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
With the rapid advancement of quantum computing,hybrid quantum–classical machine learning has shown numerous potential applications at the current stage,with expectations of being achievable in the noisy intermediate...With the rapid advancement of quantum computing,hybrid quantum–classical machine learning has shown numerous potential applications at the current stage,with expectations of being achievable in the noisy intermediate-scale quantum(NISQ)era.Quantum reinforcement learning,as an indispensable study,has recently demonstrated its ability to solve standard benchmark environments with formally provable theoretical advantages over classical counterparts.However,despite the progress of quantum processors and the emergence of quantum computing clouds,implementing quantum reinforcement learning algorithms utilizing parameterized quantum circuits(PQCs)on NISQ devices remains infrequent.In this work,we take the first step towards executing benchmark quantum reinforcement problems on real devices equipped with at most 136 qubits on the BAQIS Quafu quantum computing cloud.The experimental results demonstrate that the policy agents can successfully accomplish objectives under modified conditions in both the training and inference phases.Moreover,we design hardware-efficient PQC architectures in the quantum model using a multi-objective evolutionary algorithm and develop a learning algorithm that is adaptable to quantum devices.We hope that the Quafu-RL can be a guiding example to show how to realize machine learning tasks by taking advantage of quantum computers on the quantum cloud platform.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
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
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
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 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
We show that the Farhi-Gutmann analog quantum search is a singular algorithm in the following sense: when the original driving Hamiltonian is perturbed slightly such that it is made of projections to the starting stat...We show that the Farhi-Gutmann analog quantum search is a singular algorithm in the following sense: when the original driving Hamiltonian is perturbed slightly such that it is made of projections to the starting state and to the target state with different energies,the maximum fidelity(transition probability)between the searching state and the target state is strictly less than 1 over the entire evolution period,and the first time to achieve this maximum fidelity is of order N~(1/2)/(1+cN)~(1/2),whose behavior depends crucially on whether c=0 or not(here N is the total number of items,and the original Farhi-Gutmann case corresponds to c=0).Moreover,when c≠0 and N tends to infinity,the maximum fidelity tends to zero,and the first time to achieve the maximum fidelity tends to a positive constant!The condition for guaranteeing the algorithm's efficiency is determined explicitly.展开更多
For the unsorted database quantum search with the unknown fraction λ of target items, there are mainly two kinds of methods, i.e., fixed-point and trail-and-error.(i) In terms of the fixed-point method, Yoder et al. ...For the unsorted database quantum search with the unknown fraction λ of target items, there are mainly two kinds of methods, i.e., fixed-point and trail-and-error.(i) In terms of the fixed-point method, Yoder et al. [Phys. Rev. Lett.113 210501(2014)] claimed that the quadratic speedup over classical algorithms has been achieved. However, in this paper, we point out that this is not the case, because the query complexity of Yoder’s algorithm is actually in O(1/λ01/2)rather than O(1/λ1/2), where λ0 is a known lower bound of λ.(ii) In terms of the trail-and-error method, currently the algorithm without randomness has to take more than 1 times queries or iterations than the algorithm with randomly selected parameters. For the above problems, we provide the first hybrid quantum search algorithm based on the fixed-point and trail-and-error methods, where the matched multiphase Grover operations are trialed multiple times and the number of iterations increases exponentially along with the number of trials. The upper bound of expected queries as well as the optimal parameters are derived. Compared with Yoder’s algorithm, the query complexity of our algorithm indeed achieves the optimal scaling in λ for quantum search, which reconfirms the practicality of the fixed-point method. In addition, our algorithm also does not contain randomness, and compared with the existing deterministic algorithm, the query complexity can be reduced by about 1/3. Our work provides a new idea for the research on fixed-point and trial-and-error quantum search.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
The quantum search on the graph is a very important topic.In this work,we develop a theoretic method on searching of single vertex on the graph[Phys.Rev.Lett.114110503(2015)],and systematically study the search of man...The quantum search on the graph is a very important topic.In this work,we develop a theoretic method on searching of single vertex on the graph[Phys.Rev.Lett.114110503(2015)],and systematically study the search of many vertices on one low-connectivity graph,the joined complete graph.Our results reveal that,with the optimal jumping rate obtained from the theoretical method,we can find such target vertices at the time O(√N),where N is the number of total vertices.Therefore,the search of many vertices on the joined complete graph possessing quantum advantage has been achieved.展开更多
This paper presents and implements a specified partial adiabatic search algorithm on a quantum circuit. It studies the minimum energy gap between the first excited state and the ground state of the system Hamiltonian ...This paper presents and implements a specified partial adiabatic search algorithm on a quantum circuit. It studies the minimum energy gap between the first excited state and the ground state of the system Hamiltonian and it finds that, in the case of M = 1, the algorithm has the same performance as the local adiabatic algorithm. However, the algorithm evolves globally only within a small interval, which implies that it keeps the advantages of global adiabatic algorithms without losing the speedup of the local adiabatic search algorithm.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
Janmark, Meyer, and Wong showed that continuous-time quantum walk search on known families of strongly regular graphs(SRGs) with parameters(N, k, λ, μ) achieves full quantum speedup. The problem is reconsidered ...Janmark, Meyer, and Wong showed that continuous-time quantum walk search on known families of strongly regular graphs(SRGs) with parameters(N, k, λ, μ) achieves full quantum speedup. The problem is reconsidered in terms of scattering quantum walk, a type of discrete-time quantum walks. Here, the search space is confined to a low-dimensional subspace corresponding to the collapsed graph of SRGs. To quantify the algorithm's performance, we leverage the fundamental pairing theorem, a general theory developed by Cottrell for quantum search of structural anomalies in star graphs.The search algorithm on the SRGs with k scales as N satisfies the theorem, and results can be immediately obtained, while search on the SRGs with k scales as√N does not satisfy the theorem, and matrix perturbation theory is used to provide an analysis. Both these cases can be solved in O(√N) time steps with a success probability close to 1. The analytical conclusions are verified by simulation results on two SRGs. These examples show that the formalism on star graphs can be applied more generally.展开更多
Recently, Zhang and Lu provided a quantum search algorithm based on partial adiabatic evolution, which beats the time bound of local adiabatic search when the number of marked items in the unsorted database is larger ...Recently, Zhang and Lu provided a quantum search algorithm based on partial adiabatic evolution, which beats the time bound of local adiabatic search when the number of marked items in the unsorted database is larger than one. Later, they found that the above two adiabatic search algorithms had the same time complexity when there is only one marked item in the database. In the present paper, following the idea of Roland and Cerf [Roland J and Cerf N J 2002 Phys. Rev. A 65 042308], if within the small symmetric evolution interval defined by Zhang et al., a local adiabatic evolution is performed instead of the original "global" one, this "new" algorithm exhibits slightly better performance, although they are progressively equivalent with M increasing. In addition, the proof of the optimality for this partial evolution based local adiabatic search when M = 1 is also presented. Two other special cases of the adiabatic algorithm obtained by appropriately tuning the evolution interval of partial adiabatic evolution based quantum search, which are found to have the same phenomenon above, are also discussed.展开更多
We present a method to implement the quantum partial search of the database separated into any number of blocks with qudits, D-level quantum systems. Compared with the partial search using qubits, our method needs few...We present a method to implement the quantum partial search of the database separated into any number of blocks with qudits, D-level quantum systems. Compared with the partial search using qubits, our method needs fewer iteration steps and uses the carriers of the information more economically. To illustrate how to realize the idea with concrete physical systems, we propose a scheme to carry out a twelve-dimensional partial search of the database partitioned into three blocks with superconducting quantum interference devices (SQUIDs) in cavity QED. Through the appropriate modulation of the amplitudes of the microwave pulses, the scheme can overcome the non-identity of the cavity-SQUID coupling strengths due to the parameter variations resulting from the fabrication processes. Numerical simulation under the influence of the cavity and SQUID decays shows that the scheme could be achieved efficiently within current state-of-the-art technology.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
Finding a minimum is a fundamental calculation in many quantum algorithms.However,challenges are faced in demonstrating it effectively in real quantum computers.In practice,the number of solutions is unknown,and there...Finding a minimum is a fundamental calculation in many quantum algorithms.However,challenges are faced in demonstrating it effectively in real quantum computers.In practice,the number of solutions is unknown,and there is no universal encoding method.Besides that,current quantum computers have limited resources.To alleviate these problems,this paper proposes a general quantum minimum searching algorithm.An adaptive estimation method is adopted to calculate the number of solutions,and a quantum encoding circuit for arbitrary databases is presented for the first time,which improves the universality of the algorithm and helps it achieve a nearly 100%success rate in a series of random databases.Moreover,gate complexity is reduced by our simplified Oracle,and the realizability of the algorithm is verified on a superconducting quantum computer.Our algorithm can serve as a subroutine for various quantum algorithms to promote their implementation in the Noisy IntermediateScale Quantum era.展开更多
This paper proposes an efficient framework to utilize quantum search practically.To the best of our knowledge,this is the first paper to show a concrete usage of quantum search in general programming.In our framework,...This paper proposes an efficient framework to utilize quantum search practically.To the best of our knowledge,this is the first paper to show a concrete usage of quantum search in general programming.In our framework,we can utilize a quantum computer as a coprocessor to speed-up some parts of a program that runs on a classical computer.To do so,we propose several new ideas and techniques,such as a practical method to design a large quantum circuits for search problems and an efficient quantum comparator.展开更多
The Grover quantum search algorithm is a landmark quantum computing application, which has a speed advantage over classical algorithms for searching an unsorted database. For an√ unsorted database of N items, the cla...The Grover quantum search algorithm is a landmark quantum computing application, which has a speed advantage over classical algorithms for searching an unsorted database. For an√ unsorted database of N items, the classical algorithm needs to search O(N) times, while the Grover algorithm only needs O(√N) times. However, except for the special case of N = 4, the traditional Grover algorithm always has some probability of failure. To solve this problem, several schemes for deterministically performing quantum search have been proposed, but they all impose additional requirements on the query Oracle and cannot be implemented in many practical scenarios. Recently, Roy et al. [Phys. Rev. Res. 4, L022013(2022)] proposed a new deterministic quantum search scheme with no additional requirements on the query Oracle, which has the potential to perfectly replace the traditional Grover algorithm. In this study, we experimentally implement on a programmable silicon quantum photonic chip four deterministic quantum search algorithms, including the Roy algorithm, all of which obtained an average search success rate of over0.93, exceeding the theoretical maximum of 0.9074 that the traditional Grover algorithm can achieve. Our results demonstrate the feasibility and superiority of the deterministic quantum search algorithms and are expected to facilitate the wider application of these algorithms in future quantum information processing.展开更多
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 Beijing Academy of Quantum Information Sciencessupported by the National Natural Science Foundation of China(Grant No.92365206)+2 种基金the support of the China Postdoctoral Science Foundation(Certificate Number:2023M740272)supported by the National Natural Science Foundation of China(Grant No.12247168)China Postdoctoral Science Foundation(Certificate Number:2022TQ0036)。
文摘With the rapid advancement of quantum computing,hybrid quantum–classical machine learning has shown numerous potential applications at the current stage,with expectations of being achievable in the noisy intermediate-scale quantum(NISQ)era.Quantum reinforcement learning,as an indispensable study,has recently demonstrated its ability to solve standard benchmark environments with formally provable theoretical advantages over classical counterparts.However,despite the progress of quantum processors and the emergence of quantum computing clouds,implementing quantum reinforcement learning algorithms utilizing parameterized quantum circuits(PQCs)on NISQ devices remains infrequent.In this work,we take the first step towards executing benchmark quantum reinforcement problems on real devices equipped with at most 136 qubits on the BAQIS Quafu quantum computing cloud.The experimental results demonstrate that the policy agents can successfully accomplish objectives under modified conditions in both the training and inference phases.Moreover,we design hardware-efficient PQC architectures in the quantum model using a multi-objective evolutionary algorithm and develop a learning algorithm that is adaptable to quantum devices.We hope that the Quafu-RL can be a guiding example to show how to realize machine learning tasks by taking advantage of quantum computers on the quantum cloud platform.
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.
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.
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.
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.
文摘We show that the Farhi-Gutmann analog quantum search is a singular algorithm in the following sense: when the original driving Hamiltonian is perturbed slightly such that it is made of projections to the starting state and to the target state with different energies,the maximum fidelity(transition probability)between the searching state and the target state is strictly less than 1 over the entire evolution period,and the first time to achieve this maximum fidelity is of order N~(1/2)/(1+cN)~(1/2),whose behavior depends crucially on whether c=0 or not(here N is the total number of items,and the original Farhi-Gutmann case corresponds to c=0).Moreover,when c≠0 and N tends to infinity,the maximum fidelity tends to zero,and the first time to achieve the maximum fidelity tends to a positive constant!The condition for guaranteeing the algorithm's efficiency is determined explicitly.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11504430 and 61502526)the National Basic Research Program of China(Grant No.2013CB338002)
文摘For the unsorted database quantum search with the unknown fraction λ of target items, there are mainly two kinds of methods, i.e., fixed-point and trail-and-error.(i) In terms of the fixed-point method, Yoder et al. [Phys. Rev. Lett.113 210501(2014)] claimed that the quadratic speedup over classical algorithms has been achieved. However, in this paper, we point out that this is not the case, because the query complexity of Yoder’s algorithm is actually in O(1/λ01/2)rather than O(1/λ1/2), where λ0 is a known lower bound of λ.(ii) In terms of the trail-and-error method, currently the algorithm without randomness has to take more than 1 times queries or iterations than the algorithm with randomly selected parameters. For the above problems, we provide the first hybrid quantum search algorithm based on the fixed-point and trail-and-error methods, where the matched multiphase Grover operations are trialed multiple times and the number of iterations increases exponentially along with the number of trials. The upper bound of expected queries as well as the optimal parameters are derived. Compared with Yoder’s algorithm, the query complexity of our algorithm indeed achieves the optimal scaling in λ for quantum search, which reconfirms the practicality of the fixed-point method. In addition, our algorithm also does not contain randomness, and compared with the existing deterministic algorithm, the query complexity can be reduced by about 1/3. Our work provides a new idea for the research on fixed-point and trial-and-error quantum search.
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the National Key R&D Program of China(Grant No.2017YFA0303800)the National Natural Science Foundation of China(Grant Nos.91850205 and 11974046)。
文摘The quantum search on the graph is a very important topic.In this work,we develop a theoretic method on searching of single vertex on the graph[Phys.Rev.Lett.114110503(2015)],and systematically study the search of many vertices on one low-connectivity graph,the joined complete graph.Our results reveal that,with the optimal jumping rate obtained from the theoretical method,we can find such target vertices at the time O(√N),where N is the number of total vertices.Therefore,the search of many vertices on the joined complete graph possessing quantum advantage has been achieved.
基金supported by the National Natural Science Foundation of China (Grant No. 10876012)
文摘This paper presents and implements a specified partial adiabatic search algorithm on a quantum circuit. It studies the minimum energy gap between the first excited state and the ground state of the system Hamiltonian and it finds that, in the case of M = 1, the algorithm has the same performance as the local adiabatic algorithm. However, the algorithm evolves globally only within a small interval, which implies that it keeps the advantages of global adiabatic algorithms without losing the speedup of the local adiabatic search algorithm.
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.61502101 and 61170321)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20140651)the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20110092110024)
文摘Janmark, Meyer, and Wong showed that continuous-time quantum walk search on known families of strongly regular graphs(SRGs) with parameters(N, k, λ, μ) achieves full quantum speedup. The problem is reconsidered in terms of scattering quantum walk, a type of discrete-time quantum walks. Here, the search space is confined to a low-dimensional subspace corresponding to the collapsed graph of SRGs. To quantify the algorithm's performance, we leverage the fundamental pairing theorem, a general theory developed by Cottrell for quantum search of structural anomalies in star graphs.The search algorithm on the SRGs with k scales as N satisfies the theorem, and results can be immediately obtained, while search on the SRGs with k scales as√N does not satisfy the theorem, and matrix perturbation theory is used to provide an analysis. Both these cases can be solved in O(√N) time steps with a success probability close to 1. The analytical conclusions are verified by simulation results on two SRGs. These examples show that the formalism on star graphs can be applied more generally.
基金Project supported by the National Natural Science Foundation of China(Grant No.61173050)
文摘Recently, Zhang and Lu provided a quantum search algorithm based on partial adiabatic evolution, which beats the time bound of local adiabatic search when the number of marked items in the unsorted database is larger than one. Later, they found that the above two adiabatic search algorithms had the same time complexity when there is only one marked item in the database. In the present paper, following the idea of Roland and Cerf [Roland J and Cerf N J 2002 Phys. Rev. A 65 042308], if within the small symmetric evolution interval defined by Zhang et al., a local adiabatic evolution is performed instead of the original "global" one, this "new" algorithm exhibits slightly better performance, although they are progressively equivalent with M increasing. In addition, the proof of the optimality for this partial evolution based local adiabatic search when M = 1 is also presented. Two other special cases of the adiabatic algorithm obtained by appropriately tuning the evolution interval of partial adiabatic evolution based quantum search, which are found to have the same phenomenon above, are also discussed.
基金Project supported by the National Natural Science Foundation of China(Grant No.10774192)
文摘We present a method to implement the quantum partial search of the database separated into any number of blocks with qudits, D-level quantum systems. Compared with the partial search using qubits, our method needs fewer iteration steps and uses the carriers of the information more economically. To illustrate how to realize the idea with concrete physical systems, we propose a scheme to carry out a twelve-dimensional partial search of the database partitioned into three blocks with superconducting quantum interference devices (SQUIDs) in cavity QED. Through the appropriate modulation of the amplitudes of the microwave pulses, the scheme can overcome the non-identity of the cavity-SQUID coupling strengths due to the parameter variations resulting from the fabrication processes. Numerical simulation under the influence of the cavity and SQUID decays shows that the scheme could be achieved efficiently within current state-of-the-art technology.
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 the National Natural Science Foundation of China(Grant Nos.62074116,61874079,and 81971702)the Luojia Young Scholars Program。
文摘Finding a minimum is a fundamental calculation in many quantum algorithms.However,challenges are faced in demonstrating it effectively in real quantum computers.In practice,the number of solutions is unknown,and there is no universal encoding method.Besides that,current quantum computers have limited resources.To alleviate these problems,this paper proposes a general quantum minimum searching algorithm.An adaptive estimation method is adopted to calculate the number of solutions,and a quantum encoding circuit for arbitrary databases is presented for the first time,which improves the universality of the algorithm and helps it achieve a nearly 100%success rate in a series of random databases.Moreover,gate complexity is reduced by our simplified Oracle,and the realizability of the algorithm is verified on a superconducting quantum computer.Our algorithm can serve as a subroutine for various quantum algorithms to promote their implementation in the Noisy IntermediateScale Quantum era.
文摘This paper proposes an efficient framework to utilize quantum search practically.To the best of our knowledge,this is the first paper to show a concrete usage of quantum search in general programming.In our framework,we can utilize a quantum computer as a coprocessor to speed-up some parts of a program that runs on a classical computer.To do so,we propose several new ideas and techniques,such as a practical method to design a large quantum circuits for search problems and an efficient quantum comparator.
基金supported by the National Key Research and Development Program(Grant No.2017YFA0305200)the Key Research and Development Program of Guangdong Province of China(Grant Nos.2018B030329001,and 2018B030325001)+1 种基金the National Natural Science Foundation of China(Grant No.61974168)support from the National Young 1000 Talents Plan。
文摘The Grover quantum search algorithm is a landmark quantum computing application, which has a speed advantage over classical algorithms for searching an unsorted database. For an√ unsorted database of N items, the classical algorithm needs to search O(N) times, while the Grover algorithm only needs O(√N) times. However, except for the special case of N = 4, the traditional Grover algorithm always has some probability of failure. To solve this problem, several schemes for deterministically performing quantum search have been proposed, but they all impose additional requirements on the query Oracle and cannot be implemented in many practical scenarios. Recently, Roy et al. [Phys. Rev. Res. 4, L022013(2022)] proposed a new deterministic quantum search scheme with no additional requirements on the query Oracle, which has the potential to perfectly replace the traditional Grover algorithm. In this study, we experimentally implement on a programmable silicon quantum photonic chip four deterministic quantum search algorithms, including the Roy algorithm, all of which obtained an average search success rate of over0.93, exceeding the theoretical maximum of 0.9074 that the traditional Grover algorithm can achieve. Our results demonstrate the feasibility and superiority of the deterministic quantum search algorithms and are expected to facilitate the wider application of these algorithms in future quantum information processing.