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Routledge eBooks

An introduction to the quantum world

Koen Groenland

Published Oct 1, 2025• 0 citations
Publisher

Abstract

You don’t need to understand quantum mechanics to understand the functionality of quantum computers. But if you insist, quantum mechanics describes the behaviour of the smallest particles. It leads to many counter-intuitive phenomena: computer memory can store multiple pieces of data simultaneously, but, when measured, nature selects just a single piece and throws away all the others.

DOI
10.4324/9781003698104-3

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You don’t need to understand quantum mechanics to understand the functionality of quantum computers. But if you insist, quantum mechanics describes the behaviour of the smallest particles. It leads to many counter-intuitive phenomena: computer memory can store multiple pieces of data simultaneously, but, when measured, nature selects just a single piece and throws away all the others.
To obtain a basic understanding of how and why quantum computing works, one needs to understand quantum theory. In this book we treat quantum mechanics as an axiomatic theory, with some interpretations where possible. The implications of quantum mechanics are often counter intuitive, or rather, beyond intuition, since we have no direct experience of the quantum world as we do the classical. We assume no prior knowledge of quantum mechanics, and will develop all the basic tools and ideas necessary for a sound grasp of the fundamentals of the theory, especially what is relevant for two-state systems that we’ll use as qubits. For a more detailed picture, the reader is referred to standard texts on quantum mechanics, such as the books by J. J. Sakurai [60], R. Shankar [62], C. Cohen-Tannoudji [20], E. Merzbacher [49] etc. or the Feynman Lectures on Physics Vol III [34].
The fundamental laws of Nature that govern the physics of atoms, elementary particles, light quanta, and everything else that is small and light, have been found to fit in one grandiose framework called Quantum Mechanics. The internal logic of this framework appears to be counter intuitive and mysterious, while extremely coherent and effective. In this general introduction the author explains why he feels the need for expressing his views on how to understand these facts, even if many known scientists have already given extensive reviews of numerous ideas and approaches. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Quantum mechanics is a foundational theory in physics that describes the behavior of matter and energy on the smallest scales, typically at the level of atoms and subatomic particles. Unlike classical mechanics, which predicts deterministic outcomes, quantum mechanics is inherently probabilistic. For example, particles can exist in a combination of multiple states simultaneously. Only when we measure them can they ‘collapse’ into one of the possible outcomes. The wave function collapse means particles can behave like waves (with interference patterns) and like particles (with discrete energy levels). When squared, the wave function provides the probability of finding a system in a particular state.
Quantum mechanics (or simply quantum physics) is the branch of physics that applies to particles and systems of particles, such as atoms and molecules. In that realm the laws of classical mechanics and classical electromagnetism break down, and only quantum mechanics provides the concepts and computational methods that explain observed phenomena. Quantum mechanics uses specially developed tools, such as wave functions, that contain all of the relevant information about particles and systems. is approach is needed to understand the true nature of electromagnetic radiation and how that radiation interacts with matter. e mathematics used in quantum mechanics is highly specialized and often complex. In this chapter we’ll address some of the key questions that require quantum mechanics without presenting the full mathematical formalism. e important questions we’ll address all deal with observable physical phenomena. We’ll discuss how quantum mechanics is used to answer these questions but will omit the advanced mathematical details.
Applications of quantum mechanics have led to many successful predictions and explanations of puzzling phenomena, and we now apply quantum mechanics to gain, process, and communicate information in novel ways. We can understand quantum mechanics by understanding how we have applied it. We should not seek agreement on the nature of the world it represents, because this theory does not itself represent the physical world (though its applications do help us to represent it better). When applied to a quantum state, quantum mechanics yields probabiities for physical events: both state and probability are objective--not because they represent elements of phyiscal reality, but because each exerts norrmative authority over the beliefs of anyone who accepts quantum mechanics and applies it relative to a physical situation they may (but need not) occupy. These events may be described by statements that are meaningful in an appropriate environmental context, and quantum mechanics can help one to say when that is. Measurement creates an appropriate context, so here the Born rule indirectly yields probabilities of measurement outcomes. The quantum state of a system does not "collapse" on measurement: a new state must be assigned relative to a physical situation in which information about the outcome is accessible. Understood this way, there is no measurement problem, and violations of Bell inequalities does not demonstrate "spooky" non-local action. Quantum field theories have no physical ontology of their own: a quantum field is a mathematical object in a model whose application helps us to improve and extend our descriptions of the world in other terms. We cannot realise the scenario of Wigner's friend and its recent extensions: but the data that provide overwhelming evidence for quantum mechanics are objective in the same sense as the relative measurement outcomes described in those scenarios.