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This book is a collection of lecture notes and contributions in “Summer School on Diversities in Quantum Computation/Information” held on 1–5 August, 2010 at U-Community Hotel, Higashi-Osaka, Japan. Lecturers are world class authorities in respective areas in quantum information and quantum computing including physics, mathematics, chemistry and information science. They lectured on cutting-edge research frontiers where they are currently working, including quantum error correction, relativistic quantum information, quantum computing of link polynomials, quantum algorithms, etc. Each lecture note is written in a self-contained manner so that it may be used as a textbook for one semester graduate course or advanced undergraduate course. Contributions report current research subjects also in a self-contained manner. We believe that these articles are accessible to the readers form various disciplines. Table of Contents Matrix Techniques in Quantum Information Science Untying Knots by NMR: Experimental Implementation of an Exponentially Fast Quantum Algorithm for Approximating the Jones Polynomial Quantum Algorithms for Problems in Number Theory, Algebraic Geometry, and Group Theory Lecture Series on Relativistic Quantum Information Systematic Construction of Bell-Like Inequalities and Proposal of a New Type of Test Hybrid Quantum Annealing for Clustering Problems Theory of Macroscopic Quantum Tunneling in Two-Gap Superconductors: Corrections from Leggett's Modes