iqm.benchmarks.compressive_gst.mgst.low_level_jit.ddM

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iqm.benchmarks.compressive_gst.mgst.low_level_jit.ddM#

iqm.benchmarks.compressive_gst.mgst.low_level_jit.ddM(X: ndarray, K: ndarray, E: ndarray, rho: ndarray, J: ndarray, y: ndarray, mle: bool = False) → tuple[ndarray, ndarray]#

Compute the second derivative of the objective function with respect to the Kraus tensor K.

This function calculates the second derivative of the objective function for a given set of input parameters.

Parameters:

  • X (ndarray) – Array of input matrices.

  • K (ndarray) – Array of Kraus operators.

  • E (ndarray) – Array of measurement operators.

  • rho (ndarray) – Array of quantum states.

  • J (ndarray) – Array of indices corresponding to the sequence of operations.

  • y (ndarray) – Array of observed probabilities.

  • mle (bool) – If True, the log-likelihood objective function is used, otherwise the least squares objective function is used

Returns:

Array of shape (d, d, rK, rK, pdim, pdim, pdim, pdim)

Second derivative of the objective function with respect to matrix elements, reshaped for easier manipulation.

dconjdK: Array of shape (d, d, rK, rK, pdim, pdim, pdim, pdim)

Conjugate of the second derivative of the objective function with respect to matrix elements, reshaped for easier manipulation.

Return type:

ddK

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