Qutrit Dichromatic Calculus and Its Universality

We introduce a dichromatic calculus (RG) for qutrit systems. We show that the decomposition of the qutrit Hadamard gate is non-unique and not derivable from the dichromatic calculus. As an application of the dichromatic calculus, we depict a quantum algorithm with a single qutrit. Since it is not easy to decompose an arbitrary d by d unitary matrix into Z and X phase gates when d > 2, the proof of the universality of qudit ZX calculus for quantum mechanics is far from trivial. We construct a counterexample to Ranchin's universality proof, and give another proof by Lie theory that the qudit ZX calculus contains all single qudit unitary transformations, which implies that qudit ZX calculus, with qutrit dichromatic calculus as a special case, is universal for quantum mechanics.Comment: In Proceedings QPL 2014, arXiv:1412.810

The mass estimate in narrow-line Seyfert 1 galaxies

It is possible that narrow-line Seyfert 1 galaxies (NLS1s) are in the early stage of active galactic nuclei (AGNs) evolution. It is important to estimate the mass of supermassive black hole (SBH) in NLS1s. Here we considered the different kinds of methods to estimate the SBH masses in NLS1s. The virial mass from the H$\beta$ linewidth assuming random orbits of broad line regions (BLRs) is consistent with that from the statured soft X-ray luminosity, which showed that most of NLS1s are in the super-Eddington accretion state. The mass from the [O III] linewidth is systematically larger than that from above two methods. It is necessary to measure he bulge stellar dispersion and/or bulge luminosity in NLS1s.Comment: 2 Pages, 1 figure, in Prof. IAU Symposium No. 222, "The interplay among Black Holes, Stars and ISM in Galactic Nuclei ", eds. T. Storchi-Bergmann, Luis Ho and H. R. Schmit