title: Geometry of quantum computation with qutrits.
abstract: Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum computation with n qutrits. We show that the optimal quantum circuits are essentially equivalent to the shortest path between two points in a certain curved geometry of SU(3(n)). As an example, three-qutrit systems are investigated in detail.
authors.affiliation: School of Mathematical Sciences, Capital Normal University, Beijing 100037, P R China.
authors.forename: Bin
authors.initials: B
authors.lastname: Li
authors.forename: Zu-Huan
authors.initials: ZH
authors.lastname: Yu
authors.forename: Shao-Ming
authors.initials: SM
authors.lastname: Fei
mesh_terms: D003198:Computer Simulation; D039301:Computers, Molecular; D008962:Models, Theoretical; D011789:Quantum Theory; D012815:Signal Processing, Computer-Assisted