Quantum cryptography and quantum search algorithm are considered as two important research topics in quantum information science.An asymmetrical quantum encryption protocol based on the properties of quantum one-way f...Quantum cryptography and quantum search algorithm are considered as two important research topics in quantum information science.An asymmetrical quantum encryption protocol based on the properties of quantum one-way function and quantum search algorithm is proposed.Depending on the no-cloning theorem and trapdoor one-way functions of the publickey,the eavesdropper cannot extract any private-information from the public-keys and the ciphertext.Introducing key-generation randomized logarithm to improve security of our proposed protocol,i.e.,one privatekey corresponds to an exponential number of public-keys.Using unitary operations and the single photon measurement,secret messages can be directly sent from the sender to the receiver.The security of the proposed protocol is proved that it is informationtheoretically secure.Furthermore,compared the symmetrical Quantum key distribution,the proposed protocol is not only efficient to reduce additional communication,but also easier to carry out in practice,because no entangled photons and complex operations are required.展开更多
We apply the transitionless driving on the local adiabatic quantum search algorithm to speed up the adiabatic process. By studying quantum dynamics of the adiabatic search algorithm with the equivalent two-level syste...We apply the transitionless driving on the local adiabatic quantum search algorithm to speed up the adiabatic process. By studying quantum dynamics of the adiabatic search algorithm with the equivalent two-level system, we derive the transi- tionless driving Hamiltonian for the local adiabatic quantum search algorithm. We found that when adding a transitionless quantum driving term Ht~ (t) on the local adiabatic quantum search algorithm, the success rate is 1 exactly with arbitrary evolution time by solving the time-dependent Schr6dinger equation in eigen-picture. Moreover, we show the reason for the drastic decrease of the evolution time is that the driving Hamiltonian increases the lowest eigenvalues to a maximum of展开更多
The paper“Fixed-point quantum continuous search algorithm with optimal query complexity”[1]presents another interesting application of quantum search algorithms by addressing one of the long-standing challenges in q...The paper“Fixed-point quantum continuous search algorithm with optimal query complexity”[1]presents another interesting application of quantum search algorithms by addressing one of the long-standing challenges in quantum computing:how to efficiently perform search over continuous domains.While Grover’s algorithm has been a cornerstone in discrete quantum search with its well-known quadratic speedup[2],many real-world problems—ranging from high-dimensional optimization to spectral analysis of infinite dimensional operators—require searching over continuous,uncountably infinite solution spaces.展开更多
This study investigates the multi-solution search of the optimized quantum random-walk search algorithm on the hypercube. Through generalizing the abstract search algorithm which is a general tool for analyzing the se...This study investigates the multi-solution search of the optimized quantum random-walk search algorithm on the hypercube. Through generalizing the abstract search algorithm which is a general tool for analyzing the search on the graph to the multi-solution case, it can be applied to analyze the multi-solution case of quantum random-walk search on the graph directly. Thus, the computational complexity of the optimized quantum random-walk search algorithm for the multi-solution search is obtained. Through numerical simulations and analysis, we obtain a critical value of the proportion of solutions q. For a given q, we derive the relationship between the success rate of the algorithm and the number of iterations when q is no longer than the critical value.展开更多
Similar to the classical meet-in-the-middle algorithm,the storage and computation complexity are the key factors that decide the efficiency of the quantum meet-in-the-middle algorithm.Aiming at the target vector of fi...Similar to the classical meet-in-the-middle algorithm,the storage and computation complexity are the key factors that decide the efficiency of the quantum meet-in-the-middle algorithm.Aiming at the target vector of fixed weight,based on the quantum meet-in-the-middle algorithm,the algorithm for searching all n-product vectors with the same weight is presented,whose complexity is better than the exhaustive search algorithm.And the algorithm can reduce the storage complexity of the quantum meet-in-the-middle search algorithm.Then based on the algorithm and the knapsack vector of the Chor-Rivest public-key crypto of fixed weight d,we present a general quantum meet-in-th√e-middle search algorithm based on the target solution of fixed weight,whose computational complexity is∑(d to j=0)(O((1/2)(Cd-jn-k+1)+O(C^j_klog C^j_k))with∑(d to i=0)C^i_k memory cost.And the optimal value of k is given.Compared to thequantum meet-in-the-middle search algorithm for knapsack problem and the quantum algorithm for searching a target solution of fixed weight,the computational complexity of the algorithm is lower.And its storage complexity is smaller than the quantum meet-in-the-middle-algorithm.展开更多
The success probability of searching an objective item from an unsorted database using standard Grover's algorithm is usually not exactly 1. It is exactly 1 only when it is used to find the target state from a dat...The success probability of searching an objective item from an unsorted database using standard Grover's algorithm is usually not exactly 1. It is exactly 1 only when it is used to find the target state from a database with four items. Exact search is always important in theoretical and practical applications. The failure rate of Grover's algorithm becomes big when the database is small, and this hinders the use of the commonly used divide-and-verify strategy. Even for large database, the failure rate becomes considerably large when there are many marked items. This has put a serious limitation on the usability of the Grover's algorithm. An important improved version of the Grover's algorithm, also known as the improved Grover algorithm, solves this problem. The improved Grover algorithm searches arbitrary number of target states from an unsorted database with full success rate. Here, we give the first experimental realization of the improved Grover algorithm, which finds a marked state with certainty, in a nuclear magnetic resonance system. The optimal control theory is used to obtain an optimized control sequence. The experimental results agree well with the theoretical predictions.展开更多
In this work, we demonstrated a fixed-point quantum search algorithm in the nuclear magnetic resonance (NMR) system. We constructed the pulse sequences for the pivotal operations in the quantum search protocol. The ex...In this work, we demonstrated a fixed-point quantum search algorithm in the nuclear magnetic resonance (NMR) system. We constructed the pulse sequences for the pivotal operations in the quantum search protocol. The experimental results agree well with the theoretical predictions. The generalization of the scheme to the arbitrary number of qubits has also been given.展开更多
This study investigates the effects of systematic errors in phase inversions on the success rate and number of iterations in the optimized quantum random-walk search algorithm. Using the geometric description of this ...This study investigates the effects of systematic errors in phase inversions on the success rate and number of iterations in the optimized quantum random-walk search algorithm. Using the geometric description of this algorithm, a model of the algorithm with phase errors is established, and the relationship between the success rate of the algorithm, the database size, the number of iterations, and the phase error is determined. For a given database size, we obtain both the maximum success rate of the algorithm and the required number of iterations when phase errors are present in the algorithm. Analyses and numerical simulations show that the optimized quantum random-walk search algorithm is more robust against phase errors than Grover's algorithm.展开更多
This paper investigates the effects of decoherence generated by broken-link-type noise in the hypercube on an optimized quantum random-walk search algorithm. When the hypercube occurs with random broken links, the opt...This paper investigates the effects of decoherence generated by broken-link-type noise in the hypercube on an optimized quantum random-walk search algorithm. When the hypercube occurs with random broken links, the optimized quantum random-walk search algorithm with decoherence is depicted through defining the shift operator which includes the possibility of broken links. For a given database size, we obtain the maximum success rate of the algorithm and the required number of iterations through numerical simulations and analysis when the algorithm is in the presence of decoherence. Then the computational complexity of the algorithm with decoherence is obtained. The results show that the ultimate effect of broken-link-type decoherence on the optimized quantum random-walk search algorithm is negative.展开更多
In order to improve the attack efficiency of the New FORK-256 function, an algorithm based on Grover's quantum search algorithm and birthday attack is proposed. In this algorithm, finding a collision for arbitrary...In order to improve the attack efficiency of the New FORK-256 function, an algorithm based on Grover's quantum search algorithm and birthday attack is proposed. In this algorithm, finding a collision for arbitrary hash function only needs O(2m/3) expected evaluations, where m is the size of hash space value. It is proved that the algorithm can obviously improve the attack efficiency for only needing O(2 74.7) expected evaluations, and this is more efficient than any known classical algorithm, and the consumed space of the algorithm equals the evaluation.展开更多
In this paper we present a classical parallel quantum algorithm for the satisfiability problem. We have exploited the classical parallelism of quantum algorithms developed in [G.L. Long and L. Xiao, Phys. Rev. A 69 (...In this paper we present a classical parallel quantum algorithm for the satisfiability problem. We have exploited the classical parallelism of quantum algorithms developed in [G.L. Long and L. Xiao, Phys. Rev. A 69 (2004) 052303], so that additional acceleration can be gained by using classical parallelism. The quantum algorithm first estimates the number of solutions using the quantum counting algorithm, and then by using the quantum searching algorithm, the explicit solutions are found.展开更多
This paper proposes a scheme for implementing the adiabatic quantum search algorithm of different marked items in an unsorted list of N items with atoms in a cavity driven by lasers. N identical three-level atoms are ...This paper proposes a scheme for implementing the adiabatic quantum search algorithm of different marked items in an unsorted list of N items with atoms in a cavity driven by lasers. N identical three-level atoms are trapped in a single-mode cavity. Each atom is driven by a set of three pulsed laser fields. In each atom, the same level represents a database entry. Two of the atoms are marked differently. The marked atom has an energy gap between its two ground states. The two different marked states can be sought out respectively starting from an initial entangled state by controlling the ratio of three pulse amplitudes. Moreover, the mechanism, based on adiabatic passage, constitutes a decoherence-free method in the sense that spontaneous emission and cavity damping are avoided since the dynamics follows the dark state. Furthermore, this paper extends the algorithm with m(m〉2) atoms marked in an ideal situation. Any different marked state can be sought out.展开更多
Studies have demonstrated that a joined complete graph is a typical mathematical model that can support a fast quantum search. In this paper, we study the implementation of joined complete graphs in atomic systems and...Studies have demonstrated that a joined complete graph is a typical mathematical model that can support a fast quantum search. In this paper, we study the implementation of joined complete graphs in atomic systems and realize a quantum search of runtime ■ based on this implementation with a success probability of 50%. Even though the practical systems inevitably interact with the surrounding environment, we reveal that a successful quantum search can be realized through delicately engineering the environment itself. We consider that our study will bring about a feasible way to realize quantum information processing including quantum algorithms in reality.展开更多
Maximum frequent pattern generation from a large database of transactions and items for association rule mining is an important research topic in data mining. Association rule mining aims to discover interesting corre...Maximum frequent pattern generation from a large database of transactions and items for association rule mining is an important research topic in data mining. Association rule mining aims to discover interesting correlations, frequent patterns, associations, or causal structures between items hidden in a large database. By exploiting quantum computing, we propose an efficient quantum search algorithm design to discover the maximum frequent patterns. We modified Grover’s search algorithm so that a subspace of arbitrary symmetric states is used instead of the whole search space. We presented a novel quantum oracle design that employs a quantum counter to count the maximum frequent items and a quantum comparator to check with a minimum support threshold. The proposed derived algorithm increases the rate of the correct solutions since the search is only in a subspace. Furthermore, our algorithm significantly scales and optimizes the required number of qubits in design, which directly reflected positively on the performance. Our proposed design can accommodate more transactions and items and still have a good performance with a small number of qubits.展开更多
The multi-class classification of images is a pivotal challenge within the realm of image processing.As the volume of visual data continues to expand,there is a burgeoning interest in harnessing the unique capabilitie...The multi-class classification of images is a pivotal challenge within the realm of image processing.As the volume of visual data continues to expand,there is a burgeoning interest in harnessing the unique capabilities of quantum computation to augment the efficiency of classification tasks.However,many existing methods for training quantum image multi-classifiers parallel classical machine learning techniques,where the requisite circuit measurements increase linearly with the volume of training data.This work introduces a novel approach for training a quantum image multi-classifier based on the quantum search algorithm.We have meticulously conducted rigorous experiments on a handwritten digit dataset,a classic benchmark in the field.The results have been meticulously compared with previous works,and the comparative analysis not only validates the efficiency of our proposed approach,requiring only O(N/b)measurements during training,but also highlights a significant quadratic speedup of the algorithm.展开更多
基金This work was supported in part by the program for Innovation Team Building at Institutions of Higher Education in Chongqing under Grant No.KJTD201310,the Scientific and Technological Research Program of Chongqing Municipal Education Commission of China under Grant KJ120513,Natural Science Foundation Project of CQ CSTC of P.R.China under Grant No.cstc2011jjA40031
摘要Quantum cryptography and quantum search algorithm are considered as two important research topics in quantum information science.An asymmetrical quantum encryption protocol based on the properties of quantum one-way function and quantum search algorithm is proposed.Depending on the no-cloning theorem and trapdoor one-way functions of the publickey,the eavesdropper cannot extract any private-information from the public-keys and the ciphertext.Introducing key-generation randomized logarithm to improve security of our proposed protocol,i.e.,one privatekey corresponds to an exponential number of public-keys.Using unitary operations and the single photon measurement,secret messages can be directly sent from the sender to the receiver.The security of the proposed protocol is proved that it is informationtheoretically secure.Furthermore,compared the symmetrical Quantum key distribution,the proposed protocol is not only efficient to reduce additional communication,but also easier to carry out in practice,because no entangled photons and complex operations are required.
基金Project supported by the National Basic Research Program of China(Grant No.2013CB338002)the National Natural Science Foundation of China(Grant Nos.11504430 and 61502526)
摘要We apply the transitionless driving on the local adiabatic quantum search algorithm to speed up the adiabatic process. By studying quantum dynamics of the adiabatic search algorithm with the equivalent two-level system, we derive the transi- tionless driving Hamiltonian for the local adiabatic quantum search algorithm. We found that when adding a transitionless quantum driving term Ht~ (t) on the local adiabatic quantum search algorithm, the success rate is 1 exactly with arbitrary evolution time by solving the time-dependent Schr6dinger equation in eigen-picture. Moreover, we show the reason for the drastic decrease of the evolution time is that the driving Hamiltonian increases the lowest eigenvalues to a maximum of
摘要The paper“Fixed-point quantum continuous search algorithm with optimal query complexity”[1]presents another interesting application of quantum search algorithms by addressing one of the long-standing challenges in quantum computing:how to efficiently perform search over continuous domains.While Grover’s algorithm has been a cornerstone in discrete quantum search with its well-known quadratic speedup[2],many real-world problems—ranging from high-dimensional optimization to spectral analysis of infinite dimensional operators—require searching over continuous,uncountably infinite solution spaces.
基金supported by the National Basic Research Program of China(Grant No.2013CB338002)
摘要This study investigates the multi-solution search of the optimized quantum random-walk search algorithm on the hypercube. Through generalizing the abstract search algorithm which is a general tool for analyzing the search on the graph to the multi-solution case, it can be applied to analyze the multi-solution case of quantum random-walk search on the graph directly. Thus, the computational complexity of the optimized quantum random-walk search algorithm for the multi-solution search is obtained. Through numerical simulations and analysis, we obtain a critical value of the proportion of solutions q. For a given q, we derive the relationship between the success rate of the algorithm and the number of iterations when q is no longer than the critical value.
基金Supported by the National Basic Research Program of China under Grant No.2013CB338002the National Natural Science Foundation of China under Grant No.61502526
摘要Similar to the classical meet-in-the-middle algorithm,the storage and computation complexity are the key factors that decide the efficiency of the quantum meet-in-the-middle algorithm.Aiming at the target vector of fixed weight,based on the quantum meet-in-the-middle algorithm,the algorithm for searching all n-product vectors with the same weight is presented,whose complexity is better than the exhaustive search algorithm.And the algorithm can reduce the storage complexity of the quantum meet-in-the-middle search algorithm.Then based on the algorithm and the knapsack vector of the Chor-Rivest public-key crypto of fixed weight d,we present a general quantum meet-in-th√e-middle search algorithm based on the target solution of fixed weight,whose computational complexity is∑(d to j=0)(O((1/2)(Cd-jn-k+1)+O(C^j_klog C^j_k))with∑(d to i=0)C^i_k memory cost.And the optimal value of k is given.Compared to thequantum meet-in-the-middle search algorithm for knapsack problem and the quantum algorithm for searching a target solution of fixed weight,the computational complexity of the algorithm is lower.And its storage complexity is smaller than the quantum meet-in-the-middle-algorithm.
基金supported by the National Natural Science Foundation of China(Grant Nos.11175094 and 91221205)the National Basic Research Program of China(Grant No.2011CB9216002)the Fund of State Key Laboratory of Intense Pulsed Radiation Simulation and Effect
摘要The success probability of searching an objective item from an unsorted database using standard Grover's algorithm is usually not exactly 1. It is exactly 1 only when it is used to find the target state from a database with four items. Exact search is always important in theoretical and practical applications. The failure rate of Grover's algorithm becomes big when the database is small, and this hinders the use of the commonly used divide-and-verify strategy. Even for large database, the failure rate becomes considerably large when there are many marked items. This has put a serious limitation on the usability of the Grover's algorithm. An important improved version of the Grover's algorithm, also known as the improved Grover algorithm, solves this problem. The improved Grover algorithm searches arbitrary number of target states from an unsorted database with full success rate. Here, we give the first experimental realization of the improved Grover algorithm, which finds a marked state with certainty, in a nuclear magnetic resonance system. The optimal control theory is used to obtain an optimized control sequence. The experimental results agree well with the theoretical predictions.
基金supported by the SRFPD Program of Education Ministry ofChina (Grant No. 20090002110064)the National Natural Science Foundation of China (Grant No. 10874098)the National Basic Research Program of China (Grant Nos. 2009CB929402 and 2011CB921602)
摘要In this work, we demonstrated a fixed-point quantum search algorithm in the nuclear magnetic resonance (NMR) system. We constructed the pulse sequences for the pivotal operations in the quantum search protocol. The experimental results agree well with the theoretical predictions. The generalization of the scheme to the arbitrary number of qubits has also been given.
基金Project supported by the National Basic Research Program of China(Grant No.2013CB338002)
摘要This study investigates the effects of systematic errors in phase inversions on the success rate and number of iterations in the optimized quantum random-walk search algorithm. Using the geometric description of this algorithm, a model of the algorithm with phase errors is established, and the relationship between the success rate of the algorithm, the database size, the number of iterations, and the phase error is determined. For a given database size, we obtain both the maximum success rate of the algorithm and the required number of iterations when phase errors are present in the algorithm. Analyses and numerical simulations show that the optimized quantum random-walk search algorithm is more robust against phase errors than Grover's algorithm.
基金supported by the National Basic Research Program of China(Grant No.2013CB338002)
摘要This paper investigates the effects of decoherence generated by broken-link-type noise in the hypercube on an optimized quantum random-walk search algorithm. When the hypercube occurs with random broken links, the optimized quantum random-walk search algorithm with decoherence is depicted through defining the shift operator which includes the possibility of broken links. For a given database size, we obtain the maximum success rate of the algorithm and the required number of iterations through numerical simulations and analysis when the algorithm is in the presence of decoherence. Then the computational complexity of the algorithm with decoherence is obtained. The results show that the ultimate effect of broken-link-type decoherence on the optimized quantum random-walk search algorithm is negative.
基金Supported by the National High Technology Research and Development Program(No.2011AA010803)the National Natural Science Foundation of China(No.U1204602)
摘要In order to improve the attack efficiency of the New FORK-256 function, an algorithm based on Grover's quantum search algorithm and birthday attack is proposed. In this algorithm, finding a collision for arbitrary hash function only needs O(2m/3) expected evaluations, where m is the size of hash space value. It is proved that the algorithm can obviously improve the attack efficiency for only needing O(2 74.7) expected evaluations, and this is more efficient than any known classical algorithm, and the consumed space of the algorithm equals the evaluation.
基金supported by 973 Program under Grant No.2006CB921106National Natural Science Foundation of China under Grant No.60635040the Key Grant Project of the Ministry of Education under Grant No.306020
摘要In this paper we present a classical parallel quantum algorithm for the satisfiability problem. We have exploited the classical parallelism of quantum algorithms developed in [G.L. Long and L. Xiao, Phys. Rev. A 69 (2004) 052303], so that additional acceleration can be gained by using classical parallelism. The quantum algorithm first estimates the number of solutions using the quantum counting algorithm, and then by using the quantum searching algorithm, the explicit solutions are found.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10574022 and 10575022)the Funds of Educational Committee of Fujian Province,China (Grant No JB07043)
摘要This paper proposes a scheme for implementing the adiabatic quantum search algorithm of different marked items in an unsorted list of N items with atoms in a cavity driven by lasers. N identical three-level atoms are trapped in a single-mode cavity. Each atom is driven by a set of three pulsed laser fields. In each atom, the same level represents a database entry. Two of the atoms are marked differently. The marked atom has an energy gap between its two ground states. The two different marked states can be sought out respectively starting from an initial entangled state by controlling the ratio of three pulse amplitudes. Moreover, the mechanism, based on adiabatic passage, constitutes a decoherence-free method in the sense that spontaneous emission and cavity damping are avoided since the dynamics follows the dark state. Furthermore, this paper extends the algorithm with m(m〉2) atoms marked in an ideal situation. Any different marked state can be sought out.
基金supported by the National Key R&D Program of China(Grant No.2017YFA0303800)the National Natural Science Foundation of China(Grant Nos.11604014 and 11974046)。
摘要Studies have demonstrated that a joined complete graph is a typical mathematical model that can support a fast quantum search. In this paper, we study the implementation of joined complete graphs in atomic systems and realize a quantum search of runtime ■ based on this implementation with a success probability of 50%. Even though the practical systems inevitably interact with the surrounding environment, we reveal that a successful quantum search can be realized through delicately engineering the environment itself. We consider that our study will bring about a feasible way to realize quantum information processing including quantum algorithms in reality.
摘要Maximum frequent pattern generation from a large database of transactions and items for association rule mining is an important research topic in data mining. Association rule mining aims to discover interesting correlations, frequent patterns, associations, or causal structures between items hidden in a large database. By exploiting quantum computing, we propose an efficient quantum search algorithm design to discover the maximum frequent patterns. We modified Grover’s search algorithm so that a subspace of arbitrary symmetric states is used instead of the whole search space. We presented a novel quantum oracle design that employs a quantum counter to count the maximum frequent items and a quantum comparator to check with a minimum support threshold. The proposed derived algorithm increases the rate of the correct solutions since the search is only in a subspace. Furthermore, our algorithm significantly scales and optimizes the required number of qubits in design, which directly reflected positively on the performance. Our proposed design can accommodate more transactions and items and still have a good performance with a small number of qubits.
基金the support from the National Natural Science Foundation of China(Grant Nos.62131002,62305028,and 62071448)the Fundamental Research Funds for the Central Universities(BNU)。
摘要The multi-class classification of images is a pivotal challenge within the realm of image processing.As the volume of visual data continues to expand,there is a burgeoning interest in harnessing the unique capabilities of quantum computation to augment the efficiency of classification tasks.However,many existing methods for training quantum image multi-classifiers parallel classical machine learning techniques,where the requisite circuit measurements increase linearly with the volume of training data.This work introduces a novel approach for training a quantum image multi-classifier based on the quantum search algorithm.We have meticulously conducted rigorous experiments on a handwritten digit dataset,a classic benchmark in the field.The results have been meticulously compared with previous works,and the comparative analysis not only validates the efficiency of our proposed approach,requiring only O(N/b)measurements during training,but also highlights a significant quadratic speedup of the algorithm.