The second edition of a textbook that explains quantum computing in terms of elementary linear algebra, requiring no background in physics.

This introduction to quantum algorithms is concise but comprehensive, covering many key algorithms. It is mathematically rigorous but requires minimal background and assumes no knowledge of quantum theory or quantum mechanics. The book explains quantum computation in terms of elementary linear algebra; it assumes the reader will have some familiarity with vectors, matrices, and their basic properties, but offers a review of the relevant material from linear algebra. By emphasizing computation and algorithms rather than physics, it makes quantum algorithms accessible to students and researchers in computer science who have not taken courses in quantum physics or delved into fine details of quantum effects, apparatus, circuits, or theory.

In this second edition, part I, on essential algorithms, provides additional exercises and solved problems. Part II, on advanced algorithms, offers two new chapters: one provides students with a deeper understanding of quantum physics, and includes a discussion of recent experiments claiming “quantum supremacy”; the other new chapter focuses on the Harrow-Hassidim-Lloyd (HHL) algorithm for linear algebra. Additional material touches on some of the philosophical issues involved in quantum mechanics, addressing the divide between quantum and classical. This edition is more versatile than the first edition (published as Quantum Algorithms via Linear Algebra: A Primer), with part I suitable for advanced undergraduates and part II, now including notation and tools used by practitioners, suitable for graduate students.