Foundations of quantum computing. Part II

Stephen Allan Selesnick

Helmut Bez, Tony Croft

Quantum Computation presents the mathematics of quantum computation. The purpose is to introduce the topic of quantum computing to students in computer science, physics and mathematics who have no prior knowledge of this field. The book is written in two parts. The primary mathematical topics required for an initial understanding of quantum computation are dealt with in Part I: sets, functions, complex numbers and other relevant mathematical structures from linear and abstract algebra. Topics are illustrated with examples focussing on the quantum computational aspects which will follow in more detail in Part II. Part II discusses quantum information, quantum measurement and quantum algorithms. These topics provide foundations upon which more advanced topics may be approached with confidence. Features A more accessible approach than most competitor texts, which move into advanced, research-level topics too quickly for today's students. Part I is comprehensive in providing all necessary mathematical underpinning, particularly for those who need more opportunity to develop their mathematical competence. More confident students may move directly to Part II and dip back into Part I as a reference. Ideal for use as an introductory text for courses in quantum computing. Fully worked examples illustrate the application of mathematical techniques. Exercises throughout develop concepts and enhance understanding. End-of-chapter exercises offer more practice in developing a secure foundation.

Masahito Hayashi, Satoshi Ishizaka, Akinori Kawachi +2 more

Rajendra Kumar Bera

In Part I we laid the foundation on which quantum algorithms are built. In part II we harnessed such exotic aspects of quantum mechanics as superposition, entanglement and collapse of quantum states to show how powerful quantum algorithms can be constructed for efficient computation. In Part III (the concluding part) we discuss two aspects of quantum computation: (1) the problem of correcting errors that inevitably plague physical quantum computers during computations, by algorithmic means; and (2) a possible underlying mechanism for the collapse of the wave function during measurement.

Chadwick D Rasque

Second in series: For the foundational paper, see The MID Substrate: A Generative Physical Primitive for Quantum and Gravitational Phenomena DOI: https://doi.org/10.5281/zenodo.18284475. Part I introduces the conceptual foundation of the MID/QC framework, presenting coherence as a physical substrate with structure, gradients, and consequences. This primer outlines how coherence density, wells, and ridges shape stability, quantum behavior, gravity, and time dilation. The paper is intentionally intuitive and non‑mathematical, preparing readers for the geometric development in Part II. It establishes the core idea that coherence is not an abstract quantum property but a physical field‑like substrate from which familiar physical phenomena emerge