Quantum computing

TLDR

Quantum computing integrates classical information theory, computer science, and quantum physics. This review summarizes quantum computing and the broader field of quantum information theory, concluding with an outline of its main features and future research directions. The review explains the relationship by first covering classical information theory concepts such as Shannon’s theorem, error‑correcting codes, Turing machines, and computational complexity, then outlining quantum mechanics principles, the EPR experiment, key quantum information ideas (e.g., key distribution, teleportation, data compression, quantum error correction, universal quantum computing, algorithms), and briefly describing experimental approaches for small quantum processors like ion traps, high‑Q cavities, and NMR. The review finds that quantum mechanics and information theory are compatible, with entanglement—evidenced by EPR‑Bell correlations—providing the key distinction and serving as the central computational resource across quantum information concepts.

Abstract

The subject of quantum computing brings together ideas from classical information theory, computer science, and quantum physics. This review aims to summarise not just quantum computing, but the whole subject of quantum information theory. It turns out that information theory and quantum mechanics fit together very well. In order to explain their relationship, the review begins with an introduction to classical information theory and computer science, including Shannon's theorem, error correcting codes, Turing machines and computational complexity. The principles of quantum mechanics are then outlined, and the EPR experiment described. The EPR-Bell correlations, and quantum entanglement in general, form the essential new ingredient which distinguishes quantum from classical information theory, and, arguably, quantum from classical physics. Basic quantum information ideas are described, including key distribution, teleportation, data compression, quantum error correction, the universal quantum computer and quantum algorithms. The common theme of all these ideas is the use of quantum entanglement as a computational resource. Experimental methods for small quantum processors are briefly sketched, concentrating on ion traps, high Q cavities, and NMR. The review concludes with an outline of the main features of quantum information physics, and avenues for future research.