Several other technologies under development to exploit quantum power are discussed in this chapter. You will learn about quantum key distribution; improving measurements of phase shifts is used as an example to demonstrate the power of entanglement in beating the standard quantum limit. How the latter is used to improve detection of objects is also discussed. Finally, modelling complicated quantum systems by designing simpler and easier to control systems, represented by quantum circuits, simplifies the studying of such systems, allowing us to gain better insight into their physics and to make better predictions about them.

Quantum computing technology was born in the 1970s and 1980s when a handful of visionary thinkers such as Paul Benioff, Richard Feynman, and David Deutsch first speculated about how the precepts of quantum mechanics might impact computer science. In 1984 Gilles Brassard, a computer scientist and cryptographer, and Charles Bennett, a specialist in physics and information theory, devised a practical application for quantum mechanics in the field of secure communication.

Here we build the skills needed to master how a quantum computer can factor very large numbers much more efficiently than a classical computer; i.e., it is a chapter dedicated to Shor’s algorithm. The Fourier transform, and its quantum analogue are introduced and applied to period finding. These are then applied to show how the problem of factoring large numbers amounts to finding the period of a modular exponential function. Moreover, the consequences of such a capability on the everyday security in (internet) communications using RSA encryption is also discussed.

The origin of decoherence of qubits is described by a simple example, and the two key methods to defeat decoherence, namely decoherence-free spaces and error-correcting codes are introduced.

Here we discuss some of the interesting paradigm shifts that have been proposed for quantum computers: namely, using pseudo-pure states, cluster states, and non-deterministic gates.

After discussing the divorce of configuration and observable that is characteristic of the quantum description of reality, the reader is introduced to the awesome potential computational power that is afforded by quantum computation.

This chapter delves into the application of trapped ions in electromagnetic fields for quantum computing, starting with the technique of confining ions using a linear Paul trap. It then examines the encoding of qubits within the ions’ electronic states. The interaction between an ion and a laser, pivotal for system operations, is analyzed next. This interaction underpins the initialization of ions via laser cooling and the execution of one- and two-qubit gates. The two-qubit gates also employ the ions’ motional states to extend beyond the traditional qubit space. The process also includes a method for measuring qubit states by detecting the photons released when ions are excited. The text identifies key sources of noise that can affect ion traps. It concludes with a summary and the advantages and challenges associated with trapped-ion quantum computing.

This chapter examines the use of photon ensembles for quantum computing. It opens with a primer on photons, normal modes, and both linear and nonlinear optics. The discussion then advances to the technologies employed in generating and detecting single photons, followed by methods of qubit encoding and initialization. Subsequently, the focus shifts to qubit control, detailing the execution of single-qubit gates using linear optical elements and the Knill–Laflamme–Milburn (KLM) protocol for two-qubit gates. While the textbook predominantly centers on the circuit model, alternative models of quantum computing – specifically, one-way quantum computing and continuous-variable quantum computing – and their optical implementations are introduced. Additionally, it outlines the primary sources of noise affecting these systems. The chapter wraps up with a reflection on the comparative benefits and limitations of optical quantum computing.

This chapter delves into superconducting qubits, starting with the essentials of superconductivity and circuit design. Central to this discussion is the Josephson junction, a key element in creating superconducting qubits. The text focuses on the transmon, the archetype in this field, while acknowledging other designs. Initialization of the transmon involves sophisticated dilution refrigerators, a process that is also examined. Additionally, the principles of circuit quantum electrodynamics (QED) are introduced as the framework for qubit control and measurement. Attention is then given to noise sources and their effect on superconducting qubits, with insights that apply to various qubit systems. The chapter wraps up by highlighting the strengths and challenges of superconducting qubits for quantum computing.