qxmt.ansatze.pennylane.all_singles_doubles module

qxmt.ansatze.pennylane.all_singles_doubles module#

class qxmt.ansatze.pennylane.all_singles_doubles.AllSinglesDoublesAnsatz(device, hamiltonian)

Bases: BaseVQEAnsatz

All Singles and Doubles (AllSinglesDoubles) ansatz for quantum chemistry.

The AllSinglesDoubles ansatz is a fundamental variational quantum circuit for quantum chemistry calculations that systematically includes all possible single and double excitations from the Hartree-Fock reference state. This ansatz is particularly effective for strongly correlated molecular systems where both single and double excitations contribute significantly to the ground state wavefunction.

The ansatz constructs a quantum state by applying parameterized excitation operators:

|ψ⟩ = exp(∑ᵢ θᵢ Tᵢ) |HF⟩

where Tᵢ represents single and double excitation operators, θᵢ are variational parameters, and |HF⟩ is the Hartree-Fock reference state.

Key features: - Includes all chemically relevant single and double excitations - Maintains particle number conservation and proper spin symmetry - Provides systematic improvement over simpler ansätze like hardware-efficient circuits - Well-suited for molecules with moderate correlation effects - Computationally efficient compared to higher-order excitations

The number of parameters scales polynomially with system size, making it tractable for near-term quantum devices while providing sufficient flexibility for accurate ground state preparation in many molecular systems.

Parameters:

  • device (BaseDevice) – Quantum device for executing the variational circuit.

  • hamiltonian (MolecularHamiltonian) – Molecular Hamiltonian defining the quantum chemistry problem, including information about electrons, orbitals, and molecular geometry.

hamiltonian

Molecular Hamiltonian for the ansatz.

Type:

MolecularHamiltonian

wires

Qubit indices used in the quantum circuit.

Type:

range

hf_state

Hartree-Fock reference state as the initial quantum state.

Type:

np.ndarray

singles

Indices of all possible single excitations from occupied to virtual orbitals.

Type:

list

doubles

Indices of all possible double excitations from occupied to virtual orbitals.

Type:

list

n_params

Total number of variational parameters (sum of singles and doubles).

Type:

int

Example

>>> from qxmt.hamiltonians.pennylane.molecular import MolecularHamiltonian
>>> from qxmt.devices import BaseDevice
>>>
>>> # Create Hamiltonian and device for H2 molecule
>>> hamiltonian = MolecularHamiltonian(...)
>>> device = BaseDevice(...)
>>>
>>> # Initialize AllSinglesDoubles ansatz
>>> ansatz = AllSinglesDoublesAnsatz(device, hamiltonian)
>>>
>>> # Initialize parameters (typically small random values)
>>> params = np.random.normal(0, 0.01, ansatz.n_params)
>>>
>>> # Build and execute quantum circuit
>>> ansatz.circuit(params)

References

Note

This ansatz is ideal for molecules where single and double excitations dominate the correlation energy. For systems requiring higher-order excitations, consider more sophisticated ansätze like kUpCCGSD or adaptive approaches.

circuit(params)

Construct the AllSinglesDoubles quantum circuit.

Parameters:

params (np.ndarray) – Parameters for the AllSinglesDoubles circuit. The length of this array should match the number of single and double excitations.

Return type:

None

Note

The AllSinglesDoubles operation includes all possible single and double excitations from the Hartree-Fock reference state.

prepare_excitation()

Prepare the single and double excitations.

This method generates all possible single and double excitations from the Hartree-Fock state.

The results are stored in the following attributes: - self.singles: List of single excitation indices - self.doubles: List of double excitation indices

Note

The number of excitations depends on the number of electrons and orbitals in the system.

Return type:

None

prepare_hf_state()

Prepare the Hartree-Fock reference state.

This method creates the Hartree-Fock reference state using PennyLane’s qchem module. The Hartree-Fock state is a product state where the first n electrons occupy the lowest energy orbitals.

The state is stored in self.hf_state as a numpy array.

Note

The number of electrons and orbitals are obtained from the Hamiltonian.

Return type:

None