Implementtion of a Computation Algorithm for Deutsch-Jozsa Problem Utilizing Spatial Distribution of Photons

Several implementations of quantum computation making effective use of the quantum behavior of single-photons have been explored. These implementing methods were found unsuitble for large-scale computation, because they require 2^N-1 optical paths to represent N qubits. In this paper, a new computing scheme is described which utilizes spatial distribution of photons. The occupation of several optical paths by single-photons is adopted as qubits. This adoption gives several extension of processing capacity and computational functionality with a simple setup. An optical implementation of a solution algorithm on four-bit Deutsch-Jozsa problem is demonstrated with utilization of the spatial distribution of photons.     

Asymptotic behavior of quantum walks on the line

This paper gives various asymptotic formulae for the transition probability associated with discrete time quantum walks on the real line. The formulae depend heavily on the ‘normalized’ position of the walk. When the position is in the support of the weak-limit distribution obtained by Konno (2005) [5], one observes, in addition to the limit distribution itself, an oscillating phenomenon in the leading term of the asymptotic formula. When the position lies outside of the support, one can establish an asymptotic formula of large deviation type. The rate function, which expresses the exponential decay rate, is explicitly given. Around the boundary of the support of the limit distribution (called the ‘wall’), the asymptotic formula is described in terms of the Airy function.     

In Defence of the Economic Batch Quantity

The derivation of the formula for the economic batch quantity is fairly simple and is often used to illustrate operational research methodology. The model has recently been attacked, on the grounds that a mistaken attempt is made to minimize costs, and that in any case it misrepresents costs. In this paper alternatives are expressed symbolically. It is shown that optimizing any of the alternative functions would be equivalent or inferior to minimizing costs.     

Microstructure of polybutadiene catalyzed by alkali metal tert-butoxides and n-butylsodium. II.

A polybutadiene of high molecular weight was prepared in hydrocarbon solvent by using n-BuNa–tert-BuOM (M = Li, K) as a polymerization initiator. The microstructure of this polymer varied from 35 to 76% of 1,2 content, depending on the type of modifiers. The kinetics of polymerization was not studied, primarily due to the heterogeneous nature of the catalyst. However, other variables, such as the catalyst concentration and temperature, have been studied. The results and mechanistic implications are discussed.     

High benzene selectivity of uniform sub-nanometre pores of self-ordered mesoporous silicate

The high benzene gas selectivity of mesoporous silicate (SBA-15) was observed in the sub-nanometre micropore condensation region. The benzene/toluene ratios of the adsorbed amount were >100 and >6 in ideal and pseudo-atmospheric environments, respectively.     

Physical and rheological characterization of poly(aryloxyphosphazene) copolymers

A series of poly(aryloxyphosphazene)s was prepared with phenoxy and p-ethylphenoxy substituents in various ratios. The thermal, morphological, and rheological properties of this series of polymers were studied by differential thermal analysis, x-ray analysis, and rheometrics mechanical spectroscopy. Thermal analysis showed that the resulting polymers follow melting-point-depression- and glass-transition-temperature-composition relationships expected of random copolymers. The lower first-order transition temperature [T(1)] disappears near equimolar substitution while the higher first-order transition temperature (T_m) persists over the whole range of compositions. X-ray analysis revealed that crystalline order in the polymer chain direction is destroyed by nearly equimolar substitution but lateral order remains. The rheological characterization of a copolymer with nearly equimolar substitution showed that the polymer is in a pseudocrosslinked state indicating the existence of chain-to-chain interactions. When a small amount of an antioxidant (6-dodecyl-1,2-dihydro-2,2,4-trimethylquinoline) is added, the lateral order of the copolymer is destroyed, and its rubbery plateau modulus decreases by several fold.