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
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
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
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
In the noisy intermediate-scale quantum era,emerging classical-quantum hybrid optimization algorithms,such as variational quantum algorithms(VQAs),can leverage the unique characteristics of quantum devices to accelera...In the noisy intermediate-scale quantum era,emerging classical-quantum hybrid optimization algorithms,such as variational quantum algorithms(VQAs),can leverage the unique characteristics of quantum devices to accelerate computations tailored to specific problems with shallow circuits.However,these algorithms encounter biases and iteration difficulties due to significant noise in quantum processors.These difficulties can only be partially addressed without error correction by optimizing hardware,reducing circuit complexity,or fitting and extrapolating.A compelling solution is applying probabilistic error cancellation(PEC),a quantum error mitigation technique that enables unbiased results without full error correction.Traditional PEC is challenging to apply in VQAs due to its variance amplification,contradicting iterative process assumptions.This paper proposes a novel noise-adaptable strategy that combines PEC with the quantum approximate optimization algorithm(QAOA).It is implemented through invariant sampling circuits(invariant-PEC,or IPEC)and substantially reduces iteration variance.This strategy marks the first successful integration of PEC and QAOA,resulting in efficient convergence.Moreover,we introduce adaptive partial PEC(APPEC),which modulates the error cancellation proportion of IPEC during iteration.We experimentally validate this technique on a superconducting quantum processor,cutting sampling cost by 90.1%.Notably,we find that dynamic adjustments of error levels via APPEC can enhance the ability to escape from local minima and reduce sampling costs.These results open promising avenues for executing VQAs with large-scale,low-noise quantum circuits,paving the way for practical quantum computing advancements.展开更多
Classical computation of electronic properties in large-scale materials remains challenging.Quantum computation has the potential to offer advantages in memory footprint and computational scaling.However,general and v...Classical computation of electronic properties in large-scale materials remains challenging.Quantum computation has the potential to offer advantages in memory footprint and computational scaling.However,general and viable quantum algorithms for simulating large-scale materials are still limited.We propose and implement random-state quantum algorithms to calculate electronic-structure properties of real materials.Using a random state circuit on a small number of qubits,we employ real-time evolution with first-order Trotter decomposition and Hadamard test to obtain electronic density of states,and we develop a modified quantum phase estimation algorithm to calculate real-space local density of states via direct quantum measurements.Furthermore,we validate these algorithms by numerically computing the density of states and spatial distributions of electronic states in graphene,twisted bilayer graphene quasicrystals,and fractal lattices,covering system sizes from hundreds to thousands of atoms.Our results manifest that the random-state quantum algorithms provide a general and qubit-efficient route to scalable simulations of electronic properties in large-scale periodic and aperiodic materials.展开更多
Variational quantum algorithms(VQAs)with random structures have poor trainability due to the exponentially vanishing gradient as the circuit depth and the qubit number increase.This result leads to a general belief th...Variational quantum algorithms(VQAs)with random structures have poor trainability due to the exponentially vanishing gradient as the circuit depth and the qubit number increase.This result leads to a general belief that a deep circuit will not be feasible.In this work,we provide a viable solution to the vanishing gradient problem for deep VQAs with theoretical guarantees.Specifically,we prove that for quantum controlled-layer and quantum residual network(QResNet),architectures,the expectation of the gradient norm can be lower bounded by a value that is independent of the qubit number and the circuit depth.Our results follow from a careful analysis of the gradient behavior on parameter space consisting of rotation angles,as employed in almost all VQAs,instead of relying on impractical 2-design assumptions.We conduct several numerical experiments as verifications,where only our circuits are trainable and converge,while hardware-efficient and random circuits with similar number of parameters in comparison cannot converge.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
Efficient implementation of fundamental matrix operations on quantum computers,such as matrix products and Hadamard operations,holds significant potential for accelerating machine learning algorithms.A critical prereq...Efficient implementation of fundamental matrix operations on quantum computers,such as matrix products and Hadamard operations,holds significant potential for accelerating machine learning algorithms.A critical prerequisite for quantum implementations is the effective encoding of classical data into quantum states.We propose two quantum computing frameworks for preparing the distinct encoded states corresponding to matrix operations,including the matrix product,matrix sum,matrix Hadamard product and division.Quantum algorithms based on the digital encoding computing framework are capable of implementing the matrix Hadamard operation with a time complexity of O(poly log(mn/ε))and the matrix product with a time complexity of O(poly log(mnl/ε)),achieving an exponential speedup in contrast to the classical methods of O(mn)and O(mnl).Quantum algorithms based on the analog-encoding framework are capable of implementing the matrix Hadamard operation with a time complexity of O(k_(1)√mn·poly log(mn/ε))and the matrix product with a time complexity of O(k_(2)√1·poly log(mnl/ε)),where k_(1)and k_(2)are coefficients correlated with the elements of the matrix,achieving a square speedup in contrast to the classical counterparts.As applications,we construct an oracle that can access the trace of a matrix within logarithmic time,and propose several algorithms to respectively estimate the trace of a matrix,the trace of the product of two matrices,and the trace inner product of two matrices within logarithmic time.展开更多
The Intrusion Detection System(IDS)is a security mechanism developed to observe network traffic and recognize suspicious or malicious activities.Clustering algorithms are often incorporated into IDS;however,convention...The Intrusion Detection System(IDS)is a security mechanism developed to observe network traffic and recognize suspicious or malicious activities.Clustering algorithms are often incorporated into IDS;however,conventional clustering-based methods face notable drawbacks,including poor scalability in handling high-dimensional datasets and a strong dependence of outcomes on initial conditions.To overcome the performance limitations of existing methods,this study proposes a novel quantum-inspired clustering algorithm that relies on a similarity coefficient-based quantum genetic algorithm(SC-QGA)and an improved quantum artificial bee colony algorithm hybrid K-means(IQABC-K).First,the SC-QGA algorithmis constructed based on quantum computing and integrates similarity coefficient theory to strengthen genetic diversity and feature extraction capabilities.For the subsequent clustering phase,the process based on the IQABC-K algorithm is enhanced with the core improvement of adaptive rotation gate and movement exploitation strategies to balance the exploration capabilities of global search and the exploitation capabilities of local search.Simultaneously,the acceleration of convergence toward the global optimum and a reduction in computational complexity are facilitated by means of the global optimum bootstrap strategy and a linear population reduction strategy.Through experimental evaluation with multiple algorithms and diverse performance metrics,the proposed algorithm confirms reliable accuracy on three datasets:KDD CUP99,NSL_KDD,and UNSW_NB15,achieving accuracy of 98.57%,98.81%,and 98.32%,respectively.These results affirm its potential as an effective solution for practical clustering applications.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
Quantum algorithms are demonstrated to outperform classical algorithms for certain problems and thus are promising candidates for efficient information processing.Herein we aim to provide a brief and popular introduct...Quantum algorithms are demonstrated to outperform classical algorithms for certain problems and thus are promising candidates for efficient information processing.Herein we aim to provide a brief and popular introduction to quantum algorithms for both the academic community and the general public with interest.We start from elucidating quantum parallelism,the basic framework of quantum algorithms and the difficulty of quantum algorithm design.Then we mainly focus on a historical overview of progress in quantum algorithm research over the past three to four decades.Finally,we clarify two common questions about the study of quantum algorithms,hoping to stimulate readers for further exploration.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
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
The hardness of the integer factoring problem(IFP)plays a core role in the security of RSA-like cryptosystems that are widely used today.Besides Shor’s quantum algorithm that can solve IFP within polynomial time,quan...The hardness of the integer factoring problem(IFP)plays a core role in the security of RSA-like cryptosystems that are widely used today.Besides Shor’s quantum algorithm that can solve IFP within polynomial time,quantum annealing algorithms(QAA)also manifest certain advantages in factoring integers.In experimental aspects,the reported integers that were successfully factored by using the D-wave QAA platform are much larger than those being factored by using Shor-like quantum algorithms.In this paper,we report some interesting observations about the effects of QAA for solving IFP.More specifically,we introduce a metric,called T-factor that measures the density of occupied qubits to some extent when conducting IFP tasks by using D-wave.We find that T-factor has obvious effects on annealing times for IFP:The larger of T-factor,the quicker of annealing speed.The explanation of this phenomenon is also given.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.
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.
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 Innovation Program for Quantum Science and Technology(Grant Nos.2021ZD0301702,and 2024ZD0302000)the Natural Science Foundation of Jiangsu Province(Grant No.BK20232002)+1 种基金the National Natural Science Foundation of China(Grant Nos.U21A20436,and 12074179)the Natural Science Foundation of Shandong Province(Grant No.ZR2023LZH002)。
文摘In the noisy intermediate-scale quantum era,emerging classical-quantum hybrid optimization algorithms,such as variational quantum algorithms(VQAs),can leverage the unique characteristics of quantum devices to accelerate computations tailored to specific problems with shallow circuits.However,these algorithms encounter biases and iteration difficulties due to significant noise in quantum processors.These difficulties can only be partially addressed without error correction by optimizing hardware,reducing circuit complexity,or fitting and extrapolating.A compelling solution is applying probabilistic error cancellation(PEC),a quantum error mitigation technique that enables unbiased results without full error correction.Traditional PEC is challenging to apply in VQAs due to its variance amplification,contradicting iterative process assumptions.This paper proposes a novel noise-adaptable strategy that combines PEC with the quantum approximate optimization algorithm(QAOA).It is implemented through invariant sampling circuits(invariant-PEC,or IPEC)and substantially reduces iteration variance.This strategy marks the first successful integration of PEC and QAOA,resulting in efficient convergence.Moreover,we introduce adaptive partial PEC(APPEC),which modulates the error cancellation proportion of IPEC during iteration.We experimentally validate this technique on a superconducting quantum processor,cutting sampling cost by 90.1%.Notably,we find that dynamic adjustments of error levels via APPEC can enhance the ability to escape from local minima and reduce sampling costs.These results open promising avenues for executing VQAs with large-scale,low-noise quantum circuits,paving the way for practical quantum computing advancements.
基金supported by the Major Project for the Integration of ScienceEducation and Industry (Grant No.2025ZDZX02)。
文摘Classical computation of electronic properties in large-scale materials remains challenging.Quantum computation has the potential to offer advantages in memory footprint and computational scaling.However,general and viable quantum algorithms for simulating large-scale materials are still limited.We propose and implement random-state quantum algorithms to calculate electronic-structure properties of real materials.Using a random state circuit on a small number of qubits,we employ real-time evolution with first-order Trotter decomposition and Hadamard test to obtain electronic density of states,and we develop a modified quantum phase estimation algorithm to calculate real-space local density of states via direct quantum measurements.Furthermore,we validate these algorithms by numerically computing the density of states and spatial distributions of electronic states in graphene,twisted bilayer graphene quasicrystals,and fractal lattices,covering system sizes from hundreds to thousands of atoms.Our results manifest that the random-state quantum algorithms provide a general and qubit-efficient route to scalable simulations of electronic properties in large-scale periodic and aperiodic materials.
基金The national research foundation of Singapore(NRF-P2024-001).
文摘Variational quantum algorithms(VQAs)with random structures have poor trainability due to the exponentially vanishing gradient as the circuit depth and the qubit number increase.This result leads to a general belief that a deep circuit will not be feasible.In this work,we provide a viable solution to the vanishing gradient problem for deep VQAs with theoretical guarantees.Specifically,we prove that for quantum controlled-layer and quantum residual network(QResNet),architectures,the expectation of the gradient norm can be lower bounded by a value that is independent of the qubit number and the circuit depth.Our results follow from a careful analysis of the gradient behavior on parameter space consisting of rotation angles,as employed in almost all VQAs,instead of relying on impractical 2-design assumptions.We conduct several numerical experiments as verifications,where only our circuits are trainable and converge,while hardware-efficient and random circuits with similar number of parameters in comparison cannot converge.
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Project supported by the National Natural Science Foundation of China(Grant No.61573266)the Natural Science Basic Research Program of Shaanxi(Grant No.2021JM-133)the Fundamental Research Funds for the Central Universities and the Innovation Fund of Xidian University(Grant No.YJSJ25009)。
文摘Efficient implementation of fundamental matrix operations on quantum computers,such as matrix products and Hadamard operations,holds significant potential for accelerating machine learning algorithms.A critical prerequisite for quantum implementations is the effective encoding of classical data into quantum states.We propose two quantum computing frameworks for preparing the distinct encoded states corresponding to matrix operations,including the matrix product,matrix sum,matrix Hadamard product and division.Quantum algorithms based on the digital encoding computing framework are capable of implementing the matrix Hadamard operation with a time complexity of O(poly log(mn/ε))and the matrix product with a time complexity of O(poly log(mnl/ε)),achieving an exponential speedup in contrast to the classical methods of O(mn)and O(mnl).Quantum algorithms based on the analog-encoding framework are capable of implementing the matrix Hadamard operation with a time complexity of O(k_(1)√mn·poly log(mn/ε))and the matrix product with a time complexity of O(k_(2)√1·poly log(mnl/ε)),where k_(1)and k_(2)are coefficients correlated with the elements of the matrix,achieving a square speedup in contrast to the classical counterparts.As applications,we construct an oracle that can access the trace of a matrix within logarithmic time,and propose several algorithms to respectively estimate the trace of a matrix,the trace of the product of two matrices,and the trace inner product of two matrices within logarithmic time.
基金supported by the NSFC(Grant Nos.62176273,62271070,62441212)The Open Foundation of State Key Laboratory of Networking and Switching Technology(Beijing University of Posts and Telecommunications)under Grant SKLNST-2024-1-062025Major Project of the Natural Science Foundation of Inner Mongolia(2025ZD008).
文摘The Intrusion Detection System(IDS)is a security mechanism developed to observe network traffic and recognize suspicious or malicious activities.Clustering algorithms are often incorporated into IDS;however,conventional clustering-based methods face notable drawbacks,including poor scalability in handling high-dimensional datasets and a strong dependence of outcomes on initial conditions.To overcome the performance limitations of existing methods,this study proposes a novel quantum-inspired clustering algorithm that relies on a similarity coefficient-based quantum genetic algorithm(SC-QGA)and an improved quantum artificial bee colony algorithm hybrid K-means(IQABC-K).First,the SC-QGA algorithmis constructed based on quantum computing and integrates similarity coefficient theory to strengthen genetic diversity and feature extraction capabilities.For the subsequent clustering phase,the process based on the IQABC-K algorithm is enhanced with the core improvement of adaptive rotation gate and movement exploitation strategies to balance the exploration capabilities of global search and the exploitation capabilities of local search.Simultaneously,the acceleration of convergence toward the global optimum and a reduction in computational complexity are facilitated by means of the global optimum bootstrap strategy and a linear population reduction strategy.Through experimental evaluation with multiple algorithms and diverse performance metrics,the proposed algorithm confirms reliable accuracy on three datasets:KDD CUP99,NSL_KDD,and UNSW_NB15,achieving accuracy of 98.57%,98.81%,and 98.32%,respectively.These results affirm its potential as an effective solution for practical clustering applications.
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.
基金supported by the National Natural Science Foundation of China(Grant Nos.62102464,61772565)the Guangdong Basic and Applied Basic Research Foundation(Grant No.2020B1515020050)+1 种基金the Key Research and Development project of Guangdong Province(Grant No.2018B030325001)the China Postdoctoral Science Foundation(Grant Nos.2020M683049,2021T140761).
文摘Quantum algorithms are demonstrated to outperform classical algorithms for certain problems and thus are promising candidates for efficient information processing.Herein we aim to provide a brief and popular introduction to quantum algorithms for both the academic community and the general public with interest.We start from elucidating quantum parallelism,the basic framework of quantum algorithms and the difficulty of quantum algorithm design.Then we mainly focus on a historical overview of progress in quantum algorithm research over the past three to four decades.Finally,we clarify two common questions about the study of quantum algorithms,hoping to stimulate readers for further exploration.
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 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.
基金the National Natural Science Foundation of China(NSFC)(Grant No.61972050)the Open Foundation of StateKey Laboratory ofNetworking and Switching Technology(Beijing University of Posts and Telecommunications)(SKLNST-2020-2-16).
文摘The hardness of the integer factoring problem(IFP)plays a core role in the security of RSA-like cryptosystems that are widely used today.Besides Shor’s quantum algorithm that can solve IFP within polynomial time,quantum annealing algorithms(QAA)also manifest certain advantages in factoring integers.In experimental aspects,the reported integers that were successfully factored by using the D-wave QAA platform are much larger than those being factored by using Shor-like quantum algorithms.In this paper,we report some interesting observations about the effects of QAA for solving IFP.More specifically,we introduce a metric,called T-factor that measures the density of occupied qubits to some extent when conducting IFP tasks by using D-wave.We find that T-factor has obvious effects on annealing times for IFP:The larger of T-factor,the quicker of annealing speed.The explanation of this phenomenon is also given.
