Geometry of Quantum Computation with Qudits
M. X. Luo, Xiu‐Bo Chen, Yixian Yang, Xiaojun Wang · Scientific Reports · 2014
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.