Optimal control of one-qubit gates
K. M. Fonseca-Romero, G Useche Laverde, Federico Ardila · Journal of Physics A Mathematical and General · 2003
We consider the problem of carrying an initial Bloch vector to a final Bloch vector in a specified amount of time under the action of three control fields (a vector control field). We show that this control problem is solvable and therefore it is possible to optimize the control. We choose the physically motivated criteria of minimum energy expended in the control, minimum magnitude of the rate of change of the control and a combination of both. We find exact analytical solutions, determine the fields for a general one-qubit gate, and use the Y gate as an example. We argue that in the case of less than three controls, only the physical intuition does not provide a straight reasonable solution, and solve the problem in the case of a unique control minimizing the energy consumption.