A ZX-Calculus with Triangles for Toffoli-Hadamard, Clifford+T, and Beyond

We consider a ZX-calculus augmented with triangle nodes which is well-suited to reason on the so-called Toffoli-Hadamard fragment of quantum mechanics. We precisely show the form of the matrices it represents, and we provide an axiomatisation which makes the language complete for the Toffoli-Hadamard quantum mechanics. We extend the language with arbitrary angles and show that any true equation involving linear diagrams which constant angles are multiple of Pi are derivable. We show that a single axiom is then necessary and sufficient to make the language equivalent to the ZX-calculus which is known to be complete for Clifford+T quantum mechanics. As a by-product, it leads to a new and simple complete axiomatisation for Clifford+T quantum mechanics.Comment: In Proceedings QPL 2018, arXiv:1901.09476. Contains Appendi

The contribution of CHONS particles to the diffuse high Galactic latitude IR emission

This work purports to model the far infrared gray-body emission in the spectra of high-Galactic-latitude clouds. Several carbonaceous laboratory materials are tested for their fitness as carriers of this modified-black-body emission which, according to data delivered by the Planck satellite, and others before, is best fit with temperature 17.9 K and spectral index beta=1.78. Some of these materials were discarded for insufficient emissivity, others for inadequate beta. By contrast, CHONS clusters (beta=1.4, T=19 K) combine nicely with magnesium silicate (beta=2, T=18.7 K) to give a spectrum which falls well within the observational error bars (total emission cross-section at 250 mum: 8.6 10^{-26} cm^{2} per H atom). Only 15 % of all Galactic carbon atoms are needed for this purpose. The CHONS particles that were considered and described have a disordered (amorphous) structure but include a sizable fraction of aromatic rings, although they are much less graphitized than a-C:H/HAC. They can be seen as one embodiment of ``astronomical graphite" deduced earlier on from the then available astronomical observations. Grain heating by H atom capture is proposed as a contributor to the observed residual emissions that do not follow the dust/HI correlation.Comment: 11 pages, 13 figures To be published in MNRA