Potential value of saline-induced Pd/Pa ratio in patients with coronary artery stenosis

BackgroundFractional flow reserve (FFR) is the current gold standard for identifying myocardial ischemia in individuals with coronary artery stenosis. However, FFR is not penetrated as much worldwide due to time consumption, costs associated with adenosine, FFR-related discomfort, and complications. Resting physiological indexes may be widely accepted alternatives to FFR, while the discrepancies with FFR were found in up to 20% of lesions. The saline-induced Pd/Pa ratio (SPR) is a new simplified option for evaluating coronary stenosis. However, the clinical implication of SPR remains unclear.ObjectivesIn the present study, we aimed to compare the accuracies of SPR and resting full-cycle ratio (RFR) and to investigate the incremental value of SPR in clinical practice.MethodsIn this multicenter prospective study, 112 coronary lesions (105 patients) were evaluated by SPR, RFR, and FFR.ResultsThe overall median age was 71 years, and 84.8% were men. SPR was correlated more strongly with FFR than with RFR (r = 0.874 vs. 0.713, respectively; p < 0.001). Using FFR < 0.80 as the reference standard variable, the area under the receiver-operating characteristic (ROC) curve for SPR was superior to that of RFR (0.932 vs. 0.840, respectively; p = 0.009).ConclusionSaline-induced Pd/Pa ratio predicted FFR more accurately than RFR. SPR could be an alternative method for evaluating coronary artery stenosis and further investigation including elucidation of the mechanism of SPR is needed (225 words)

Quantum computation of Groebner basis

In this essay, we examine the feasibility of quantum computation of Gr\"obner basis which is a fundamental tool of algebraic geometry. The classical method for computing Gr\"obner basis is based on Buchberger's algorithm, and our question is how to adopt quantum algorithm there. A Quantum algorithm for finding the maximum is usable for detecting head terms of polynomials, which are required for the computation of S-polynomials. The reduction of S-polynomials with respect to a Gr\"obner basis could be done by the quantum version of Gauss-Jordan elimination of matrices which represents polynomials. However, the frequent occurrence of zero-reductions of polynomials is an obstacle to the effective application of quantum algorithms. This is because zero-reductions of polynomials occur in non-full-rank matrices, for which quantum linear systems algorithms (through the inversion of matrices) are inadequate, as ever-known quantum linear solvers (such as Harrow-Hassidim-Lloyd) require the clandestine computations of the inverses of eigenvalues. Such algorithms should be used in limited situations with the guarantee that the matrices could be inverted. For example, the transformation from the non-reduced Gr\"obner basis to the reduced one is of this sort, and the quantum algorithms surely achieve the partial speedup of the computations

Feasibility of first principles molecular dynamics in fault-tolerant quantum computer by quantum phase estimation

This article shows a proof of concept regarding the feasibility of ab initio molecular simulation, wherein the wavefunctions and the positions of nuclei are simultaneously determined by the quantum algorithm, as is realized by the so-called Car-Parrinello method by classical computing. The approach used in this article is of a hybrid style, which shall be realized by future fault-tolerant quantum computer. First, the basic equations are approximated by polynomials. Second, those polynomials are transformed to a specific form, wherein all variables (representing the wavefunctions and the atomic coordinates) are given by the transformations acting on a linear space of monomials with finite dimension, and the unknown variables could be determined as the eigenvalues of those transformation matrices. Third, the eigenvalues are determined by quantum phase estimation. Following these three steps, namely, symbolic, numeric, and quantum steps, we can determine the optimized electronic and atomic structures of molecules

Quantum computation of Groebner basis through F4 and F5 algorithms

Our main concern in this article is how to apply quantum algorithms to compute Groebner basis through Faugere's F4 and F5 algorithms, which are regarded as the most effective algorithms for this purpose. We give examples and pseudo-codes for these algorithms and investigate where we can apply quantum algorithms. As a result, we have the designs (or the pseudo-codes) of quantum versions of the F4 and F5 algorithms by replacing classical algorithms with quantum ones. The quantum versions of F4 and F5 algorithms are, in nature, the extensions of the quantum Gaussian-Jordan elimination of Diepp, since the computations of Groebner bases are practicable through the matrix representations. In the computation of Groebner bases, quantum algorithms serve to construct the matrices as small as possible (according to the fundamental idea of F4 and F5) and to find the pivotal element as quickly as possible