Geometry of Discrete Quantum Computing

Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2^{n} infinite precision complex numbers denoting a vector in a Hilbert space. Such numbers are in general uncomputable using any real-world resources, and, if we have the idea of physical law as some kind of computational algorithm of the universe, we would be compelled to alter our descriptions of physics to be consistent with computable numbers. Our purpose here is to examine the geometric implications of using finite fields Fp and finite complexified fields Fp^2 (based on primes p congruent to 3 mod{4}) as the basis for computations in a theory of discrete quantum computing, which would therefore become a computable theory. Because the states of a discrete n-qubit system are in principle enumerable, we are able to determine the proportions of entangled and unentangled states. In particular, we extend the Hopf fibration that defines the irreducible state space of conventional continuous n-qubit theories (which is the complex projective space CP{2^{n}-1}) to an analogous discrete geometry in which the Hopf circle for any n is found to be a discrete set of p+1 points. The tally of unit-length n-qubit states is given, and reduced via the generalized Hopf fibration to DCP{2^{n}-1}, the discrete analog of the complex projective space, which has p^{2^{n}-1} (p-1)\prod_{k=1}^{n-1} (p^{2^{k}}+1) irreducible states. Using a measure of entanglement, the purity, we explore the entanglement features of discrete quantum states and find that the n-qubit states based on the complexified field Fp^2 have p^{n} (p-1)^{n} unentangled states (the product of the tally for a single qubit) with purity 1, and they have p^{n+1}(p-1)(p+1)^{n-1} maximally entangled states with purity zero.Comment: 24 page

The Market for Hawaii-Grown Natural and Organic Beef

Characteristics of the organic food market with relevance to marketing Hawaii beef products are discussed

Diethyl 3,4-dimethylthieno[2,3-it b]thiophene-2,5-dicarboxylate

In the title compound, C14H16O4S2, the thieno[2,3-b]thiophene ring systems are planar [maximum deviation = 0.008 (2) Å]. The molecular conformation is stabilized by intramolecular C-HO hydrogen bonds, while the crystal packing is stabilized by C-HO, C-H and - stacking [centroid-centroid distance = 3.6605 (14) Å] interactions, which lead to supramolecular layers in the ab plane

Towards a canonical classical natural deduction system

This paper studies a new classical natural deduction system, presented as a typed calculus named \lml. It is designed to be isomorphic to Curien-Herbelin's calculus, both at the level of proofs and reduction, and the isomorphism is based on the correct correspondence between cut (resp. left-introduction) in sequent calculus, and substitution (resp. elimination) in natural deduction. It is a combination of Parigot's $\lambda\mu$-calculus with the idea of ``coercion calculus'' due to Cervesato-Pfenning, accommodating let-expressions in a surprising way: they expand Parigot's syntactic class of named terms. This calculus aims to be the simultaneous answer to three problems. The first problem is the lack of a canonical natural deduction system for classical logic. \lml is not yet another classical calculus, but rather a canonical reflection in natural deduction of the impeccable treatment of classical logic by sequent calculus. The second problem is the lack of a formalization of the usual semantics of Curien-Herbelin's calculus, that explains co-terms and cuts as, respectively, contexts and hole-filling instructions. The mentioned isomorphism is the required formalization, based on the precise notions of context and hole-expression offered by \lml. The third problem is the lack of a robust process of ``read-back'' into natural deduction syntax of calculi in the sequent calculus format, that affects mainly the recent proof-theoretic efforts of derivation of $\lambda$-calculi for call-by-value. An isomorphic counterpart to the $Q$-subsystem of Curien-Herbelin's-calculus is derived, obtaining a new $\lambda$-calculus for call-by-value, combining control and let-expressions.Fundação para a Ciência e a Tecnologia (FCT

Fabrication of Cr2O3 Nanoparticles Using Okra Plant Extract for Antimicrobial Activity

Cr2O3 NPs were synthesized using Okra extract with two methods; the simple chemical method and sol-gel method. XRD analysis showed that the crystal size of Cr2O3 in a simple chemical method was (16.15) nm and with sol-gel method were 16.6 nm, 16.14 nm and 16 nm using annealing temperature of 200, 400 and 600 °C respectively. FE-SEM analysis showed that the nanoparticles of Cr2O3 NPs when using a simple chemical and the sol-gel methods, with particle sizes of (83.74-132.1) nm, (18.92-27.68) nm, (24.19-39.08) nm, and (12.04-15.83) nm that corresponding to a simple chemical method at 200 °C, sol-gel method at 200, 400 and 600 °C respectively. UV-Vis demonstrated that the band gap value of Cr2O3 NPs was 2.9 eV with a simple chemical method, while in a sol-gel method was (3.15, 3.3, 3.5) eV at different temperatures. The study showed an effective antibacterial activity of Cr2O3 NPs such was (12-14) mm  of Gram's negative bacteria and (15-18) mm for Gram's positive bacteria in simple chemical method at (200) °C. The higher antibacterial activity of three different temperatures of sol-gel method was (20) mm for Gram's negative bacteria and (23) mm for Gram's positive bacteria at 200°C

Two-loop QCD corrections of the massive fermion propagator

The off-shell two-loop correction to the massive quark propagator in an arbitrary covariant gauge is calculated and results for the bare and renormalized propagator are presented. The calculations were performed by means of a set of new generalized recurrence relations proposed recently by one of the authors. From the position of the pole of the renormalized propagator we obtain the relationship between the pole mass and the \bar{MS} mass. This relation confirms the known result by Gray et al.. The bare amplitudes are given for an arbitrary gauge group and for arbitrary space-time dimensions.Comment: 18 pages LaTeX, misprints in formula (12) are correcte