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| 1 | A quantum algorithm for the dihedral hidden subgroup problem based on lattice basis reduction algorithm显示文摘To optimize the algorithms for the dihedral hidden subgroup problem,we present a new algorithm based on lattice basis reduction algorithm.For n\120,we reduce the dihedral hidden subgroup problem to shortest vector problem.A subroutine is given to get a transition quantum state by constructing a phase filter function,and then the measurement basis are derived based on the lattice basis reduction algorithm for solving low density subset sum problem.Finally,the parity of slope s is revealed by the measurement.This algorithm needs preparing mn quantum states,m qubits to store and O(n2)classical space,which is superior to existing algorithms. | Fada Li Wansu Bao Xiangqun Fu | 2014 | Chinese Science Bulletin2014，59，21： | 5 |
| 2 | Experimental quantum deletion in an NMR quantum information processor显示文摘We report an NMR experimental realization of a rapid quantum deletion algorithm that deletes marked states in an unsorted database.Unlike classical deletion,where search and deletion are equivalent,quantum deletion can be implemented with only a single query,which achieves exponential speed-up compared to the optimal classical analog.In the experimental realization,the GRAPE algorithm was used to obtain an optimized NMR pulse sequence,and the efficient method of maximum-likelihood has been used to reconstruct the experimental output state. | LONG Yu FENG GuanRu PEARSON Jasong LONG GuiLu | 2014 | Science China(Physics,Mechanics & Astronomy)2014，57，7： | 3 |
| 3 | Realization of Kraus operators and POVM measurements using a duality quantum computer显示文摘In this paper,we discuss the ability of realizing Kraus operators and POVM measurements in a duality quantum computer.We prove that not all the Kraus operators can be realized in a duality quantum computer.We introduce a new type of duality quantum circuit,multiduality circuit,by repeating the previous version of duality quantum circuit as a unit,and we can realize universal Kraus operators and POVM measurements with this new circuit.We also give a measure of the complexity of the Kraus operations in terms of the minimum number the units required to realize the Kraus operations in multiduality circuit. | Yang Liu Jing-Xin Cui | 2014 | Chinese Science Bulletin2014，59，19： | 1 |
| 4 | Existence and construction of simultaneous cloning machines for mixed states显示文摘It is a well-known fact that the no-cloning theorem forbids the creation of identical copies of an arbitrary unknown quantum state.In other words,there does not exist a quantum cloning machine that can clone all quantum states.However,it is possible to clone given quantum states under certain conditions,for instance,k distinct pure states|ψ1,|ψ2,...,|ψk can be cloned simultaneously if and only if they are orthogonal.This paper discusses the existence and construction of simultaneous cloning machines for mixed states.It is proved that k distinct mixed statesρ1,ρ2,...,ρkof the n-dimensional quantum system Cncan be cloned simultaneously,that is,there exists a quantum channel Φ on MnMn and a state Σ in Mn,such that Φ(ρiΣ)=ρiρi for all i,if and only ifρiρj=0(i j).Also,the constructing procedure of the desired simultaneous cloning machine is given. | GUO ZhiHua CAO HuaiXin QU ShiXian | 2015 | Science China(Physics,Mechanics & Astronomy)2015，58，4： | 0 |
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