qml.labs.dla.pauli_coefficients¶

pauli_coefficients(H)[source]¶

Computes the coefficients of one or multiple Hermitian matrices in the Pauli basis.

The coefficients are ordered lexicographically in the Pauli group, ["III", "IIX", "IIY", "IIZ", "IXI", ...].

Parameters:: H (tensor_like[complex]) – a Hermitian matrix of dimension (2**n, 2**n) or a collection of Hermitian matrices of dimension (batch, 2**n, 2**n).
Returns:: The coefficients of H in the Pauli basis with shape (4**n,) for a single matrix input and (batch, 4**n) for a collection of matrices. The output is real-valued.
Return type:: np.ndarray

See pauli_decompose() for theoretical background information.

Examples

Consider the Hamiltonian \(H=\frac{1}{4} X_0 + \frac{2}{5} Z_0 X_1\) with matrix

>>> H = 1 / 4 * qml.X(0) + 2 / 5 * qml.Z(0) @ qml.X(1)
>>> mat = H.matrix()
>>> mat
array([[ 0.  +0.j,  0.4 +0.j,  0.25+0.j,  0.  +0.j],
       [ 0.4 +0.j,  0.  +0.j,  0.  +0.j,  0.25+0.j],
       [ 0.25+0.j,  0.  +0.j,  0.  +0.j, -0.4 +0.j],
       [ 0.  +0.j,  0.25+0.j, -0.4 +0.j,  0.  +0.j]])

Then we can obtain the coefficients of \(H\) in the Pauli basis via

>>> from pennylane.labs.dla import pauli_coefficients
>>> pauli_coefficients(mat)
array([ 0.  ,  0.  ,  0.  ,  0.  ,  0.25,  0.  ,  0.  ,  0.  ,  0.  ,
        0.  , -0.  ,  0.  ,  0.  ,  0.4 ,  0.  ,  0.  ])

The function can be used on a batch of matrices:

>>> ops = [1 / 4 * qml.X(0), 1 / 2 * qml.Z(0), 3 / 5 * qml.Y(0)]
>>> batch = np.stack([op.matrix() for op in ops])
>>> pauli_coefficients(batch)
array([[0.  , 0.25, 0.  , 0.  ],
       [0.  , 0.  , 0.  , 0.5 ],
       [0.  , 0.  , 0.6 , 0.  ]])

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qml.labs.dla.pauli_coefficients¶

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