Optimal qudit operator bases for efficient characterization of quantum gates
Daniel M. Reich, Giulia Gualdi, Christiane P Koch · Journal of Physics A Mathematical and Theoretical · 2014
For target unitary operations which preserve the basis of measurement operators, the average fidelity of the corresponding N -qubit gate can be determined efficiently. That is, the number of required experiments is independent of system size and the classical computational resources scale only polynomially in the number N of qubits. Here we address the question of how to optimally choose the measurement basis for fidelity estimation when replacing two-level qubits by d -level qudits. We define optimality in terms of the maximal number of unitaries that preserve the measurement basis. Our definition allows us to construct the optimal measurement basis in terms of their spectra and eigenbases: the measurement operators are unitaries with d -nary spectrum and partition into Abelian groups whose eigenbases are mutually unbiased.