qml.qchem.taylor_hamiltonian

taylor_hamiltonian(pes, max_deg=4, min_deg=3, mapping='binary', n_states=2, wire_map=None, tol=1e-12)

Return Taylor vibrational Hamiltonian.

The construction of the Hamiltonian is based on Eqs. 4-7 of arXiv:1703.09313. The Hamiltonian is then converted to a qubit operator with a selected mapping method.

Parameters

• pes (VibrationalPES) – object containing the vibrational potential energy surface data

• max_deg (int) – maximum degree of Taylor form polynomial

• min_deg (int) – minimum degree of Taylor form polynomial

• mapping (str) – Method used to map to qubit basis. Input values can be "binary" or "unary". Default is "binary".

• n_states (int) – maximum number of allowed bosonic states

• wire_map (dict) – A dictionary defining how to map the states of the Bose operator to qubit wires. If None, integers used to label the bosonic states will be used as wire labels. Defaults to None.

• tol (float) – tolerance for discarding the imaginary part of the coefficients

Returns

the Taylor Hamiltonian

Return type

Operator

Example

>>> pes_onemode = np.array([[0.309, 0.115, 0.038, 0.008, 0.000, 0.006, 0.020, 0.041, 0.070]])
>>> pes_twomode = np.zeros((1, 1, 9, 9))
>>> dipole_onemode = np.zeros((1, 9, 3))
>>> gauss_weights = np.array([3.96e-05, 4.94e-03, 8.85e-02,
...                           4.33e-01, 7.20e-01, 4.33e-01,
...                           8.85e-02, 4.94e-03, 3.96e-05])
>>> grid = np.array([-3.19, -2.27, -1.47, -0.72,  0.0,  0.72,  1.47,  2.27,  3.19])
>>> pes_object = qml.qchem.VibrationalPES(
...     freqs=np.array([0.025]),
...     grid=grid,
...     uloc=np.array([[1.0]]),
...     gauss_weights=gauss_weights,
...     pes_data=[pes_onemode, pes_twomode],
...     dipole_data=[dipole_onemode],
...     localized=True,
...     dipole_level=1,
... )
>>> qml.qchem.taylor_hamiltonian(pes_object, 4, 2)
(
    -0.003833496032473659 * X(0)
    + (0.0256479442871582+0j) * I(0)
    + (-0.013079509779221888+0j) * Z(0)
)

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