Composability of global phase invariant distance and its application to approximation error management

Many quantum algorithms can be written as a composition of unitaries, some of which can be exactly synthesized by a universal fault-tolerant gate set like Clifford+T, while others can be approximately synthesized. A quantum compiler synthesizes each approximately synthesizable unitary up to some approximation error, such that the error of the overall unitary remains bounded by a certain amount. In this paper we consider the case when the errors are measured in the global phase invariant distance. Apart from deriving a relation between this distance and the Frobenius norm, we show that this distance composes. If a unitary is written as a composition (product and tensor product) of other unitaries, we derive bounds on the error of the overall unitary as a function of the errors of the composed unitaries. Our bound is better than the sum-of-error bound, derived by Bernstein- Vazirani(1997), for the operator norm. This builds the intuition that working with the global phase invariant distance might give us a lower resource count while synthesizing quantum circuits. Next we consider the following problem. Suppose we are given a decomposition of a unitary, that is, the unitary is expressed as a composition of other unitaries. We want to distribute the errors in each component such that the resource-count (specifically T-count) is optimized. We consider the specific case when the unitary can be decomposed such that the $R_z(\theta)$ gates are the only approximately synthesizable component. We prove analytically that for both the operator norm and global phase invariant distance, the error should be distributed equally among these components(given some approximations) . The optimal number of T-gates obtained by using the global phase invariant distance is less. Furthermore, for approx-QFT the error due to pruning of rotation gates is less when measured in this distance.

Quantitative towers in finite difference calculus approximating the continuum

Multivector fields and differential forms at the continuum level have respectively two commutative associative products, a third composition product between them and various operators like $\partial$, d and ‘*’ which are used to describe many nonlinear problems. The point of this paper is to construct consistent direct and inverse systems of finite dimensional approximations to these structures and to calculate combinatorially how these finite dimensional models differ from their continuum idealizations. In a Euclidean background, there is an explicit answer which is natural statistically.

Sharp Bounds on the Augmented Zagreb Index of Graph Operations

Let G be a finite and simple graph with edge set E(G). The augmented Zagreb index of G is ( ) ∑ dG (u )dG (v) 3 AZI (G ) = ---------------------- , dG (u ) + dG (v) − 2 uv∈E(G ) where dG(u) denotes the degree of a vertex u in G. In this paper, we give some bounds of this index for join, corona, cartesian and composition product of graphs by general sum-connectivity index and general Randić index and compute the sharp amount of that for the regular graphs.

STUDIES ON THE QUALITATIVE INDICATORS OF AFRICAN OSTRICH HAM WITH VEGETABLE ENZYMES

Expanding the food products range is one of the most promising challenges in the food industry today. The production of whole meat products has always determined the technological level of the enterprise, reflecting its ability to improve consumer nutrition. Using the same type of raw meat, by changing the modes and conditions of its preparation, impact on the tissue structure, directional autolysis and variation of thermal processes, they produce products with different nutritional characteristics. Research of chemical composition has established that penetration of salting active substances into the meat fabrics and their interaction with proteins changes physical and chemical composition of a product, determining the basic properties of salted meat (swelling, consistence, viscosity, etc.). Change in meat proteins during salting is accompanied by an increase in bound moisture in the product and causes an increase in a product yield. The protein content in the control sample is 26.17 %, in the experimental samples № 1, 2 - 26,88 -27,64 % due to the introduction of a functional additive and plant enzyme papain, which has a positive effect on the taste of the developed semi-finished products and makes them more juicy. Organoleptic evaluation of products is important in determining the quality of meat products, since a person's reaction depends on the appearance, color, smell, taste, consistency of the finished product. It has been established that organoleptic characteristics of meat products vary depending on the chemical composition, product, degree of biochemical changes (meat maturation), technological processing (cooking, smoking, etc.), the use of spices, food and flavorings. Results of the study on the organoleptic parameters show that the use of the enzyme papain improves the taste and aroma, as the experimental sample differs from the control one with increased juiciness and tenderness, without foreign odors and tastes.

The knot Floer cube of resolutions and the composition product

We examine the relationship between the oriented cube of resolutions for knot Floer homology and HOMFLY-PT homology. By using a filtration induced by additional basepoints on the Heegaard diagram for a knot [Formula: see text], we see that the filtered complex decomposes as a direct sum of HOMFLY-PT complexes of various subdiagrams. Applying Jaeger’s composition product formula for knot polynomials, we deduce that the graded Euler characteristic of this direct sum is the HOMFLY-PT polynomial of [Formula: see text].

Coarse indices of twisted operators

Several formulas for computing coarse indices of twisted Dirac type operators are introduced. One type of such formulas is by composition product in [Formula: see text]-theory. The other type is by module multiplications in [Formula: see text]-theory, which also yields an index theoretic interpretation of the duality between Roe algebra and stable Higson corona.

IbM-JOINT BUSINESS GROUP"PASTRIES BEPANG OR RENCINA AND OTHER TRADITIONAL CAKES"

The joint group of pastries "Bepang or Rencina and other Traditional Cakes" is a business group that is home industry. The main problem of this business is that the product is still large, so it is not interesting to see or to eat it. In addition there is no packing system or packaging that meets the standards of quality marketing, so the product quickly damaged. Other things labeling products have not written down the name of the product, without any expiration date, product composition, product superiority, name making and so on. Another problem faced is the marketing of its products. Previously traded transactions can only be done by face-to-face, while it opens the opportunity to sell over the phone, and even now is very easy and often done via the Internet, such as in facebook account, twitter and others for promotion. Implementation of IbM program is implemented as an effort to empower the KUBE group in the field of entrepreneurship and product marketing through training activities that focuses on business development and marketing. Methods of program implementation that will be conducted are: (1) business management training, (2) Business marketing training, (3) and (4) assistance. All of these methods are a unity of this IbM program. The strategic target audience in this activity is the community of Joint Business Group belonging to the form of business of bepang pastry (rencina) and other wet cakes located in Karondoran Village, East Langowan District, Minahasa Regency. The number of trainees is 20 people. The results of the training activities conducted are very positively responded because it is closely related to their daily activities, so that felt is a major requirement. After implementing community service in the form of training, the joint venture groups have been successfully motivated entrepreneurship so as to be able to prepare a business plan, forming the organizational structure of the business group together, making a simple product packaging design. Keywords:IbM, Joint Business Group

Corporate Investment and Innovation in the Presence of Competitor Constraints

We study the relation between investment behavior and competitor financial constraints. Using interfirm patent citations and text-based product market similarities to identify intransitive competitor networks, we find that firms increase investment spending, patenting activity, and opportunistic hiring when competitor constraints become more binding. In addition, firms shift their investment composition (product market and patent portfolios) to compete more aggressively with relatively constrained competitors. To mitigate endogeneity concerns, we exploit the 2004 AJCA tax holiday and the 1989 junk bond crisis as exogenous shocks to competitor constraints, and we find similar effects. Received August 11, 2017; editorial decision November 6, 2018 by Editor David Denis. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.