cirq.apply_matrix_to_slices

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Left-multiplies an NxN matrix onto N slices of a numpy array.

cirq.apply_matrix_to_slices(
    target: np.ndarray,
    matrix: np.ndarray,
    slices: Sequence[_TSlice],
    *,
    out: Optional[np.ndarray] = None
) -> np.ndarray

One example is that the 4x4 matrix of a fractional SWAP gate can be expressed as

\(\) \begin{bmatrix} 1 & & \ & X**t & \ & & 1 \ \end{bmatrix}

Where X is the 2x2 Pauli X gate and t is the power of the swap with t=1 being a full swap. X**t is a power of the Pauli X gate's matrix. Applying the fractional swap is equivalent to applying a fractional X within the inner 2x2 subspace; the rest of the matrix is identity. This can be expressed using apply_matrix_to_slices as follows:

def fractional_swap(target):
    assert target.shape == (4,)
    return apply_matrix_to_slices(
        target=target,
        matrix=cirq.unitary(cirq.X**t),
        slices=[1, 2]
    )