The purpose of this volume is examine bio-informatics and quantum information, which are growing rapidly at present, and to attempt to connect the two, with a view to enumerating and solving the many fundamental problems they entail. To this end, we look for interdisciplinary bridges in mathematics, physics, and information and life sciences. In particular, research into a new paradigm for information science and life science on the basis of quantum theory is emphasized. Sample Chapter(s). Markov Fields on Graphs (599 KB). Contents: Markov Fields on Graphs (L Accardi & H Ohno); Some Aspects of Time Operators (A Arai); Time Optimal Quantum Control of Mixed States (A Carlini et al.); On a Quantum Model of the Recognition Process (K-H Fichtner et al.); Perspectives of White Noise Analysis (T Hida); Review on Quantum Chaos Algorithm and Generalized Quantum Turing Machine (S Iriyama & M Ohya); Cauchy Problems for Some Biological Systems OCo Modelling by Stochastic Differential Equations (A Jamiolkowski); On Non-Markovian Time Evolution in Open Quantum Systems (A Kossakowski & R Rebolledo); Adaptive Dynamics and Its Applications to Chaos and NPC Problem (M Ohya); Micro-Macro Duality and Emergence of Macroscopic Levels (I Ojima); Josephson Flux Qubit (H Takayanagi); Note on Quantum Mutual Entropy Type Measures (N Watanabe); Toward in Silico Biology (From Sequence to Systems) (I Yamato et al.); and other papers. Readership: Physicists, researchers in quantum information and bioinformatics.