The Riemann hypothesis is intimately connected to the counting functions for the primes. In particular, Perron’s explicit formula relates the prime counting function to fixed points of iterations of the explicit form...The Riemann hypothesis is intimately connected to the counting functions for the primes. In particular, Perron’s explicit formula relates the prime counting function to fixed points of iterations of the explicit formula with particular relations involving the trivial and non-trivial roots of the Riemann Zeta function and the Primes. The aim of the paper is to demonstrate this relation at the fixed points of iterations of explicit formula, defined by functions of the form limT∈Ν→∞fT(zw)=zw,where, zwis a real number.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
In order to decrease the deformation and stress and increase the natural frequency of the fixed table,a method of optimization driven by the sensitivity and topology analyses is proposed.The finite element model of th...In order to decrease the deformation and stress and increase the natural frequency of the fixed table,a method of optimization driven by the sensitivity and topology analyses is proposed.The finite element model of the fixed table is constructed and analyzed by using ANSYS software.Based on the results of static analysis and modal analysis,the maximum deformation,the maximum stress,and natural frequencies are obtained.Then,the sensitivity analysis and topology optimization are carried out to find out the parameters to be optimized.The fixed table is reconstructed according to optimal design scheme.In the comparison of the results between original model and the optimized one,the maximum deformation and stress are decreased by 71.73%and 60.27%respectively.At the same time,the natural frequencies from the first mode to the sixth mode are increased by 30.28%,29.57%,29.51%,31.52%,22.19%,and 21.80%,respectively.The method can provide technology guide for the design and optimization of machining structure.展开更多
在过去10年里,基于量子力学的量子信号表示研究已经出现一些重要结果.然而,关于量子信号处理方面的研究却相对滞后,其中就包括量子信号的滤波处理.首先,改进了现有的数字信号的量子表示模型(quantum representation of digital signals,...在过去10年里,基于量子力学的量子信号表示研究已经出现一些重要结果.然而,关于量子信号处理方面的研究却相对滞后,其中就包括量子信号的滤波处理.首先,改进了现有的数字信号的量子表示模型(quantum representation of digital signals,QRDS),使其适用于任意长度的时间信号,同时还修改了QRDS模型中二补码的编码方法,使得新的编码更符合实际问题.然后,基于改进的模型引入了中值滤波方案,该方案回避了量子计算不能直接实现卷积运算的缺陷.为了实现该滤波方案的量子电路,又给出了基本量子运算模块:比较器模块、交换模块和中值计算模块.最后,通过实例验证了文中所提滤波方案的有效性和合理性.展开更多
文摘The Riemann hypothesis is intimately connected to the counting functions for the primes. In particular, Perron’s explicit formula relates the prime counting function to fixed points of iterations of the explicit formula with particular relations involving the trivial and non-trivial roots of the Riemann Zeta function and the Primes. The aim of the paper is to demonstrate this relation at the fixed points of iterations of explicit formula, defined by functions of the form limT∈Ν→∞fT(zw)=zw,where, zwis a real number.
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National Major Scientific&Technological Special Program for"High-Grade CNC and Basic Manufacturing Equipment"of China(No.2012ZX04011-031)Science and Technology Programs of Sichuan Province,China(No.2010GZ0250,No.2011GZ0075)
文摘In order to decrease the deformation and stress and increase the natural frequency of the fixed table,a method of optimization driven by the sensitivity and topology analyses is proposed.The finite element model of the fixed table is constructed and analyzed by using ANSYS software.Based on the results of static analysis and modal analysis,the maximum deformation,the maximum stress,and natural frequencies are obtained.Then,the sensitivity analysis and topology optimization are carried out to find out the parameters to be optimized.The fixed table is reconstructed according to optimal design scheme.In the comparison of the results between original model and the optimized one,the maximum deformation and stress are decreased by 71.73%and 60.27%respectively.At the same time,the natural frequencies from the first mode to the sixth mode are increased by 30.28%,29.57%,29.51%,31.52%,22.19%,and 21.80%,respectively.The method can provide technology guide for the design and optimization of machining structure.
文摘在过去10年里,基于量子力学的量子信号表示研究已经出现一些重要结果.然而,关于量子信号处理方面的研究却相对滞后,其中就包括量子信号的滤波处理.首先,改进了现有的数字信号的量子表示模型(quantum representation of digital signals,QRDS),使其适用于任意长度的时间信号,同时还修改了QRDS模型中二补码的编码方法,使得新的编码更符合实际问题.然后,基于改进的模型引入了中值滤波方案,该方案回避了量子计算不能直接实现卷积运算的缺陷.为了实现该滤波方案的量子电路,又给出了基本量子运算模块:比较器模块、交换模块和中值计算模块.最后,通过实例验证了文中所提滤波方案的有效性和合理性.