm almost depends on the calculation of the order of 2 in the multiplication group.
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.
基金国家自然科学基金，国家重点基础研究发展计划(973计划)，the HangTian Science Foundation
文摘A quantum algorithm for solving the classical NP-complete problem - the Hamilton circuit is presented. The algorithm employs the quantum SAT and the quantum search algorithms. The algorithm is square-root faster than classical algorithm, and becomes exponentially faster than classical algorithm if nonlinear quantum mechanical computer is used.
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Project supported by the National Natural Science Foundation of China(Grant No.62101600)the Science Foundation of China University of Petroleum,Beijing(Grant No.2462021YJRC008)the State Key Laboratory of Cryptology(Grant No.MMKFKT202109).
文摘Using quantum algorithms to solve various problems has attracted widespread attention with the development of quantum computing.Researchers are particularly interested in using the acceleration properties of quantum algorithms to solve NP-complete problems.This paper focuses on the well-known NP-complete problem of finding the minimum dominating set in undirected graphs.To expedite the search process,a quantum algorithm employing Grover’s search is proposed.However,a challenge arises from the unknown number of solutions for the minimum dominating set,rendering direct usage of original Grover’s search impossible.Thus,a swap test method is introduced to ascertain the number of iterations required.The oracle,diffusion operators,and swap test are designed with achievable quantum gates.The query complexity is O(1.414^(n))and the space complexity is O(n).To validate the proposed approach,qiskit software package is employed to simulate the quantum circuit,yielding the anticipated results.
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.
基金supported by the National Natural Science Foundation of China(Grant Nos.62071015 and 62171264)。
文摘Toeplitz matrix-vector multiplication is widely used in various fields,including optimal control,systolic finite field multipliers,multidimensional convolution,etc.In this paper,we first present a non-asymptotic quantum algorithm for Toeplitz matrix-vector multiplication with time complexity O(κpolylogn),whereκand 2n are the condition number and the dimension of the circulant matrix extended from the Toeplitz matrix,respectively.For the case with an unknown generating function,we also give a corresponding non-asymptotic quantum version that eliminates the dependency on the L_(1)-normρof the displacement of the structured matrices.Due to the good use of the special properties of Toeplitz matrices,the proposed quantum algorithms are sufficiently accurate and efficient compared to the existing quantum algorithms under certain circumstances.
基金supported by the Fundamental Research Funds for the Central Universities(Grant No.2019XD-A01)the National Natural Science Foundation of China(Grant Nos.61972048 and 61976024)。
文摘Neighborhood preserving embedding(NPE)is an important linear dimensionality reduction technique that aims at preserving the local manifold structure.NPE contains three steps,i.e.,finding the nearest neighbors of each data point,constructing the weight matrix,and obtaining the transformation matrix.Liang et al.proposed a variational quantum algorithm(VQA)for NPE[Phys.Rev.A 101032323(2020)].The algorithm consists of three quantum sub-algorithms,corresponding to the three steps of NPE,and was expected to have an exponential speedup on the dimensionality n.However,the algorithm has two disadvantages:(i)It is not known how to efficiently obtain the input of the third sub-algorithm from the output of the second one.(ii)Its complexity cannot be rigorously analyzed because the third sub-algorithm in it is a VQA.In this paper,we propose a complete quantum algorithm for NPE,in which we redesign the three sub-algorithms and give a rigorous complexity analysis.It is shown that our algorithm can achieve a polynomial speedup on the number of data points m and an exponential speedup on the dimensionality n under certain conditions over the classical NPE algorithm,and achieve a significant speedup compared to Liang et al.’s algorithm even without considering the complexity of the VQA.
文摘We present a novel quantum algorithm to evaluate the hamming distance between two unknown oracles via measuring the degree of entanglement between two ancillary qubits.In particular,we use the power of the entanglement degree based quantum computing model that preserves at most the locality of interactions within the quantum model structure.This model uses one of two techniques to retrieve the solution of a quantum computing problem at hand.In the first technique,the solution of the problem is obtained based on whether there is an entanglement between the two ancillary qubits or not.In the second,the solution of the quantum computing problem is obtained as a function in the concurrence value,and the number of states that can be generated from the Boolean variables.The proposed algorithm receives two oracles,each oracle represents an unknown Boolean function,then it measures the hamming distance between these two oracles.The hamming distance is evaluated based on the second technique.It is shown that the proposed algorithm provides exponential speedup compared with the classical counterpart for Boolean functions that have large numbers of Boolean variables.The proposed algorithm is explained via a case study.Finally,employing recently developed experimental techniques,the proposed algorithm has been verified using IBM’s quantum computer simulator.
基金Supported by the National Natural Science Foundation of Chinaunder Grant Nos. 61501247, 61373131 and 61702277the Six Talent Peaks Project ofJiangsu Province (Grant No. 2015-XXRJ-013)+2 种基金Natural Science Foundation of JiangsuProvince (Grant No. BK20171458)he Natural Science Foundation of the HigherEducation Institutions of Jiangsu Province (China under Grant No. 16KJB520030)theNUIST Research Foundation for Talented Scholars under Grant No. 2015r014, PAPDand CICAEET funds.
文摘Suppose a practical scene that when two or more parties want to schedule anappointment, they need to share their calendars with each other in order to make itpossible. According to the present result the whole communication cost to solve thisproblem should be their calendars’ length by using a classical algorithm. In this work, weinvestigate the appointment schedule issue made by N users and try to accomplish it inquantum information case. Our study shows that the total communication cost will bequadratic times smaller than the conventional case if we apply a quantum algorithm in theappointment-scheduling problem.
