Creating Very True Quantum Algorithms for Quantum Energy Based Computing

An interpretation of quantum mechanics is discussed. It is assumed that quantum is energy. An algorithm by means of the energy interpretation is discussed. An algorithm, based on the energy interpretation, for fast determining a homogeneous linear function f(x) := s.x = s ₁ x ₁ + s ₂ x ₂ + ? + s _N x _N is proposed. Here x = (x ₁, … , x _N ), x _j ∈ R and the coefficients s = (s ₁, … , s _N ), s _j ∈ N. Given the interpolation values \((f(1), f(2),...,f(N))=\vec {y}\), the unknown coefficients \(s = (s_{1}(\vec {y}),\dots , s_{N}(\vec {y}))\) of the linear function shall be determined, simultaneously. The speed of determining the values is shown to outperform the classical case by a factor of N. Our method is based on the generalized Bernstein-Vazirani algorithm to qudit systems. Next, by using M parallel quantum systems, M homogeneous linear functions are determined, simultaneously. The speed of obtaining the set of M homogeneous linear functions is shown to outperform the classical case by a factor of N × M.     

New Method of Calculating a Multiplication by using the Generalized Bernstein-Vazirani Algorithm

We present a new method of more speedily calculating a multiplication by using the generalized Bernstein-Vazirani algorithm and many parallel quantum systems. Given the set of real values \(\{a_{1},a_{2},a_{3},\ldots ,a_{N}\}\) and a function \(g:\textbf {R}\rightarrow \{0,1\}\), we shall determine the following values \(\{g(a_{1}),g(a_{2}),g(a_{3}),\ldots , g(a_{N})\}\) simultaneously. The speed of determining the values is shown to outperform the classical case by a factor of \(N\). Next, we consider it as a number in binary representation; M₁ = (g(a₁),g(a₂),g(a₃),…,g(a _N )). By using \(M\) parallel quantum systems, we have \(M\) numbers in binary representation, simultaneously. The speed of obtaining the \(M\) numbers is shown to outperform the classical case by a factor of \(M\). Finally, we calculate the product; \( M_{1}\times M_{2}\times \cdots \times M_{M}. \) The speed of obtaining the product is shown to outperform the classical case by a factor of N × M.     

Mid-infrared supercontinuum generation in a four-hole As2S5 chalcogenide microstructured optical fiber

We demonstrate the supercontinuum (SC) generation in a four-hole As₂S₅ chalcogenide microstructured optical fiber (MOF) experimentally. The As₂S₅ glass has better property of transmission than As₂S₃ glass in the visible range. The four-hole As₂S₅ MOF is fabricated by a rod-in-tube method. The SCs generated by different pump wavelengths at 2,000, 2,300 and 2,500 nm in the MOF whose length is from 2.3 to 20 cm are demonstrated. Those pump wavelengths correspond to the chromatic dispersion wavelength in the normal chromatic dispersion region, the anomalous chromatic dispersion region close to zero-dispersion wavelength (ZDW) and the anomalous chromatic dispersion region far from ZDW, respectively. Wider SCs can be obtained when pumped at a wavelength in the anomalous dispersion region close to ZDW. The widest SC range of 4,280 nm (from 1,370 to 5,650 nm) covering two octaves was obtained in a 4.8-cm-long fiber pumped at 2,300 nm.     

Multiple bosonic mode coupling in the electron self-energy of (La2-xSrx)CuO4

High resolution angle-resolved photoemission spectroscopy data along the (0,0)-(pi,pi) nodal direction with significantly improved statistics reveal fine structure in the electron self-energy of the underdoped (La2-xSrx)CuO4 samples in the normal state. Fine structure at energies of (40-46) meV and (58-63) meV, and possible fine structure at energies of (23-29) meV and (75-85) meV, have been identified. These observations indicate that, in (La2-xSrx)CuO4, more than one bosonic modes are involved in the coupling with electrons.     

Hemorrhagic cerebral metastases from thyroid cancer on T2*-weighted gradient echo MRI

We report a case of multiple hemorrhagic cerebral metastases from papillary thyroid cancer, with reference to T(2)*-weighted gradient echo (GRE) magnetic resonance imaging (MRI). Small metastatic nodules were recognized as round nodules with signal loss on T(2)*-weighted GRE MRI, and were more pronounced compared with other sequences. Lesions were later confirmed as hemorrhagic on T(1)- and T(2)-weighted MRI. T(2)*-weighted GRE MRI was a sensitive tool for early detection of metastases displaying hemorrhagic changes.     

Copper(I)-catalyzed boryl substitution of unactivated alkyl halides

Borylation of alkyl halides with diboron proceeded in the presence of a copper(I)/Xantphos catalyst and a stoichiometric amount of K(O-t-Bu) base. The boryl substitution proceeded with normal and secondary alkyl chlorides, bromides, and iodides, but alkyl sulfonates did not react. Menthyl halides afforded the corresponding borylation product with excellent diastereoselectivity, whereas (R)-2-bromo-5-phenylpentane gave a racemic product. Reaction with cyclopropylmethyl bromide resulted in ring-opening products, suggesting the reaction involves a radical pathway.     

Copper-mediated and copper-catalyzed cross-coupling of indoles and 1,3-azoles: double C-H activation

A new bronze age: the described copper-mediated cross-coupling with double C-H activation can provide a convergent access to indole-containing biheteroaryls that are of high interest in pharmaceutical and medicinal chemistry. In this strategy an easily attachable and detachable 2-pyrimidyl directing group is used. Moreover, a variant that is catalytic in copper is achieved by using atmospheric oxygen as an ideal co-oxidant.