Ground State Spin Logic

Designing and optimizing cost functions and energy landscapes is a problem encountered in many fields of science and engineering. These landscapes and cost functions can be embedded and annealed in experimentally controllable spin Hamiltonians. Using an approach based on group theory and symmetries, we examine the embedding of Boolean logic gates into the ground state subspace of such spin systems. We describe parameterized families of diagonal Hamiltonians and symmetry operations which preserve the ground state subspace encoding the truth tables of Boolean formulas. The ground state embeddings of adder circuits are used to illustrate how gates are combined and simplified using symmetry. Our work is relevant for experimental demonstrations of ground state embeddings found in both classical optimization as well as adiabatic quantum optimization.Comment: 6 pages + 3 pages appendix, 7 figures, 1 tabl

Community Detection in Quantum Complex Networks

Determining community structure is a central topic in the study of complex networks, be it technological, social, biological or chemical, in static or interacting systems. In this paper, we extend the concept of community detection from classical to quantum systems---a crucial missing component of a theory of complex networks based on quantum mechanics. We demonstrate that certain quantum mechanical effects cannot be captured using current classical complex network tools and provide new methods that overcome these problems. Our approaches are based on defining closeness measures between nodes, and then maximizing modularity with hierarchical clustering. Our closeness functions are based on quantum transport probability and state fidelity, two important quantities in quantum information theory. To illustrate the effectiveness of our approach in detecting community structure in quantum systems, we provide several examples, including a naturally occurring light-harvesting complex, LHCII. The prediction of our simplest algorithm, semiclassical in nature, mostly agrees with a proposed partitioning for the LHCII found in quantum chemistry literature, whereas our fully quantum treatment of the problem uncovers a new, consistent, and appropriately quantum community structure.Comment: 16 pages, 4 figures, 1 tabl

Chiral Quantum Walks

Given its importance to many other areas of physics, from condensed matter physics to thermodynamics, time-reversal symmetry has had relatively little influence on quantum information science. Here we develop a network-based picture of time-reversal theory, classifying Hamiltonians and quantum circuits as time-symmetric or not in terms of the elements and geometries of their underlying networks. Many of the typical circuits of quantum information science are found to exhibit time-asymmetry. Moreover, we show that time-asymmetry in circuits can be controlled using local gates only, and can simulate time-asymmetry in Hamiltonian evolution. We experimentally implement a fundamental example in which controlled time-reversal asymmetry in a palindromic quantum circuit leads to near-perfect transport. Our results pave the way for using time-symmetry breaking to control coherent transport, and imply that time-asymmetry represents an omnipresent yet poorly understood effect in quantum information science.Comment: 9 pages, 4 figures, REVTeX 4.1 - published versio

Effects of different diet alternatives to replace the use of pharmacological levels of zinc on growth performance and fecal dry matter of weanling pigs

A total of 300 weanling pigs (Line 400 × 200, DNA, Columbus, NE, initially 4.83 kg) were used in a 46-d trial to evaluate the effects of different nutritional strategies to replace pharmacological levels of Zn, provided by zinc oxide (ZnO), in nursery diets on growth performance and fecal dry matter (DM). Six treatments with 10 replicate pens per treatment and 5 pigs per pen were used. Diets consisted of: (1) positive control (ZnO providing 3,000 mg/kg added Zn from d 0 to 7 and 2,000 mg/kg added Zn from d 8 to 25 and 21% crude protein, CP); (2) negative control (NC; no added ZnO); (3) NC plus 1.2% Na diformate; (4) NC with 4% coarse ground wheat bran; (5) NC but formulated to 18% CP; and (6) the combination of NC with 18% CP, 1.2% Na diformate, and 4% coarse ground wheat bran. The diets formulated to 18% CP contained 1.2% standardized ileal digestible (SID) Lys from d 0 to 25, whereas the 21% CP diets contained 1.4% SID Lys from d 0 to 7 and 1.35% SID Lys from d 7 to 25. From d 25 to 46, all pigs were fed a common diet. From d 0 to 7, no differences in any variables were observed between treatments. From d 7 to 25, pigs fed the diet with added ZnO had greater (P < 0.01) average daily gain (ADG) and average daily feed intake (ADFI) than all other treatments. Pigs fed the diet formulated to 18% CP had decreased (P < 0.01) ADG when compared with pigs fed the other diets. From d 25 to 46, no previous treatment effects on ADG or gain to feed ratio (G:F) were observed. Overall (d 0 to 46), pigs fed the diet with added ZnO from d 0 to 25 had greater (P < 0.01) ADG, ADFI, and final body weight than pigs fed added Na Diformate, or 4% coarse ground wheat bran, or with the 18% CP diet, or with pigs fed the combination of the additives intermediate. There was no evidence for differences in overall G:F. Pigs fed the NC diet had the lowest fecal DM and highest fecal scores (P < 0.05), indicating the greatest incidence of loose stools. Pigs fed added ZnO had greater fecal DM than pigs fed the NC, 4% added wheat bran, or 18% CP diets, or with pigs fed the combination of additives intermediate (P < 0.01). These results suggest that adding pharmacological levels of Zn from ZnO improves nursery pig performance and increases DM content of feces when compared with pigs fed diets with either Na diformate, 4% course wheat bran, or 18% CP alone. However, a combination of all three alternatives appeared to be additive and partially restored growth performance similar to adding pharmacological levels of Zn

Exploring the “Middle Earth” of network spectra via a Gaussian matrix function

We study a Gaussian matrix function of the adjacency matrix of artificial and real-world networks. We motivate the use of this function on the basis of a dynamical process modeled by the time-dependent Schrodinger equation with a squared Hamiltonian. In particular, we study the Gaussian Estrada index - an index characterizing the importance of eigenvalues close to zero. This index accounts for the information contained in the eigenvalues close to zero in the spectra of networks. Such method is a generalization of the so-called "Folded Spectrum Method" used in quantum molecular sciences. Here we obtain bounds for this index in simple graphs, proving that it reaches its maximum for star graphs followed by complete bipartite graphs. We also obtain formulas for the Estrada Gaussian index of Erdos-Renyi random graphs as well as for the Barabasi-Albert graphs. We also show that in real-world networks this index is related to the existence of important structural patters, such as complete bipartite subgraphs (bicliques). Such bicliques appear naturally in many real-world networks as a consequence of the evolutionary processes giving rise to them. In general, the Gaussian matrix function of the adjacency matrix of networks characterizes important structural information not described in previously used matrix functions of graphs

A Survey of Added Vitamins and Trace Minerals in Diets Utilized in the U.S. Swine Industry

From November 2021 to February 2022, 37 swine nutritionists representing 29 production systems and 8 nutrition supplier companies in the United States were surveyed about added vitamins and trace mineral concentrations in swine diets. Respondents were asked to provide vitamin and trace mineral inclusion rates, weight ranges associated with each dietary phase, and number of sows utilizing their nutritional recommendations. Survey participants represented 4.38 million sows, or 72% of the U.S. industry. Data were compiled into 3 nursery phases (weaning to 15 lb; 15 to 25 lb; and 25 to 50 lb), 3 finishing phases (50 to 120; 120 to 220; and 220 lb to market), gilt development, gestation, lactation, and boar diets. Within each dietary phase, the vitamins and trace minerals of interest included: vitamin A, vitamin D, vitamin E, vitamin K, thiamin, riboflavin, niacin, pantothenic acid, pyridoxine, biotin, folic acid, vitamin B12, choline, vitamin C, carnitine, copper, iodine, iron, manganese, selenium, zinc, cobalt, and chromium. Descriptive statistics used included: average, weighted average (determined by the total number of sows), median, minimum, maximum, 25th percentile (lowest quartile), and 75th percentile (highest quartile). In addition, all average vitamin and trace mineral concentrations within each phase of production were compared to the requirement estimates reported in the NRC. The results of this survey follow similar trends observed in a previous survey in 2016. Nutritionists generally supplemented vitamins and trace minerals well above the NRC (2012) requirements. However, greater variation among respondents was observed in all vitamins and trace minerals, particularly in the fat soluble vitamins. Also, the use of alternative sources of vitamin D (25-OH-D3), E (natural, d-alpha-tocopherol), and organic or chelated minerals like copper, manganese, selenium, and zinc is becoming more frequent. In addition, comparisons to the most recent NRC (2012) requirement estimates highlight the necessity of future research to better understand vitamin and trace mineral requirements in swine diets

Effects of Increasing Levels of Soybean Meal in Nursery Diets on Growth Performance and Fecal Characteristics of 22- to 60-lb Pigs

Two experiments were conducted to determine the effects of increasing soybean meal (SBM) on late nursery pig performance. In Exp. 1, a total of 266 pigs (241 × 600 DNA; initially 22.2 ± 0.37 lb) were used in a 21-d trial with 14 replicate pens per treatment and 4 to 5 pigs per pen. Pens of pigs were randomly assigned to 1 of 4 dietary treatments which were corn-based with SBM levels of 25.0, 28.9, 32.5, or 36.2%. In Exp. 2, a total of 340 pigs (241 × 600 DNA; initially 29.8 ± 0.40 lb) were used in a 21-d trial with 14 replicate pens per treatment and 4 to 5 pigs per pen. Pens of pigs were randomly assigned to 1 of 5 dietary treatments which were corn-based with SBM levels of 25.0, 28.9, 32.5, or 36.2, or 40.0%. In both experiments, at weaning, pigs were distributed into pens based on body weight, gender, sow parity, and age. Before the start of the experimental period, pigs were fed a phase 1 followed by a phase 2 control diet. After 21 and 26 d for Exp. 1 and 2, respectively, pens of pigs were randomly allotted to treatments in a randomized complete block design with BW as the blocking factor. An addition of SBM replaced feed-grade amino acids (AAs) to form experimental diets and all diets were formulated to be nearly isocaloric with SBM NE considered to be 100% of corn NE. Dietary additions of feed-grade AA were adjusted to meet or exceed AA requirements in relation to Lys for Ile, Met, Cys, Thr, Trp, and Val. Diets were fed in meal form. In Exp. 1, increasing SBM from 25.0 to 36.2%, decreased ADG (linear, P = 0.012), ADFI (linear, P \u3c 0.001), and final BW (linear, P = 0.021) with the greatest change occurring when SBM increased from 28.9 to 32.5%. No evidence for difference was observed for F/G (P = 0.729). In Exp. 2, starting with a heavier initial weight, increasing SBM from 25.0 to 40.0%, decreased ADFI (linear, P = 0.017) with the greatest change occurring when SBM increased from 32.5 to 36.2%. However, no evidence for difference (P ≥ 0.198) was observed for ADG, final BW, and F/G. This study showed that when pigs were fed high levels of SBM starting from 22 lb in the nursery period, pig performance was negatively affected. However, delaying the use of elevated SBM levels until pigs reach 30 lb resulted in reduced feed intake without impacting growth or feed efficiency. Thus, feeding up to 28.9% SBM for nursery pigs starting at 22 lb does not compromise performance, and starting pigs on higher SBM diets when pigs are closer to 30 lb did not affect ADG or F/G

Effects of Increasing Soybean Meal Levels on Growth Performance and Carcass Characteristics of Pigs in Grower and Late-Finishing Phases

Four experiments were conducted to determine the effects of increasing soybean meal (SBM) on grower and late-finishing pig performance. In Exp. 1, a total of 615 pigs (initially 95.2 ± 1.51 lb) were used in a 28-d trial with 14 replicate pens per treatment and 8 to 10 pigs per pen. Pens of pigs were randomly assigned to 1 of 5 dietary treatments which were corn-based with soybean meal levels of 19.1, 22.6, 26.3, 29.9, or 33.5%. In Exp. 2, a total of 615 pigs (initially 225.5 ± 3.42 lb) were used in a 30-d trial with 14 replicate pens per treatment and 8 to 10 pigs per pen. Pens of pigs were randomly assigned to 1 of 5 dietary treatments which were corn-based with soybean meal levels of 11.2, 14.2, 17.2, 20.2, or 23.2%. In both experiments, treatments were assigned in a completely randomized design and soybean meal inclusion was increased, replacing feed grade amino acids to form the treatments. For Exp. 1, increasing SBM increased (linear, P = 0.038) ADG and improved (P \u3c 0.001) feed efficiency, with the greatest change from increasing SBM from 19.1 to 22.6%. For late-finishing pigs (Exp. 2), no differences (P \u3e 0.10) were observed for any growth performance or carcass criteria. Experiments conducted in a second series were conducted with the same basic procedures as Exp. 1 and 2, but all diets contained DDGS, and were conducted in a commercial facility. In Exp. 3, a total of 1,080 pigs (initially 86.1 ± 1.72 lb) were used in a 28-d trial with 10 replicate pens per treatment and 27 pigs per pen. Pens of pigs were assigned to 1 of 4 dietary treatments which were corn-20% DDGS-based and soybean meal was added at 18.2, 23.5, 28.9, or 34.3%. For Exp. 4, a total of 1,080 pigs (initially 225.2 ± 2.50 lb) were used in a 33-d trial with 10 replicate pens per treatment and 27 pigs per pen. Pens of pigs were assigned to 1 of 4 dietary treatments which were corn-10% DDGS-based with soybean meal levels of 9.5, 13.5, 17.5, or 21.5%. When DDGS was included in the diet, no differences (P \u3e 0.10) were observed for any growth performance criteria for early- or late-finishing pigs. In conclusion, increasing levels of SBM (up to 33.5% of the diet) in grower pig diets linearly improved ADG and feed efficiency in corn-soybean meal-based diets. However, when DDGS was included in the diet, pig performance was not affected when SBM ranged from 18.2 to 34.3%. For late-finishing pig diets, increasing the SBM from approximately 10 to 23% in diets with or without DDGS did not result in any changes in growth and carcass parameters. These results suggest that high levels of SBM in the diet (no feed-grade amino acids) are well tolerated and do not negatively affect pig growth