hamiltonian_utils

hamiltonian_utils ¶

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.

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.

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]`	The Hamiltonian and the eigenvalue.

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 "Scalable Quantum Simulation of Molecular Energies" (arXiv:1512.06860 ⧉).