qxmt.ansatze.pennylane.kupccgsd module#

class qxmt.ansatze.pennylane.kupccgsd.KUpCCGSDAnsatz(device, hamiltonian, k=1, delta_sz=0)

Bases: BaseVQEAnsatz

k-Unitary Pair Coupled Cluster with Generalized Singles and Doubles (kUpCCGSD) ansatz.

The kUpCCGSD ansatz is an extension of the Unitary Pair Coupled Cluster (UpCC) framework that incorporates both generalized single and double excitations. This ansatz is particularly suitable for quantum chemistry calculations as it maintains physical properties such as particle number conservation and spin symmetry while providing a variational quantum circuit for molecular ground state preparation.

The ansatz constructs a quantum state by applying k repetitions of the UpCCGSD unitary operator to the Hartree-Fock reference state:

|ψ⟩ = [U_CCGSD(θ)]^k |HF⟩

where U_CCGSD(θ) includes both single and double excitation operators with parameters θ. The generalized singles include additional spin-flip excitations controlled by the delta_sz parameter, allowing for more flexible electronic structure descriptions.

Key features: - Maintains particle number and spin conservation - Includes generalized single excitations with spin selection rules - Supports multiple repetitions (k) of the unitary operator for enhanced expressibility - Compatible with various molecular systems and basis sets

Parameters:

device (BaseDevice) – Quantum device to use for executing the ansatz circuit.
hamiltonian (MolecularHamiltonian) – Molecular Hamiltonian defining the quantum chemistry problem. Must contain information about electrons, orbitals, and molecular geometry.
k (int, optional) – Number of repetitions of the UpCCGSD unitary operator. Higher values increase circuit depth but may improve state preparation accuracy. Defaults to 1.
delta_sz (int, optional) – Spin selection rule for generalized single excitations. Specifies the allowed change in spin projection (sz[p] - sz[r] = delta_sz) where p and r are orbital indices. Valid values are 0, +1, and -1. Defaults to 0.

hamiltonian

Molecular Hamiltonian for the ansatz.

Type:: MolecularHamiltonian

wires

Qubit indices used in the quantum circuit.

Type:: range

k

Number of UpCCGSD unitary repetitions.

Type:: int

delta_sz

Spin selection rule parameter for generalized singles.

Type:: int

hf_state

Hartree-Fock reference state as initial quantum state.

Type:: np.ndarray

params_shape

Shape of the parameter array required for the ansatz.

Type:: tuple

n_params

Total number of variational parameters.

Type:: int

Example

>>> from qxmt.hamiltonians.pennylane.molecular import MolecularHamiltonian
>>> from qxmt.devices import BaseDevice
>>>
>>> # Create Hamiltonian and device
>>> hamiltonian = MolecularHamiltonian(...)
>>> device = BaseDevice(...)
>>>
>>> # Initialize kUpCCGSD ansatz with 2 repetitions
>>> ansatz = KUpCCGSDAnsatz(device, hamiltonian, k=2, delta_sz=0)
>>>
>>> # Get parameter shape and initialize parameters
>>> param_shape = ansatz.params_shape
>>> params = np.random.normal(0, 0.1, ansatz.n_params)
>>>
>>> # Build quantum circuit
>>> ansatz.circuit(params)

References

PennyLane documentation: https://docs.pennylane.ai/en/stable/code/api/pennylane.kUpCCGSD.html

Note

This ansatz is designed for near-term quantum devices and provides a balance between circuit depth and expressibility. The choice of k and delta_sz parameters should be optimized based on the specific molecular system and available quantum hardware.

circuit(params)

Construct the UCCSD quantum circuit.

Parameters:: params (np.ndarray) – Parameters for the KUpCCGSD circuit. The length of this array should match the number of parameters required by the circuit.
Return type:: None

prepare_excitation_wires()

Prepare the excitation wires for single and double excitations.

This method: 1. Generates all possible single and double excitations from the Hartree-Fock state 2. Converts these excitations to wire indices that can be used in the quantum circuit

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

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