title: Geometry of quantum computation with qudits.
abstract: The circuit complexity of quantum qubit system evolution as a primitive problem in quantum computation has been discussed widely. We investigate this problem in terms of qudit system. Using the Riemannian geometry the optimal quantum circuits are equivalent to the geodetic evolutions in specially curved parametrization of SU(d(n)). And the quantum circuit complexity is explicitly dependent of controllable approximation error bound.
authors: 1] Information Security and National Computing Grid Laboratory, Southwest Jiaotong University, Chengdu 610031, China [2] State key Laboratory of Networking and Switching Technology (Beijing University of Posts and Telecommunications), Beijing 100876, China [3] State Key Laboratory of Information Security (Graduate University of Chinese Academy of Sciences), Beijing 100049, China.
authors: Ming-Xing
authors: MX
authors: Luo
authors: State key Laboratory of Networking and Switching Technology (Beijing University of Posts and Telecommunications), Beijing 100876, China.
authors: Xiu-Bo
authors: XB
authors: Chen
authors: State key Laboratory of Networking and Switching Technology (Beijing University of Posts and Telecommunications), Beijing 100876, China.
authors: Yi-Xian
authors: YX
authors: Yang
authors: School of Electronic Engineering, Dublin City University, Dublin 9, Ireland.
authors: Xiaojun
authors: X
authors: Wang