Quantum ground state isoperimetric inequalities for the energy spectrum of local Hamiltonians

We investigate the relationship between the energy spectrum of a local Hamiltonian and the geometric properties of its ground state. By generalizing a standard framework from the analysis of Markov chains to arbitrary (non-stoquastic) Hamiltonians we are naturally led to see that the spectral gap can always be upper bounded by an isoperimetric ratio that depends only on the ground state probability distribution and the range of the terms in the Hamiltonian, but not on any other details of the interaction couplings. This means that for a given probability distribution the inequality constrains the spectral gap of any local Hamiltonian with this distribution as its ground state probability distribution in some basis (Eldar and Harrow derived a similar result in order to characterize the output of low-depth quantum circuits). Going further, we relate the Hilbert space localization properties of the ground state to higher energy eigenvalues by showing that the presence of k strongly localized ground state modes (i.e. clusters of probability, or subsets with small expansion) in Hilbert space implies the presence of k energy eigenvalues that are close to the ground state energy. Our results suggest that quantum adiabatic optimization using local Hamiltonians will inevitably encounter small spectral gaps when attempting to prepare ground states corresponding to multi-modal probability distributions with strongly localized modes, and this problem cannot necessarily be alleviated with the inclusion of non-stoquastic couplings

Quantum information in the Posner model of quantum cognition

Matthew Fisher recently postulated a mechanism by which quantum phenomena could influence cognition: Phosphorus nuclear spins may resist decoherence for long times, especially when in Posner molecules. The spins would serve as biological qubits. We imagine that Fisher postulates correctly. How adroitly could biological systems process quantum information (QI)? We establish a framework for answering. Additionally, we construct applications of biological qubits to quantum error correction, quantum communication, and quantum computation. First, we posit how the QI encoded by the spins transforms as Posner molecules form. The transformation points to a natural computational basis for qubits in Posner molecules. From the basis, we construct a quantum code that detects arbitrary single-qubit errors. Each molecule encodes one qutrit. Shifting from information storage to computation, we define the model of Posner quantum computation. To illustrate the model's quantum-communication ability, we show how it can teleport information incoherently: A state's weights are teleported. Dephasing results from the entangling operation's simulation of a coarse-grained Bell measurement. Whether Posner quantum computation is universal remains an open question. However, the model's operations can efficiently prepare a Posner state usable as a resource in universal measurement-based quantum computation. The state results from deforming the Affleck-Kennedy-Lieb-Tasaki (AKLT) state and is a projected entangled-pair state (PEPS). Finally, we show that entanglement can affect molecular-binding rates, boosting a binding probability from 33.6% to 100% in an example. This work opens the door for the QI-theoretic analysis of biological qubits and Posner molecules.Comment: Published versio

Impacts of Federal Policies and Programs on Wetlands

Human activities have resulted in the loss of about half of the original 221 million acres of wetlands in the conterminous 48 states. Federal laws, policies, and programs have had major impacts on the nation's wetland resources. Initially, they encouraged and subsidized the draining and filling of wetlands, the flooding of wetlands behind dams, and the diversion and alteration of streamflows to riparian wetlands. More recently, federal policies have been directed to conserving and preventing further net losses. The focus of this study is on the impacts of federal policies on riparian wetlands, i.e., those formed at the interface of rivers and streams and uplands and that require occasional flooding to maintain the health of their ecosystems. The study identifies the trends in wetland acreage, describes the principal federal policies and programs impacting riparian wetlands, summarizes what is currently known or can be deduced from existing research about the impacts of these policies and programs on riparian wetlands, identifies key knowledge gaps, and suggests priorities for additional research. The policies that once directly and indirectly encouraged drainage of wetlands as well as water use and development practices harmful to wetlands have for the most part been abandoned. In some cases they have been replaced by new policies designed to protect the remaining wetlands and to encourage wetland restoration and creation. From the mid-1950s to the early 1990s conversion of wetlands to agriculture accounted for some 70 percent of total conversions. From 1982 to 1992, however, agriculture actually contributed a small net increase in the number of wetland acres. Changes in federal agricultural policies played a major role in this turn around. Overall, net wetland losses have been slowed but not ended since a "no net loss" policy was established in 1989. Several lines of research could contribute to the design and implementation of policies to achieve the "no net loss" goal. Research is needed to understand how farmers' incentives to convert wetlands to agricultural uses would be affected should Swampbuster become toothless as farm subsidies are eliminated or agricultural prices rise. And, if this analysis suggests wetland losses to agriculture would likely accelerate, alternative market-based and regulatory strategies for curbing these losses should be examined. As wetlands are lost to development and other pressures, achieving the no net loss goal requires that these losses be compensated. Research on the physical characteristics and the ability of different wetlands to provide social values such as fish and wildlife habitat, retention of flood waters, and water quality improvements would provide a better basis for determining how much society should invest in protecting, enhancing, restoring, or creating wetlands and whether these investments adequately compensate for the functions of lost wetlands. Research also is needed to determine how mitigation banking might be made more efficient and effective in ensuring social values are adequately compensated when wetlands are lost.

Effect of concentrate feeding level in winter and turnout date to pasture in spring on biological and economical performance of weanling cattle in suckler beef production systems

peer-reviewedThree experiments were carried out to determine the effects of supplementary concentrate feeding level (Low, LC; High, HC) to grass silage and/or turnout date to pasture in spring (Early, ET; Late, LT) for a second grazing season on performance to slaughter of spring-born, weaned beef calves (n = 188). Experiment 1 comprised of two concentrate levels (0.5 and 1.5 kg/day). Experiment 2 comprised of two turnout dates (19 March, 9 April). Experiment 3 comprised of two concentrate levels (0.5 kg and 2.0 kg/day) and two turnout dates (22 March, 12 April). In Experiment 1, live-weight gain during the indoor winter period was 25 kg higher (P 0.05) total live-weight gain for both treatments. In Experiment 2, live weight at turnout to pasture was 11 kg lower (P 0.05), subsequently. In Experiments 1 and 2, live-weight gain during the finishing period and carcass weight, conformation and fat scores did not differ (P > 0.05) between the treatments. In Experiment 3, at turnout to pasture, HC were 35 kg heavier (P < 0.001) than LC, and ET were 12 kg lighter (P < 0.05) than LT, whereas 8 days after late turnout, ET were 13 kg heavier (P < 0.05) than LT. There was a concentrate level × turnout date interaction (P < 0.05) for live weight at the end of the grazing season, whereby the LC, LT treatment were lighter than the other treatments, which did not differ. Live weight at slaughter and carcass weight did not differ (P > 0.05) between the concentrate levels, whereas they were higher (P < 0.05) for ET than LT. Economic and stochastic analysis of Experiment 3 indicated that, in the context of whole-farm systems, (i) feeding HC was dependent on date of sale such that only where progeny were sold at the start of the second grazing season, net farm margin (NFM) was increased, (ii) ET only increased NFM where progeny were retained through to finish and, (iii) taking progeny through to finish was more profitable than selling earlier in the animals’ lifetime. In conclusion, subsequent compensatory growth at pasture diminishes the growth and economic advantage from concentrate supplementation or early turnout to pasture, of young late-maturing cattle

Bioeconomic modelling of male Holstein-Friesian dairy calf-to-beef production systems on Irish farms

peer-reviewedWith the abolition of milk quota in 2015 and increase in the use of Holstein-Friesian sires in recent years there is predicted to be an increase in the number of male Holstein-Friesian animals available for beef production. In broad terms, farmers have two options for finishing these animals; as bulls or steers. In either case, Irish beef cattle systems are based on maximising lifetime live-weight gain from grass-based diets. Managing the relationship between the supply and demand for grazed grass is complicated in these pasture-based systems due to the seasonal variability in grass growth. The Grange Dairy Beef Systems Model (GDBSM) was used to simulate the relationship between grazed grass supply and demand and then determine the profitability of Holstein-Friesian male animals finished as bulls at 16 (B16), 19 (B19) and 22 (B22) months of age and steers at 24 (S24) months of age. Combinations of these cattle finishing options were also evaluated. The most profitable system was S24. All systems were very sensitive to variations in beef and concentrate prices and less sensitive to calf price changes with fertiliser price changes having very little effect. Bull systems were more sensitive than the steer system to variation in beef, calf and concentrate prices. There was no advantage of combination systems in terms of utilisation of grass grown or net margin

The impact of livestock and fisheries on food availability and demand in 2020

People in developed countries consume about 3 to 4 times as much meat and fish, and 5 to 6 times as much milk products per capita as in developing Asia and Africa. Yet, meat, milk, and fish consumption per capita has barely grown in the developed countries as a whole over the past 20 years. Growth in per capita consumption and production has occurred in developing regions such as developing Asia, where income has increased from a low level and urbanization is rapid. By 2020, according to projections by IFPRI's IMPACT model, the share of the developing countries in total world meat consumption will rise from 47 percent currently to 64 percent. The net impact on food access for the poor of the world will depend on their role as producers of meat, milk, and fish, their role as consumers, and their need for protein. The amount of cereals per capita consumed directly by rural people will decline as they diversify their diets into animal proteins, but feed use will increase greatly. Available evidence suggests that on balance poor consumers in developing countries will probably be better off.Livestock productivity Sudan. ,Fishery production. ,Food consumption Developing countries. ,Food consumption forecasting. ,

Good approximate quantum LDPC codes from spacetime circuit Hamiltonians

We study approximate quantum low-density parity-check (QLDPC) codes, which are approximate quantum error-correcting codes specified as the ground space of a frustration-free local Hamiltonian, whose terms do not necessarily commute. Such codes generalize stabilizer QLDPC codes, which are exact quantum error-correcting codes with sparse, low-weight stabilizer generators (i.e. each stabilizer generator acts on a few qubits, and each qubit participates in a few stabilizer generators). Our investigation is motivated by an important question in Hamiltonian complexity and quantum coding theory: do stabilizer QLDPC codes with constant rate, linear distance, and constant-weight stabilizers exist? We show that obtaining such optimal scaling of parameters (modulo polylogarithmic corrections) is possible if we go beyond stabilizer codes: we prove the existence of a family of $[[N,k,d,\varepsilon]]$ approximate QLDPC codes that encode $k = \widetilde{\Omega}(N)$ logical qubits into $N$ physical qubits with distance $d = \widetilde{\Omega}(N)$ and approximation infidelity $\varepsilon = \mathcal{O}(1/\textrm{polylog}(N))$. The code space is stabilized by a set of 10-local noncommuting projectors, with each physical qubit only participating in $\mathcal{O}(\textrm{polylog} N)$ projectors. We prove the existence of an efficient encoding map, and we show that arbitrary Pauli errors can be locally detected by circuits of polylogarithmic depth. Finally, we show that the spectral gap of the code Hamiltonian is $\widetilde{\Omega}(N^{-3.09})$ by analyzing a spacetime circuit-to-Hamiltonian construction for a bitonic sorting network architecture that is spatially local in $\textrm{polylog}(N)$ dimensions.Comment: 51 pages, 13 figure