workbench_algorithms.utils.hamiltonian_utils

Utility functions for block encodings.

get_exactly_representable_qubitized_hamiltonian

get_exactly_representable_qubitized_hamiltonian(
    alpha, bits_of_precision
)

Returns a Hamiltonian where \(\arccos(\lambda)\) is exactly representable with bits_of_precision bits.

Note

Only the first excited state of this hamiltonian is guaranteed to be an energy that corresponds to a phase that is exactly representable using the input bits_of_precision.

Parameters:

Name	Type	Description	Default
alpha	float	Arbitrary coefficient which determines the specific type of Hamiltonian.	required
bits_of_precision	int	Number of bits the phase is to be measured to. Must be greater than 2.	required

Returns:

Type	Description
Tuple[PauliSum, float]	containing the Hamiltonian and the eigenvalue.

generate_h2_hamiltonian

generate_h2_hamiltonian(bond_length)

Generate the hydrogen Haimltonian given a bond length.

Parameters:

Name	Type	Description	Default
bond_length	float	One of [0.2, 0.5, 0.7, 1.0, 2.0].	required

Returns:

Type	Description
PauliSum	H2 Hamiltonian.

fetch_h2_gs_data

fetch_h2_gs_data(bond_length)

Returns ground state energy and wavefunction for checking.

Parameters:

Name	Type	Description	Default
bond_length	float	H-H bond length, in Angstroms.	required

Returns:

Type	Description
g_energy (float	Ground state energy.
g_state (list	Ground state wavefunction.

fetch_h2_gs_prep_angle

fetch_h2_gs_prep_angle(bond_length)

Returns ground state preparation circuit parameter.

Parameters:

Name	Type	Description	Default
bond_length	float	H-H bond length, in Angstroms.	required

Returns:

Type	Description
angle (float	Ground state preparation circuit parameter.

h2_ground_state_prep

h2_ground_state_prep(qc, sys_reg, ansatz_param)

Circuit for ground state preparation for H2.

Parameters:

Name	Type	Description	Default
qc	QPU	QPU	required
sys_reg	Qubits	System register to implement state preparation.	required
ansatz_param	float	Ground state prep circuit parameter (in Radians).	required

Notes

• See Fig. 1 of arxiv:1512.06860.