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fock_evolution

qoptcraft.evolution.fock_evolution

fock_evolution(scattering_matrix, fock_in, method='permanent glynn')

Evolution of a single Fock state using the definition given by basic quantum mechanics.

Parameters:

Name Type Description Default
scattering_matrix NDArray

scattering matrix of a linear optical interferometer.

 required
fock_in Fock

fock state to evolve.

 required
method str

method to calculate the evolution of the Fock state. Options are 'heisenberg', 'permanent glynn' or 'permanent ryser'. Default is 'permanent glynn'.

 'permanent glynn'

Returns:

Name Type Description
NDArray NDArray

fock state given in the photon basis.
Source code in qoptcraft/evolution/fock_evolution.py 
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def fock_evolution(
    scattering_matrix: NDArray,
    fock_in: tuple[int, ...],
    method: Literal["heisenberg", "permanent glynn", "permanent ryser"] = "permanent glynn",
) -> NDArray:
    """Evolution of a single Fock state using the definition given by basic
    quantum mechanics.

    Args:
        scattering_matrix (NDArray): scattering matrix of a linear optical interferometer.
        fock_in (Fock): fock state to evolve.
        method (str): method to calculate the evolution of the Fock state. Options are
            'heisenberg', 'permanent glynn' or 'permanent ryser'. Default is 'permanent glynn'.

    Returns:
        NDArray: fock state given in the photon basis.
    """
    if method == "heisenberg":
        return fock_evolution_heisenberg(scattering_matrix, fock_in)
    if method.split()[0] == "permanent":
        return fock_evolution_permanent(scattering_matrix, fock_in, method=method.split()[1])
    raise ValueError("Options for method are 'heisenberg', 'permanent glynn' or 'permanent ryser'.")

fock_evolution_heisenberg(scattering_matrix, fock_in)

Evolution of a single Fock state using the definition given by basic quantum mechanics.

Parameters:

Name Type Description Default
scattering_matrix NDArray

scattering matrix of a linear optical interferometer.

 required
fock_in Fock

fock state to evolve.

 required

Returns:

Name Type Description
NDArray NDArray

fock state given in the photon basis.
Source code in qoptcraft/evolution/fock_evolution.py 
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def fock_evolution_heisenberg(scattering_matrix: NDArray, fock_in: tuple[int, ...]) -> NDArray:
    """Evolution of a single Fock state using the definition given by basic
    quantum mechanics.

    Args:
        scattering_matrix (NDArray): scattering matrix of a linear optical interferometer.
        fock_in (Fock): fock state to evolve.

    Returns:
        NDArray: fock state given in the photon basis.
    """
    modes = len(fock_in)

    state_out: PureState = Fock(*([0] * modes))
    for mode_2 in range(modes):
        for _ in range(fock_in[mode_2]):
            state_aux = state_out
            state_out = scattering_matrix[0, mode_2] * state_aux.creation(0)
            for mode_1 in range(1, modes):
                state_out += scattering_matrix[mode_1, mode_2] * state_aux.creation(mode_1)
    coef = np.prod(factorial(fock_in))
    return state_out / np.sqrt(coef)

fock_evolution_permanent(scattering_matrix, fock_in, method='glynn', photon_basis=None)

Evolution of a single Fock state using the definition given by basic quantum mechanics.

Parameters:

Name Type Description Default
scattering_matrix NDArray

scattering matrix of a linear optical interferometer.

 required
fock_in Fock

fock state to evolve.

 required
method str

method to compute the permanent. Must be 'glynn' or 'ryser'. Defaults to 'glynn'.

 'glynn'

Returns:

Name Type Description
NDArray NDArray

fock state given in the photon basis.
Source code in qoptcraft/evolution/fock_evolution.py 
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def fock_evolution_permanent(
    scattering_matrix: NDArray,
    fock_in: tuple[int, ...],
    method: Literal["glynn", "ryser"] = "glynn",
    photon_basis: BasisPhoton = None,
) -> NDArray:
    """Evolution of a single Fock state using the definition given by basic
    quantum mechanics.

    Args:
        scattering_matrix (NDArray): scattering matrix of a linear optical interferometer.
        fock_in (Fock): fock state to evolve.
        method (str): method to compute the permanent. Must be 'glynn' or 'ryser'.
            Defaults to 'glynn'.

    Returns:
        NDArray: fock state given in the photon basis.
    """
    if len(fock_in) != scattering_matrix.shape[0]:
        raise ValueError("Dimension of scattering_matrix and number of modes don't match.")
    if photon_basis is None:
        photon_basis = get_photon_basis(len(fock_in), sum(fock_in))
    dim = len(photon_basis)
    state_out = np.empty(dim, dtype=np.complex128)

    for row, fock_out in enumerate(photon_basis):
        sub_matrix = in_out_submatrix(scattering_matrix, fock_in, fock_out)
        coef = np.prod(factorial(fock_in)) * np.prod(factorial(fock_out))
        state_out[row] = permanent(sub_matrix, method=method) / np.sqrt(coef)
    return state_out

in_out_submatrix(matrix, fock_in, fock_out)

Return a matrix with row index 'i' repeated 'row_rep' times and column index 'j' repeated 'col_rep' times.

Parameters:

Name Type Description Default
matrix m, m) array

Linear optical scattering matrix with m modes.

 required

Returns:

Type Description
NDArray

(n, n) array: Optical scattering matrix with m modes and n photons.
Source code in qoptcraft/evolution/fock_evolution.py 
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@numba.jit(nopython=True)
def in_out_submatrix(matrix, fock_in: tuple[int, ...], fock_out: tuple[int, ...]) -> NDArray:
    """Return a matrix with row index 'i' repeated 'row_rep' times
    and column index 'j' repeated 'col_rep' times.

    Args:
        matrix ((m, m) array): Linear optical scattering matrix with m modes.

    Returns:
        (n, n) array: Optical scattering matrix with m modes and n photons.
    """
    modes = len(fock_in)
    photons = sum(fock_in)
    interm_matrix = np.empty((matrix.shape[0], photons), dtype="complex128")
    col = 0
    for mode in range(modes):
        for _ in range(fock_in[mode]):
            interm_matrix[:, col] = matrix[:, mode]
            col += 1
    final_matrix = np.empty((photons, photons), dtype="complex128")
    row = 0
    for mode in range(modes):
        for _ in range(fock_out[mode]):
            final_matrix[row, :] = interm_matrix[mode, :]
            row += 1
    return final_matrix