ZX-Calculus: Cyclotomic Supplementarity and Incompleteness for Clifford+T quantum mechanics

The ZX-Calculus is a powerful graphical language for quantum mechanics and quantum information processing. The completeness of the language -- i.e. the ability to derive any true equation -- is a crucial question. In the quest of a complete ZX-calculus, supplementarity has been recently proved to be necessary for quantum diagram reasoning (MFCS 2016). Roughly speaking, supplementarity consists in merging two subdiagrams when they are parameterized by antipodal angles. We introduce a generalised supplementarity -- called cyclotomic supplementarity -- which consists in merging n subdiagrams at once, when the n angles divide the circle into equal parts. We show that when n is an odd prime number, the cyclotomic supplementarity cannot be derived, leading to a countable family of new axioms for diagrammatic quantum reasoning.We exhibit another new simple axiom that cannot be derived from the existing rules of the ZX-Calculus, implying in particular the incompleteness of the language for the so-called Clifford+T quantum mechanics. We end up with a new axiomatisation of an extended ZX-Calculus, including an axiom schema for the cyclotomic supplementarity.Comment: Mathematical Foundations of Computer Science, Aug 2017, Aalborg, Denmar

Peroral Endoscopic Myotomy Can Improve Esophageal Motility in Patients with Achalasia from a Large Sample Self-Control Research (66 Patients)

<div><p>Background</p><p>Peroral endoscopic myotomy (POEM) as a new approach to achalasia attracts broad attention. The primary objective of this study was to evaluate the results with esophageal motility after POEM through the first large sample clinical research.</p><p>Patients and Methods</p><p>We have a self-control research with all patients (205 in total) who underwent POEM from 2010 to 2014 at our Digestive Endoscopic Center, 66 patients of which underwent high resolution manometry (HRM) before and after POEM in our motility laboratory. Follow-ups last for 5.6 months on average. Outcome variables analyzed included upper esophageal sphincter pressure (UESP), upper esophageal sphincter residual pressure (UESRP), lower esophageal sphincter pressure (LESP), lower esophageal sphincter residual pressure (LESRP) and esophageal body peristalsis. We have a statistical analysis to illustrate how POEM impacts on the change of esophageal motility.</p><p>Results</p><p>The symptoms related to dysphagia were relieved in 95% of patients in recent term after POEM. While HRM showed a statistically significant reduction of URSRP, LESP and LESRP (P<0.01), however, peristalsis was not consistently affected. There were 11 patients who had undergone other prior endoscopic treatment (endoscopic dilation or botulinum toxin injection) and 55 patients had not. The statistical difference (P>0.05) did not occur for these two groups on LESP and LESRP reduction.</p><p>Conclusions</p><p>POEM clearly relieved the symptoms related to dysphagia by lowering the pressure of upper esophageal sphincter (UES) and lower esophageal sphincter (LES),and other endoscopic treatment before POEM did not affect the improvement of LES pressure. These results are concluded from our short-term follow-up study, while the long-term efficacy remains to be further illustrated.</p><p>Trial Registration</p><p>Chinese Clinical Trial Register <a href="http://www.chictr.org/cn/proj/show.aspx?proj=2947" target="_blank">ChiCTR-TRC-12002204</a>)</p></div

Variables on pressure of esophagus.

<p>Variables on pressure of esophagus.</p

Patient Characteristics.

<p>Patient Characteristics.</p

Guiding role of esophageal variceal diameter in treatment of endoscopic ligation: an animal experimental study

Abstract In this study, according to the Location, Diameter, Risk factor (LDRf) classification principle, the influence and effect of esophageal varices diameter on the degree of complete ligation of multicyclic ligator were investigated. Methods. The esophageal veins of healthy piglets were filled with methylene blue solution, and the in vitro pig esophageal varices model was made, which were divided into three groups according to the diameter of esophageal varices: D1, 0.4–1.0 cm; D2, 1.1–1.5 cm; and D3, 1.6–2.0 cm. Finally, the ligation effect of each group was analyzed statistically. A total of 407 ligations were performed on the simulated esophageal variceal model. There were 103 ligations in the D1 group and 98 were complete (95.15%, 98/103); 151 ligations in the D2 group and 47 were complete (31.13%, 47/151); and 153 ligations in the D3 group but none were complete (0%, 0/153). There was significant difference in the degree of complete ligation between the two groups (χ2 = 38.0014, P ≤ 0.001). In the varicose ligation model, the complete ligation effect was the most complete and robust when the varicose diameter was 0.4–1.0 cm. This study showed that the varicose vein diameter in LDRf classification was reasonable and feasible to guide endoscopic varicose vein ligation