CNOT-count optimized quantum circuit of the Shor's algorithm

We present improved quantum circuit for modular exponentiation of a constant, which is the most expensive operation in Shor's algorithm for integer factorization. While previous work mostly focuses on minimizing the number of qubits or the depth of circuit, we try to minimize the number of CNOT gate which primarily determines the running time on a ion trap quantum computer. First, we give the implementation of basic arithmetic with known lowest number of CNOT gate and the construction of improved modular exponentiation of a constant by accumulating intermediate date and windowing technique. Then, we precisely estimate the number of improved quantum circuit to perform Shor's algorithm for factoring a $n$-bit integer, which is $217\frac{n^3}{\log_2n}+4n^2+n$. According to the number of CNOT gates, we analyze the running time and feasibility of Shor's algorithm on a ion trap quantum computer. Finally, we discuss the lower bound of CNOT numbers needed to implement Shor's algorithm

Investigation of the Scanning Microarc Oxidation Process

Scanning microarc oxidation (SMAO) is a coating process which is based on conventional microarc oxidation (MAO). The key difference is that deposition in SMAO is achieved by using a stainless steel nozzle to spray an electrolyte stream on the substrate surface as opposed to immersing the workpiece in an electrolyzer. In the present study, SMAO discharge characteristics, coating morphology, and properties are analyzed and compared to results obtained from MAO under similar conditions. Results show that MAO and SMAO have comparable spark and microarc lifetimes and sizes, though significant differences in incubation time and discharge distribution were evident. Results also showed that the voltage and current density for MAO and SMAO demonstrate similar behavior but have markedly different transient and steady-state values. Results obtained from coating A356 aluminum sheet show that oxide thickness and growth rate in SMAO are strongly dependent on interelectrode spacing and travel speed. Analysis of the SMAO coating morphology and structure showed that a denser and slightly harder layer was deposited in comparison to MAO and is attributed to reduced porosity and increased formation of α-Al2O3. Preliminary results indicate that SMAO represents a viable process for coating of aluminum surfaces

Resonant sequential scattering in two-frequency-pumping superradiance from a Bose-Einstein condensate

We study sequential scattering in superradiance from a Bose-Einstein condensate pumped by a two-frequency laser beam. We find that the distribution of atomic side modes presents highly different patterns for various frequency difference between the two pump components. A novel distribution is observed, with a frequency difference of eight times the recoil frequency. These observations reveal that the frequency overlap between the end-fire modes related to different side modes plays an essential role in the dynamics of sequential superradiant scattering. The numerical results from a semiclassical model qualitatively agree with our observations.Comment: Submitted to PR