Geometry of quantum computation with qutrits.

Scientific reports

PubMedID: 24005379

Li B, Yu ZH, Fei SM. Geometry of quantum computation with qutrits. Sci Rep. 2013;32594.
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.