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
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
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
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
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 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.
