Integrability, entropy and quantum computation

摘要

The important requirements are stated for the success of quantum computation. These requirements involve coherent preserving Hamiltonians well as exact integrability of the corresponding Feynman path integrals. Also we explain the role of metric entropy of quantum computational systems. Finally, we observe that unless we understand quantum nondemolition measurements, quantum integrability, quantum chaos and the direction of time arrow, the quantum control and computational paradigms will remain elusive and the design of systems based on quantum dynamical evolution may not be feasible.