average_gate_fidelity_from_unitaries

average_gate_fidelity_from_unitaries(unitary_1, unitary_2)

Return the average gate fidelity between two unitary matrices.

Parameters:

• unitary_1 (ndarray | Array) – The first unitary matrix, representing the ideal or target quantum operation.

• unitary_2 (ndarray | Array) – The second unitary matrix, representing the implemented or actual quantum operation. It could be a multidimensional array where the last two dimensions correspond to the unitary matrices themselves.

Return type:

float | ndarray | Array

Returns:

The average gate fidelity between the two unitaries. If unitary_2 is multidimensional, it is an array.

Raises:

SimphonyError – If the provided matrices are not of the same shape or are not square matrices.

Note

The formula used for calculating the average gate fidelity \(F\) is:

\[F = \frac{| \text{Tr}(U_1^{\dagger} U_2) |^2 / d + 1}{d + 1},\]

where \(d\) is the dimension of the matrices.