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
The characteristics of the normal equation created in recovering the Earth gravity model （EGM） by least-squares （LS） adjustment from the in-situ disturbing potential is discussed in detail. It can be concluded tha...The characteristics of the normal equation created in recovering the Earth gravity model （EGM） by least-squares （LS） adjustment from the in-situ disturbing potential is discussed in detail. It can be concluded that the normal equation only depends on the orbit, and the choice of a priori gravity model has no effect on the LS solution. Therefore, the accuracy of the recovered gravity model can be accurately simulated. Starting from this point, four sets of disturbing potential along the orbit with different level of noise were simulated and were used to recover the EGM. The results show that on the current accuracy level of the accelerometer calibration, the accuracy of the EGM is not sufficient to reflect the time variability of the Earth＇s gravity field, as the dynamic method revealed.展开更多
Let L be a type II1 factor with separable predual and r be a normal faithful tracial state of c~. We first show that the set of subfactors of L with property F, the set of type II1 subfactors of L with similarity prop...Let L be a type II1 factor with separable predual and r be a normal faithful tracial state of c~. We first show that the set of subfactors of L with property F, the set of type II1 subfactors of L with similarity property and the set of all McDuff sub/actors of t are open and closed in the Hausdorff metric d2 induced by the trace norm; then we show that the set of all hyperfinite von Neumann subalgebras of L is closed in d2. We also consider the connection of perturbation of operator algebras under d2 with the fundamental group and the generator problem of type II1 factors. When M is a finite yon Neumann algebra with a normal faithful trace, the set of all von Neumann subalgebras B of M such that B ∪→ M is rigid is closed in the Hausdorff metric d2.展开更多
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Funded by the National Natural Science Foundation of China （No.40274004）, and the Open Fund of Key Laboratory of Geospace Environment and Geodesy, Ministry of Education, China （No. 06-09）. The authors are grateful to Prof. CHAO Dingbo for his critical comments and also thank Dr. Dadzie very much for his proof-reading.
文摘The characteristics of the normal equation created in recovering the Earth gravity model （EGM） by least-squares （LS） adjustment from the in-situ disturbing potential is discussed in detail. It can be concluded that the normal equation only depends on the orbit, and the choice of a priori gravity model has no effect on the LS solution. Therefore, the accuracy of the recovered gravity model can be accurately simulated. Starting from this point, four sets of disturbing potential along the orbit with different level of noise were simulated and were used to recover the EGM. The results show that on the current accuracy level of the accelerometer calibration, the accuracy of the EGM is not sufficient to reflect the time variability of the Earth＇s gravity field, as the dynamic method revealed.
基金supported by National Natural Science Foundation of China(Grant No.11371222)Natural Science Foundation of Shandong Province(Grant No.ZR2012AM024)
文摘Let L be a type II1 factor with separable predual and r be a normal faithful tracial state of c~. We first show that the set of subfactors of L with property F, the set of type II1 subfactors of L with similarity property and the set of all McDuff sub/actors of t are open and closed in the Hausdorff metric d2 induced by the trace norm; then we show that the set of all hyperfinite von Neumann subalgebras of L is closed in d2. We also consider the connection of perturbation of operator algebras under d2 with the fundamental group and the generator problem of type II1 factors. When M is a finite yon Neumann algebra with a normal faithful trace, the set of all von Neumann subalgebras B of M such that B ∪→ M is rigid is closed in the Hausdorff metric d2.
