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).

Right after the 1965 discovery of the CMB, F. Hoyle and his student J.N. Narlikar constructed a new version of the steady-state model, starting with Hoyle’s matter creation scalar field, and this model is the focus of the chapter. The creation of matter in the pockets near massive objects violated earlier adherence to inhomogeneity. The 1972 version of the model introduced an intriguing explanation of the CMB as a radiating of the boundary between the regions of the universe with positive and negative mass: any amount of matter entering such a boundary will act as a perfect thermalizer, with radiation of 3 kelvin reaching us from all directions. It was perhaps the first worked out model of the multi-universe. Hoyle and Narlikar argued for perfect thermalization, implying a black body spectrum. In this, their model was unlike many other unorthodoxies motivated by the erroneous measurements of 1979 indicating disagreement with the shape of the spectrum.

The pion, the mediator of the nuclear force proposed in 1935 by Yukawa. The first particle discovered in the cosmic rays looked like the pion, but was later found to be a lepton, the muon. Experiments at high altitudes on cosmic rays led finally to the discovery of the pion. More experiments soon showed other surprises, the strange particles.

How the properties of the charged pion have been measured.

The discoveries of the charged leptons and of the neutrinos.

How, in 1928, A. M. Dirac found the fundamental relativistic wave equation and the Dirac Lagrangian. Dirac’s fundamental predictions of the existence for each fermion of an antiparticle with the same mass but opposite ‘charges’. How the positron and the antiproton were discovered. The important concepts of helicity and chirality.

The Majorana equation for completely neutral fermions.