Demonstration of Shor’s factoring algorithm for N $$=$$ 21 on IBM quantum processors

We report a proof-of-concept demonstration of a quantum order-finding algorithm for factoring the integer 21. Our demonstration involves the use of a compiled version of the quantum phase estimation routine, and builds upon a previous demonstration. We go beyond this work by using a configuration of approximate Toffoli gates with residual phase shifts, which preserves the functional correctness and allows us to achieve a complete factoring of $$N=21$$ N = 21 . We implemented the algorithm on IBM quantum processors using only five qubits and successfully verified the presence of entanglement between the control and work register qubits, which is a necessary condition for the algorithm’s speedup in general. The techniques we employ may be useful in carrying out Shor’s algorithm for larger integers, or other algorithms in systems with a limited number of noisy qubits.

Main Alloying Influence on Second Phase Dissolution during Solution Treatment of Al-Zn-Mg-Cu Alloys

Second phase dissolution of Al-Zn-Mg-Cu alloys during solution treatment was closely associated with the content of main alloying elements. In present work, the phase characteristics of several Al-Zn-Mg-Cu alloys with various main alloying contents were investigated, and the second phase dissolution of these alloys during solution treatment was analyzed. The results showed that the extrusion alloys possessed abundant second phases, mainly including Mg(Zn,Cu,Al)2 phase and Fe-rich particles. The DSC analysis proved that the larger endothermic peak corresponded to the alloy with larger main alloying content, and the XRD spectrogram also backed up the advantage of Mg(Zn,Cu,Al)2 phase. After solution treated at 450°C, the residual phases remained in the alloys and the quantity of them were positively correlated with the main alloying content. With the increase of solution temperature, the electrical conductivity of the alloys showed a decremental trend, while the alloys with relatively low main alloying contents exhibited an inversion at the solution temperature of 475°C. The SEM observation demonstrated that no Mg(Zn,Cu,Al)2 phase was observed in the alloys with relatively low main alloying contents while seldom still remained in the alloy with high main alloying content after solution treated at 470°C. After solution treated at 475°C, Mg(Zn,Cu,Al)2 phase completely dissolved into the matrix for the alloy with high main alloying content. The statistics of residual phase quantity also proved this.

The Variation of Heavy Metals Bioavailability in Sediments of Liujiang River Basin, SW China Associated to Their Speciations and Environmental Fluctuations, a Field Study in Typical Karstic River

The bioavailability of heavy metals (HMs) in sediments is closely related to the security of the aquatic environment, but their impacts are poorly researched, particularly in karstic rivers. Therefore, Liujiang River Basin was taken as an example in this study. Seven HMs were analyzed to determine the bioavailability and speciations of HMs in sediments. Moreover, the impacts of environmental factors on HMs were identified. The obtained results suggested that HMs in the sediments are all within their permissible exposure limit (PEL), but Cd and Zn are significantly higher than the soil baseline. Most HMs were found to be in a residual fraction, while their exchangeable fraction was found to be in an extremely low ratio. HMs in bioavailable parts are significantly higher than in the exchangeable and carbonate-bound phases but lower than in the non-residual phase, which demonstrated that HM bioavailability is not confined to the exchangeable and carbonate-bound phases. The correlation coefficients commonly decreased with decreasing speciation ratios, which suggested that the overall bioavailability of metals should be determined by speciation ratios instead of speciations themselves. Noteworthily, most HMs in the residual form were found to be significantly correlated with their overall bioavailability, which highlighted the potential bioavailability of residual form. The non-correlations between pH, electrical conductivity (EC), total dissolved solids (TDS), and HM bioavailability suggested that HMs in the carbonate-bound phase are stable and unsusceptible to environmental variations, while the significant correlations between redox potential (Eh), turbidity, organic matter (OM), main grain size (Mz), and HM bioavailability suggested that HMs in the reducible and oxidizable forms are susceptible to environmental fluctuations. Therefore, the variation of HM bioavailability in karstic rivers is largely regulated by their reducible and oxidizable forms instead of their carbonate-bound form.

Investigation and modification of the inversed vortex phase field method for phase unwrapping

The paper focuses on the problem of the phase unwrapping in spaceborne remote-sensing interferometric synthesized aperture radar (InSAR) systems. Major unwrapping methods and techniques are considered and the modification of the inversed vortex phase field method of phase unwrapping for interferometric data processing of space-borne synthesized aperture radars is proposed. The modification includes the separation and unwrapping of the low-frequency phase only, and obtaining of the residual phase interferogram, which phase range does not exceed 1-2 ambiguity height values. This approach significantly reduces the number of phase residues and increases the processing speed. The other modification implies filter processing of the residual phase without phase unwrapping, which includes iterative separation of the low-frequency using the Gaussian filter and phase subtraction. This approach moves phase fringes to the relief inflection areas, and is similar to the minimum-cost flow unwrapping results. The computational complexity of the algorithm is proportional to the interferogram size and the number of the phase residues of the low-frequency phase interferogram. The accuracy of digital elevation models obtained by the algorithm was estimated using the ALOS PALSAR radar data and the reference altitude data. The results show, that the accuracy is compared with the minimum-cost flow method, but has the less computational complexity.

SPECIATION OF METALS IN SEDIMENTS FROM DAMS AND RIVERS ALONG GOLD MINING VICINITIES IN ZAMFARA STATE

Sediments samples from three dams and rivers in Zamfara State were analyzed for chemical association of the metals (Zn, Cd, Cr, Pb and Hg) using sequential extraction method to determine the amount of the heavy metals available for absorption. The concentrations were determined in four fractions. The concentration of heavy metals in the food crop (tomatoes) was also determined using atomic absorption spectrometry (AAS). The sequential extraction was carried out using (1.0 g) of powder sample weighed into a glass centrifuge (60 ml) and fractions were obtained. Comparing the way the metals were bound to the different fractions in the sediments, it showed clearly that the metals in the sediments are bound to different fractions with different strength. Cd and Cr were primarily in the carbonate bound fraction while Zn and Hg appear mainly in the residual phase. Pb was found in carbonate, exchangeable and water soluble fractions. The distribution of the five metals studied revealed their differences in mobility. From the five elements studied, Cd (14.739- 39.931%) and Pb (0.105- 9.832%) appeared to be the most readily solubilized, thus making these elements the most potentially bioavailable. This may present a real threat as Cd and Pb are transferred into the food chain from soil contaminated by these metals. Zn and Cr levels in the tomatoes, were within international standard while Cd (0.1022 mg/l), Pb (0.2104 mg/l) and Hg (1.8818 mg/l) levels were far above (0.01, 0.01 and 0.001mg/l) USEPA standard for drinking water. Two indices such as contamination

The Synchronization Transceiver Design and Experimental Verification for the LuTan-1 SAR Satellite

The deviation between the two oscillators in BiSAR systems will cause a residual modulation of echo signal. Therefore, the phase synchronization is an important issue that must be addressed for BiSAR systems. An advanced non-interrupted phase synchronization scheme is used for the LuTan-1 SAR satellite. The synchronization transceiver (STR) is designed for transmitting and receiving synchronization signals. In addition, STR mainly consists of master and auxiliary transceivers and switch module. Furthermore, the function and working principle of STR are introduced, and the detailed design of each part is described. The measured results are also evaluated to prove the performance of the STR. In addition, the phase synchronization accuracy is also demonstrated to verify the effectiveness of the non-interrupted synchronization scheme. The standard deviation (STD) of the residual phase is less than 0.3 degrees. The results have guiding significance for the synchronization unit design of LuTan-1 and the future BiSAR system.

Medial entorhinal cortex activates in a traveling wave in the rat

Traveling waves are hypothesized to support the long-range coordination of anatomically distributed circuits. Whether separate strongly interacting circuits exhibit traveling waves remains unknown. The hippocampus exhibits traveling ‘theta’ waves and interacts strongly with the medial entorhinal cortex (MEC). To determine whether the MEC also activates in a traveling wave, we performed extracellular recordings of local field potentials (LFP) and multi-unit activity along the MEC. These recordings revealed progressive phase shifts in activity, indicating that the MEC also activates in a traveling wave. Variation in theta waveform along the region, generated by gradients in local physiology, contributed to the observed phase shifts. Removing waveform-related phase shifts left significant residual phase shifts. The residual phase shifts covaried with theta frequency in a manner consistent with those generated by weakly coupled oscillators. These results show that the coordination of anatomically distributed circuits could be enabled by traveling waves but reveal heterogeneity in the mechanisms generating those waves.