Extracting a function encoded in amplitudes of a quantum state by tensor network and orthogonal function expansion

There are quantum algorithms for finding a function $f$ satisfying a set of conditions, such as solving partial differential equations, and these achieve exponential quantum speedup compared to existing classical methods, especially when the number $d$ of the variables of $f$ is large. In general, however, these algorithms output the quantum state which encodes $f$ in the amplitudes, and reading out the values of $f$ as classical data from such a state can be so time-consuming that the quantum speedup is ruined. In this study, we propose a general method for this function readout task. Based on the function approximation by a combination of tensor network and orthogonal function expansion, we present a quantum circuit and its optimization procedure to obtain an approximating function of $f$ that has a polynomial number of degrees of freedom with respect to $d$ and is efficiently evaluable on a classical computer. We also conducted a numerical experiment to approximate a finance-motivated function to demonstrate that our method works.Comment: 16 pages, 8 figure

Ablation for idiopathic left ventricular tachycardia in a patient with double outlet right ventricle who underwent Fontan operation: a case report

Background The incidence of ventricular tachycardia (VT) in patients following Fontan operation is reported as 3.5%. Furthermore, in patients with repaired double outlet right ventricle (DORV), scar-related VT and outflow tract VT have been reported; however, Purkinje-related VT has not previously been reported. In this report, we present the case of idiopathic left VT (ILVT) in a patient with DORV who underwent Fontan operation. Case summary A 31-year-old man was diagnosed as having DORV with complete atrioventricular defect at birth. When he was 17 years old, he underwent surgical repair, including extracardiac Fontan operation and common atrioventricular valve replacement. Five years later, VT was detected. Since some medications were ineffective in suppressing VT, he was referred to our hospital for definitive treatment. Ventricular tachycardia was induced by atrial and ventricular programmed electrical stimulations. The mechanism of the VT was determined to be re-entry. The earliest activation site was located at the mid-inferior septum of the hypoplastic left ventricle, in which Purkinje potentials were observed before the local ventricular electrogram. Radiofrequency catheter ablation (RFCA) was performed at this site to eliminate VT. Discussion Most VTs originate from surgical scars in patients with congenital heart disease. Catheter ablation was feasible in scar-related VT. To the best of our knowledge, this is the first report of ILVT treated successfully with RFCA in a DORV patient who had undergone Fontan operation

Experimental petrology of ancient lunar mare basalt Asuka-881757: Spinel crystallization as a petrologic indicator

The paucity of titanian chromites in lunar-meteorite basalt Asuka (A)-881757 is unusual compared to the general occurrence of co-existing chromites and ulvospinels in the Apollo and Luna mare basalts. The unique spinel crystallization of A-881757 is expected to hold a key to elucidate the crystallization and cooling episodes of the basalt. In this study, we investigated the possible reason for the missing chromite by conducting isothermal and cooling experiments on the bulk-rock composition of A-881757 and discuss the petrogenesis of the ancient low-Ti mare basalt in light of spinel crystallization. A series of isothermal experiments showed the A-881757 basalt magma is not saturated with chromite under the expected lunar oxygen fugacity condition (IW～IW-1). A peritectic reaction among chromite, melt, and pyroxene is present for A-881757 basalt magma under the more oxidized condition which is one or two log unit higher than the lunar condition. The cooling experiment successfully reproduced the chromian ulvospinels with similar compositions to those in A-881757. The result of the cooling experiments further implies that ulvospinels solely crystallized from highly-fractionated interstitial melts in the late crystallization stage. The disparity in the crystallization of the liquidus chromite between the low-Ti and very low-Ti basalts might reflect the difference of bulk Cr_2O_3 concentration. The low liquidus temperature and the paucity of the liquidus olivine in A-881757 infer that the A-881757 basalt represents a liquid derived from near-surface fractionation processes. Chromites might possibly have been present during that near-surface fractionation episode prior to the eruption of the magma

Cooling rates of olivine xenocrysts in the EET79001 shergottite

The chemical zoning profiles of olivine xenocrysts in lithology A of the Elephant Moraine (EET) 79001 basaltic shergottite have been measured in order to investigate its cooling history. Olivines are zoned from Fa_ in the cores to Fa_ in the rims. The major and minor element compositions of olivine xenocryst cores in EET79001 correspond to those of homogeneous olivines in the lherzolitic shergottites, reconfirming the previous studies. We assume that the initial profile of olivine was uniform and it was modified by atomic diffusion due to contact with the Fe-rich surrounding melt when olivine was incorporated as a xenocryst. Comparing the observed Fe zoning profiles with the calculated ones, we have estimated the minimum cooling rates of the xenocrystic olivines by numerically solving the diffusion equation. The inferred minimum cooling rates (0.07-0.5℃) are faster than that for Zagami estimated from the width of pyroxene lamella, consistent with a hypothesis that EET79001 experienced significant undercooling unlike Shergotty and Zagami. We also performed the calculations by applying two different Fe-Mg interdiffusion coefficients to evaluate them. There is no significant difference in the curvature of the calculated profiles between the two diffusion coefficients, whereas one gives roughly fivefold higher cooling rates than the other

The variation of Zn content in spinel group minerals and daubreelites of primitive achondrites

We have studied the Zn content of spinel group mineral and daubreelite in primitive achondrites in order to clarify how the content of Zn, a moderately volatile element, reflects their formation process. Primitive achondrites have achondritic texture and chondrite-related chemistry and mineralogy. Because of these characteristics, primitive achondrites are thought to represent the transition from chondrites to achondrites. We have compared the Zn content in spinel group minerals of primitive achondrites with those of chondrites and ureilites. Although Zn is a moderately volatile element, the Zn content in spinel group mineral of primitive achondrites, ureilites and metamorphosed chondrites is higher than unmetamorphosed chondrites. This fact suggests that high Zn content in spinel group mineral of primitive achondrites may result from secondary crystallization or reequilibration of spinel mineral from a sulfide melt containing Cr, Mn and Zn which was partially melted during thermal metamorphism. We also found that the Zn content in spinel group minerals decreases from primitive achondrites and ureilites to HED and Martian meteorites. We suggest that Zn was significantly volatilized from completely molten magma in these meteorites. We found that spinel group minerals and daubreelites appear to be the major reservoir of Zn in most meteorites. Zn may be preferentially retained in the tight spinel structure

ダイチョウガン ノ サイシン ノ シンダン チリョウ

Colorectal cancer has the third mortality in 2013 and the second morbidity in 2011 of all cancers in Japan. Therefore, it is very important to know the newest information about colorectal cancer. The latest endoscopy has been equipped with not also magnifying function but image enhancing function, such as narrow band imaging and blue laser imaging. These functions enable us to know distinguish benign from malignancy of colorectal polyps without a biopsy. As a therapeutic progress, endoscopic submucosal dissection for the early colorectal cancer has been spread due to approval by the Japanese health insurance system in 2012. Drug therapy for the colorectal cancer has progressed due to the new drug and regimen. Above all, the molecular target drug has improved the prognosis of stage IV colorectal cancer with or without other chemotherapy.The molecular target drugs for colorectal cancer are currently anti VEGF antibody（bevacizumab）and anti EGFR antibody（cetuximab, panitumumab）in clinical use. Moreover, regorafenib and TAS-102 showed efficacy for the colorectal cancer and have been in clinical use. As a result, overall survival rate of stage IV colorectal cancer has reached more than３０months in case of use up all these drugs