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
When the Grover’s algorithm is applied to search an unordered database, the probability of success usually decreases with the increase of marked items. To address this phenomenon, a fixed-phase quantum search algorit...When the Grover’s algorithm is applied to search an unordered database, the probability of success usually decreases with the increase of marked items. To address this phenomenon, a fixed-phase quantum search algorithm with more flexible behavior is proposed. In proposed algorithm, the phase shifts can be fixed at the different values to meet the needs of different practical problems. If research requires a relatively rapid speed, the value of the phase shifts should be appropriately increased, if search requires a higher success probability, the value of the phase shifts should be appropriately decreased. When the phase shifts are fixed at , the success probability of at least 99.38% can be obtained in iterations.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
The current Grover quantum searching algorithm cannot identify the difference in importance of the search targets when it is applied to an unsorted quantum database, and the probability for each search target is equal...The current Grover quantum searching algorithm cannot identify the difference in importance of the search targets when it is applied to an unsorted quantum database, and the probability for each search target is equal. To solve this problem, a Grover searching algorithm based on weighted targets is proposed. First, each target is endowed a weight coefficient according to its importance. Applying these different weight coefficients, the targets are represented as quantum superposition states. Second, the novel Grover searching algorithm based on the quantum superposition of the weighted targets is constructed. Using this algorithm, the probability of getting each target can be approximated to the corresponding weight coefficient, which shows the flexibility of this algorithm. Finally, the validity of the algorithm is proved by a simple searching example.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
Despite the rapid development of quantum research in recent years,there is very little research in computational geometry.In this paper,to achieve the convex hull of a point set in a quantum system,a quantum convex hu...Despite the rapid development of quantum research in recent years,there is very little research in computational geometry.In this paper,to achieve the convex hull of a point set in a quantum system,a quantum convex hull algorithm based on the quantum maximum or minimum searching algorithm(QUSSMA)is proposed.Firstly,the novel enhanced quantum representation of digital images is employed to represent a group of point set,and then the QUSSMA algorithm and vector operation are used to search the convex hull of the point set.In addition,the algorithm is simulated and compared with the classical algorithm.It is concluded that the quantum algorithm accelerates the classical algorithm when the Mpvalue of the convex hull point is under a certain condition.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)(C^(d-j)_(n-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
Shenvi et al.have proposed a quantum algorithm based on quantum walking called Shenvi-Kempe-Whaley(SKW)algorithm,but this search algorithm can only search one target state and use a specific search target state vector...Shenvi et al.have proposed a quantum algorithm based on quantum walking called Shenvi-Kempe-Whaley(SKW)algorithm,but this search algorithm can only search one target state and use a specific search target state vector.Therefore,when there are more than two target nodes in the search space,the algorithm has certain limitations.Even though a multiobjective SKW search algorithm was proposed later,when the number of target nodes is more than two,the SKW search algorithm cannot be mapped to the same quotient graph.In addition,the calculation of the optimal target state depends on the number of target states m.In previous studies,quantum computing and testing algorithms were used to solve this problem.But these solutions require more Oracle calls and cannot get a high accuracy rate.Therefore,to solve the above problems,we improve the multi-target quantum walk search algorithm,and construct a controllable quantum walk search algorithm under the condition of unknown number of target states.By dividing the Hilbert space into multiple subspaces,the accuracy of the search algorithm is improved from p_(c)=(1/2)-O(1/n)to p_(c)=1-O(1/n).And by adding detection gate phase,the algorithm can stop when the amplitude of the target state becomes the maximum for the first time,and the algorithm can always maintain the optimal number of iterations,so as to reduce the number of unnecessary iterations in the algorithm process and make the number of iterations reach t_(f)=(π/2)(?).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
We investigate the correlations between two qubits in the Grover search algorithm with arbitrary initial states by numerical simulation.Using a set of suitable bases,we construct the reduced density matrix and give th...We investigate the correlations between two qubits in the Grover search algorithm with arbitrary initial states by numerical simulation.Using a set of suitable bases,we construct the reduced density matrix and give the numerical expression of correlations relating to the iterations.For different initial states,we obtain the concurrence and quantum discord compared with the success probability in the algorithm.The results show that the initial states affect the correlations and the limit point of the correlations in the searching process.However,the initial states do not influence the whole cyclical trend.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
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
When the Grover＇ s original algorithm is applied to search an unordered database, the success probability decreases rapidly with the increase of marked items. Aiming at this problem, a general quantum search algorith...When the Grover＇ s original algorithm is applied to search an unordered database, the success probability decreases rapidly with the increase of marked items. Aiming at this problem, a general quantum search algorithm with small phase rotations is proposed. Several quantum search algorithms can be derived from this algorithm according to different phase rotations. When the size of phase rotations are fixed at 0. 01π, the success probability of at least 99. 99% can be obtained in 0（√N/M） iterations.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
Continuous search problems(CSPs),which involve finding solutions within a continuous domain,frequently arise in fields such as optimization,physics,and engineering.Unlike discrete search problems,CSPs require navigati...Continuous search problems(CSPs),which involve finding solutions within a continuous domain,frequently arise in fields such as optimization,physics,and engineering.Unlike discrete search problems,CSPs require navigating an uncountably infinite space,presenting unique computational challenges.In this work,we propose a fixed-point quantum search algorithm that leverages continuous variables to address these challenges,achieving a quadratic speedup.Inspired by the discrete search results,we manage to establish a lower bound on the query complexity of arbitrary quantum search for CSPs,demonstrating the optimality of our approach.In addition,we demonstrate how to design the internal structure of the quantum search oracle for specific problems.Furthermore,we develop a general framework to apply this algorithm to a range of problem types,including optimization and eigenvalue problems involving continuous variables.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
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
Two schemes for the implementation of the two-qubit Grover search algorithm in the ion trap system are proposed. These schemes might be experimentally realizable with presently available techniques. The experimental i...Two schemes for the implementation of the two-qubit Grover search algorithm in the ion trap system are proposed. These schemes might be experimentally realizable with presently available techniques. The experimental implementation of the schemes would be an important step toward more complex quantum computation in the ion trap system.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
Quantum coherence plays a central role in Grover’s search algorithm.We study the Tsallis relative a entropy of coherence dynamics of the evolved state in Grover’s search algorithm.We prove that the Tsallis relative ...Quantum coherence plays a central role in Grover’s search algorithm.We study the Tsallis relative a entropy of coherence dynamics of the evolved state in Grover’s search algorithm.We prove that the Tsallis relative a entropy of coherence decreases with the increase of the success probability,and derive the complementarity relations between the coherence and the success probability.We show that the operator coherence of the first H■relies on the size of the database N,the success probability and the target states.Moreover,we illustrate the relationships between coherence and entanglement of the superposition state of targets,as well as the production and deletion of coherence in Grover iterations.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
文摘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.
文摘When the Grover’s algorithm is applied to search an unordered database, the probability of success usually decreases with the increase of marked items. To address this phenomenon, a fixed-phase quantum search algorithm with more flexible behavior is proposed. In proposed algorithm, the phase shifts can be fixed at the different values to meet the needs of different practical problems. If research requires a relatively rapid speed, the value of the phase shifts should be appropriately increased, if search requires a higher success probability, the value of the phase shifts should be appropriately decreased. When the phase shifts are fixed at , the success probability of at least 99.38% can be obtained in iterations.
基金supported by the National Basic Research Program of China(Grant No.2013CB338002)
文摘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the National Natural Science Foundation of China (60773065).
文摘The current Grover quantum searching algorithm cannot identify the difference in importance of the search targets when it is applied to an unsorted quantum database, and the probability for each search target is equal. To solve this problem, a Grover searching algorithm based on weighted targets is proposed. First, each target is endowed a weight coefficient according to its importance. Applying these different weight coefficients, the targets are represented as quantum superposition states. Second, the novel Grover searching algorithm based on the quantum superposition of the weighted targets is constructed. Using this algorithm, the probability of getting each target can be approximated to the corresponding weight coefficient, which shows the flexibility of this algorithm. Finally, the validity of the algorithm is proved by a simple searching example.
基金supported by the National Basic Research Program of China(Grant No.2013CB338002)
文摘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 Shanghai Science and Technology Project in 2020 under Grant No.20040501500。
文摘Despite the rapid development of quantum research in recent years,there is very little research in computational geometry.In this paper,to achieve the convex hull of a point set in a quantum system,a quantum convex hull algorithm based on the quantum maximum or minimum searching algorithm(QUSSMA)is proposed.Firstly,the novel enhanced quantum representation of digital images is employed to represent a group of point set,and then the QUSSMA algorithm and vector operation are used to search the convex hull of the point set.In addition,the algorithm is simulated and compared with the classical algorithm.It is concluded that the quantum algorithm accelerates the classical algorithm when the Mpvalue of the convex hull point is under a certain condition.
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
文摘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)(C^(d-j)_(n-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Project supported by the National Natural Science Foundation of China(Grant Nos.11975132 and 61772295)the Natural Science Foundation of Shandong Province,China(Grant No.ZR2019YQ01)the Project of Shandong Provincial Higher Educational Science and Technology Program,China(Grant No.J18KZ012)。
文摘Shenvi et al.have proposed a quantum algorithm based on quantum walking called Shenvi-Kempe-Whaley(SKW)algorithm,but this search algorithm can only search one target state and use a specific search target state vector.Therefore,when there are more than two target nodes in the search space,the algorithm has certain limitations.Even though a multiobjective SKW search algorithm was proposed later,when the number of target nodes is more than two,the SKW search algorithm cannot be mapped to the same quotient graph.In addition,the calculation of the optimal target state depends on the number of target states m.In previous studies,quantum computing and testing algorithms were used to solve this problem.But these solutions require more Oracle calls and cannot get a high accuracy rate.Therefore,to solve the above problems,we improve the multi-target quantum walk search algorithm,and construct a controllable quantum walk search algorithm under the condition of unknown number of target states.By dividing the Hilbert space into multiple subspaces,the accuracy of the search algorithm is improved from p_(c)=(1/2)-O(1/n)to p_(c)=1-O(1/n).And by adding detection gate phase,the algorithm can stop when the amplitude of the target state becomes the maximum for the first time,and the algorithm can always maintain the optimal number of iterations,so as to reduce the number of unnecessary iterations in the algorithm process and make the number of iterations reach t_(f)=(π/2)(?).
基金Supported by the National High Technology Research and Development Program(No.2011AA010803)the National Natural Science Foundation of China(No.U1204602)
文摘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Project supported by the National Natural Science Foundation of China(Grant Nos.11975132 and 61772295)the Natural Science Foundation of Shandong Province,China(Grant No.ZR2019YQ01)Shandong Province Higher Educational Science and Technology Program,China(Grant No.J18KZ012).
文摘We investigate the correlations between two qubits in the Grover search algorithm with arbitrary initial states by numerical simulation.Using a set of suitable bases,we construct the reduced density matrix and give the numerical expression of correlations relating to the iterations.For different initial states,we obtain the concurrence and quantum discord compared with the success probability in the algorithm.The results show that the initial states affect the correlations and the limit point of the correlations in the searching process.However,the initial states do not influence the whole cyclical trend.
基金Project supported by the National Basic Research Program of China(Grant No.2013CB338002)
文摘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)
文摘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
基金Supported by National Natural Science Foundation of China （ No. 60773065 ）.
文摘When the Grover＇ s original algorithm is applied to search an unordered database, the success probability decreases rapidly with the increase of marked items. Aiming at this problem, a general quantum search algorithm with small phase rotations is proposed. Several quantum search algorithms can be derived from this algorithm according to different phase rotations. When the size of phase rotations are fixed at 0. 01π, the success probability of at least 99. 99% can be obtained in 0（√N/M） iterations.
文摘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 Natural Science Foundation of China(Grant Nos.92265208,11925404,92165209,92365301,and 92265210)the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0300200).
文摘Continuous search problems(CSPs),which involve finding solutions within a continuous domain,frequently arise in fields such as optimization,physics,and engineering.Unlike discrete search problems,CSPs require navigating an uncountably infinite space,presenting unique computational challenges.In this work,we propose a fixed-point quantum search algorithm that leverages continuous variables to address these challenges,achieving a quadratic speedup.Inspired by the discrete search results,we manage to establish a lower bound on the query complexity of arbitrary quantum search for CSPs,demonstrating the optimality of our approach.In addition,we demonstrate how to design the internal structure of the quantum search oracle for specific problems.Furthermore,we develop a general framework to apply this algorithm to a range of problem types,including optimization and eigenvalue problems involving continuous variables.
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
文摘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.
文摘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Project supported by Fok Ying Tung Education Foundation （Grant No 81008）, the National Natural Science Foundation of China （Grant Nos 60008003 and 10225421）, and Funds from Fuzhou University, China.
文摘Two schemes for the implementation of the two-qubit Grover search algorithm in the ion trap system are proposed. These schemes might be experimentally realizable with presently available techniques. The experimental implementation of the schemes would be an important step toward more complex quantum computation in the ion trap system.
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)
文摘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 Natural Science Foundation of China(Grant Nos.12161056,12075159,12171044)Beijing Natural Science Foundation(Grant No.Z190005)the Academician Innovation Platform of Hainan Province。
文摘Quantum coherence plays a central role in Grover’s search algorithm.We study the Tsallis relative a entropy of coherence dynamics of the evolved state in Grover’s search algorithm.We prove that the Tsallis relative a entropy of coherence decreases with the increase of the success probability,and derive the complementarity relations between the coherence and the success probability.We show that the operator coherence of the first H■relies on the size of the database N,the success probability and the target states.Moreover,we illustrate the relationships between coherence and entanglement of the superposition state of targets,as well as the production and deletion of coherence in Grover iterations.
