Chapter 2 serves as a primer on quantum mechanics tailored for quantum computing. It reviews essential concepts such as quantum states, operators, superposition, entanglement, and the probabilistic nature of quantum measurements. This chapter focuses on two-level quantum systems (i.e. qubits). Mathematical formulations that are specific to quantum mechanics are introduced, such as Dirac (bra–ket) notation, the Bloch sphere, density matrices, and Kraus operators. This provides the reader with the necessary tools to understand quantum algorithms and the behaviour of quantum systems. The chapter concludes with a review of the quantum harmonic oscillator, a model to describe quantum systems that are complementary to qubits and used in some quantum computer implementations.

This chapter explores the origin, key components, and essential concepts of quantum computing. It begins by charting the series of discoveries by various scientists that crystallized into the idea of quantum computing. The text then examines how certain applications have driven the evolution of quantum computing from a theoretical concept to an international endeavour. Additionally, the text clarifies the distinctions between quantum and classical computers, highlighting the DiVincenzo criteria, which are the five criteria for quantum computing. It also introduces the circuit model as the foundational paradigm for quantum computation. Lastly, the chapter sheds light on the reasons for the belief that quantum computers are more powerful than classical ones (touching on quantum computational complexity) and physically realizable (touching on quantum error correction).

The third chapter examines the capabilities of liquid-state NMR systems for quantum computing. It begins by grounding the reader in the basics of spin dynamics and NMR spectroscopy, followed by a discussion on the encoding of qubits into the spin states of the nucleus of atoms inside molecules. The narrative progresses to describe the implementation of single-qubit gates via external magnetic fields, weaving in key concepts such as the rotating-wave approximation, the Rabi cycle, and pulse shaping. The technique for orchestrating two-qubit gates, leveraging the intrinsic couplings between the spins of nuclei of atoms within a molecule, is subsequently detailed. Additionally, the chapter explains the process of detecting qubits’ states through the collective nuclear magnetization of the NMR sample and outlines the steps for qubit initialization. Attention then shifts to the types of noise that affect NMR quantum computers, shedding light on decoherence and the critical T1 and T2 times. The chapter wraps up by providing a synopsis, evaluating the strengths and weaknesses of liquid-state NMR for quantum applications, and a note on the role of entanglement in quantum computing.

The final chapter details some methods for evaluating the performance of quantum computers. It begins by delineating the essential features of quantum benchmarks and organizes them into a three-tiered framework. Initially, it discusses early-stage benchmarks that provide a detailed analysis of basic operations on a few qubits, emphasizing fidelity tests and tomography. Then, it progresses to intermediate-stage benchmarks that provide a more generalized appraisal of gate quality, circuit depth, and length. Concluding the benchmarking spectrum, later-stage benchmarks are introduced, aimed at evaluating the overall reliability and efficiency of quantum computers operating with a large number of qubits (e.g. 1000 or more).

Ecosystem structure and functioning is the focus of much ecological research because many ecosystem properties such as production, energy flow, nutrient cycles, and stability lie at the core of understanding ecological processes. Net primary production (NPP) is primarily influenced by climate and nutrients. On a global scale, NPP in terrestrial biomes tends to be greatest near the tropics, where the combination of constant and moderately high temperature and adequate rainfall promote plant growth. NPP in marine biomes peaks at about 40° S latitude, which is associated with large areas of upwelling and high nutrient availability. On a regional and local scale, the availability of nutrients such as nitrogen and phosphorus influence terrestrial, marine, and freshwater production. Ecosystem structure is based on the interactions between producers, consumers, detritivores, and decomposers. A substantial but variable amount of energy is lost with each transfer from one trophic level to the level above, which has the effect of limiting food chain length (FCL). In some aquatic systems, longer food chains are associated with CO2 export from the water into the atmosphere, and with the biomagnification of toxic substances.

Anthropologist Richard Leakey sent Jane Goodall to Gombe (now Gombe Stream National Park) to study chimpanzees in the wild. As an anthropologist, he was keenly interested in human behavior, and believed that chimpanzees would provide a window to understanding it. It took Goodall six months of crawling around in the woods before any chimpanzees would allow her to get close enough to observe them. But her persistence paid off, as she was able to document chimpanzees showing some very human behavior including tool making, cooperative hunting and war making. Partway through her career, she elected to devote the rest of her career to environmental activism and education, and Gombe research was continued by a growing community of researchers including her student, Anne Pusey. Pusey was fascinated by mother–infant relationships, by developmental changes in juveniles as they matured, and by how chimpanzees manage to avoid breeding with close relatives. Other researchers at Gombe studied the relationship between rank and reproductive success, and how disease was influencing survival rates in three different populations in the region. Unfortunately, life table studies indicate that disease and a lack of immigrants into the region are threatening the viability of this iconic group of chimpanzees.

A species’ behavioral, developmental, and reproductive life history will influence how quickly it can recover after a population crash. Some species can recover very quickly, while others, such as the North Atlantic right whale, cannot recover quickly, because even under ideal conditions they develop slowly and have very low reproductive rates. Ecologists have described various life history classification schemes that identify important tradeoffs in resource allocation, and focus attention on interesting life history questions. The quantitative relationship between metabolic rate and body size can help ecologists understand some life history tradeoffs, such as the relationship between number and size of offspring. There is a fundamental tradeoff between parental investment in any one reproductive event and the number of lifetime reproductive events, which in some cases can lead to a semelparous reproductive life history. Variable environments can select for phenotypic plasticity, which can lead to organisms with similar genotypes expressing alternative behavioral, developmental or reproductive life history traits. In some cases, phenotypic plasticity may help species adjust to rapidly changing environmental conditions, including climate change.

Organisms may compete for a great variety of limiting resources, such as food and habitat and, in the case of plants, light and pollinators. Direct mechanisms of competition, as highlighted by interactions between yellow crazy ants and hermit crabs on Tokelau, include resource and interference competition, while indirect mechanisms of competition that are mediated by other species are also widespread in ecological communities. Introductions of species into novel environments allow ecologists to study competitive interactions in real time. Interspecific competition can lead to competitive exclusion when two or more species occupy similar niches. A variable environment, niche shift, and niche partitioning can promote species coexistence. Theoretical models, such as the Lotka–Volterra competition model, help identify conditions in which two or more competing species can coexist. When conservation ecologists introduce two or more species as biological control agents, they must consider potential competitive interactions among the introduced species, keeping in mind the factors that promote the coexistence of the introduced species.

Humans have profoundly changed nutrient cycles on a global, regional, and local level. Agricultural runoff carrying heavy loads of nitrogen and phosphorus compounds caused eutrophication of the Black Sea. This led to a series of events that culminated in the annual formation of a dead zone within the Black Sea, and the consequent loss of biological diversity of several trophic levels. The nitrogen cycle depends heavily on the activities of microorganisms to fix nitrogen, and to transform nitrogen in the processes of nitrification, ammonification, denitrification, and anammox. Technological advances such as the Haber–Bosch process have vastly increased the amount of reactive nitrogen entering ecosystems, leading to increases in agricultural production, but also polluting many aquatic systems. The phosphorus cycle is similar to the nitrogen cycle, in that globally there are vast stores of phosphorus compounds, but most of it is inaccessible to organisms. In contrast to the nitrogen cycle, there is only a small atmospheric component to the phosphorus cycle; most phosphorus becomes available through weathering of rocks. Both nutrient cycles are similar in one very important way; nitrogen and phosphorus are recycled many times between organisms and the environment before exiting an ecosystem.

Dan Janzen and Winnie Hallwachs, his wife and colleague, have spent two lifetimes studying ecological interactions between organisms, mostly at Area de Conservacion Guanacaste (ACG) in northwestern Costa Rica. Early in his career, Janzen investigated many basic questions in evolutionary community ecology. One study of plant reproductive success and life history strategies showed that legume species use one of two alternative strategies to reproduce successfully – producing huge numbers of tiny defenseless seeds or small numbers of large, well-defended seeds. A second study explained high biological diversity in rainforests as arising because baby plants survive poorly near their parents (because seed predators consume them there), and only become established a considerable distance away from them. He also emphasizes that current selection pressures may differ from historical pressures, so it is critical to understand ecosystems in the context of their evolutionary history. Both Janzen and Hallwachs have now shifted their focus to inventorying the diversity of Lepidoptera, their parasitoids and host plants at ACG, so that their complex interactions can be understood by researchers and by students who use ACQ as a natural classroom.