VQE

The Variational Quantum Eigensolver (VQE) is a hybrid quantum-classical algorithm designed to find the ground state energy of a Hamiltonian by variationally optimizing a parameterized quantum circuit. It's widely used in quantum chemistry to compute molecular ground state energies and electronic structure properties. Nevertheless, it can also be used to find the ground state of combinatorial optimization problems, like this implementation is intends to do.

For further information see qiskit’s VQE tutorial.

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Compatible Backends

The VQE algorithm supports the following backends:

• IBM

By default, VQE uses the IBM backend.

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Initialization

The following section outlines the default configurations of VQE. You can also specify other compatible backends for the algorithm. When backend=None is specified, the default backend will be initialized automatically. In this case, if the backend requires a token, it will be taken from the environment variables.

Default Configuration

from luna_quantum.solve.parameters.algorithms import VQE
from luna_quantum.solve.parameters.algorithms.base_params import ScipyOptimizerParams

algorithm = VQE(
    backend=None,
    ansatz='EfficientSU2',
    ansatz_config={},
    shots=1024,
    optimizer=ScipyOptimizerParams(
        method='cobyla',
        tol=None,
        bounds=None,
        jac=None,
        hess=None,
        maxiter=100,
        options={}
    ),
    initial_params_seed=None,
    initial_params_range=(0, 6.283185307179586)
)

Parameter Details

For a complete overview of available parameters and their usage, see the VQE API Reference.

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Usage

from luna_quantum import LunaSolve

LunaSolve.authenticate("<YOUR_LUNA_API_KEY>")

# Define your model and algorithm
model = ...
algorithm = ...

solve_job = algorithm.run(model, name="my-solve-job")

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API Reference

Bases: LunaAlgorithm[IBM]

Parameters for the Variational Quantum Eigensolver (VQE) algorithm.

VQE is a hybrid quantum-classical algorithm designed to find the ground state energy of a Hamiltonian by variationally optimizing a parameterized quantum circuit. It's widely used in quantum chemistry to compute molecular ground state energies and electronic structure properties.

Attributes:

Name	Type	Description
ansatz	Literal['NLocal', 'EfficientSU2', 'RealAmplitudes', 'PauliTwoDesign']	The variational form (parameterized circuit) to use. Default is "EfficientSU2", a hardware-efficient ansatz using SU(2) rotation gates that works well on NISQ devices due to its shallow depth and flexibility.
ansatz_config	dict[str, Any]	Configuration options for the selected ansatz, such as: entanglement: Pattern of entangling gates ("linear", "full", etc.) reps: Number of repetitions of the ansatz structure rotation_blocks: Types of rotation gates to use Default is an empty dictionary, using the ansatz's default settings.
shots	int | None	Number of measurement samples per circuit execution. Higher values improve accuracy by reducing statistical noise at the cost of longer runtime. Default is 1024, which balances accuracy with execution time.
optimizer	ScipyOptimizerParams | Dict	Configuration for the classical optimization routine that updates the variational parameters. Default is a ScipyOptimizer instance with default settings. See ScipyOptimizer class or https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html for details of contained parameters.
initial_params_seed	int | None	Seed for random number generator for intial params.
initial_params_range	tuple[float, float]	Range of initial parameter values.

ansatz class-attribute instance-attribute

ansatz: Literal[
    "NLocal", "EfficientSU2", "RealAmplitudes", "PauliTwoDesign"
] = "EfficientSU2"

ansatz_config class-attribute instance-attribute

ansatz_config: dict[str, Any] = Field(default_factory=dict)

backend class-attribute instance-attribute

backend: BACKEND_TYPE | None = Field(default=None, exclude=True, repr=False)

initial_params_range class-attribute instance-attribute

initial_params_range: tuple[float, float] = Field(default=(0, 2 * pi))

initial_params_seed class-attribute instance-attribute

initial_params_seed: int | None = None

model_config class-attribute instance-attribute

model_config = ConfigDict(
    arbitrary_types_allowed=True, extra="allow", validate_assignment=True
)

optimizer class-attribute instance-attribute

optimizer: ScipyOptimizerParams = Field(
    default_factory=lambda: ScipyOptimizerParams()
)

shots class-attribute instance-attribute

shots: int | None = 1024

get_compatible_backends classmethod

get_compatible_backends() -> tuple[type[IBM]]

Check at runtime if the used backend is compatible with the solver.

Returns:

Type	Description
tuple[type[IBackend], ...]	True if the backend is compatible with the solver, False otherwise.

get_default_backend classmethod

get_default_backend() -> IBM

Return the default backend implementation.

This property must be implemented by subclasses to provide the default backend instance to use when no specific backend is specified.

Returns:

Type	Description
IBackend	An instance of a class implementing the IBackend interface that serves as the default backend.

run

run(
    model: Model | str,
    name: str | None = None,
    backend: BACKEND_TYPE | None = None,
    client: LunaSolve | str | None = None,
    *args: Any,
    **kwargs: Any,
) -> SolveJob

Run the configured solver.

Parameters:

Name	Type	Description	Default
model	Model or str	The model to be optimized or solved. It could be an Model instance or a string identifier representing the model id.	required
name	str | None	If provided, the name of the job. Defaults to None.	None
backend	BACKEND_TYPE | None	Backend to use for the solver. If not provided, the default backend is used.	None
client	LunaSolve or str	The client interface used to interact with the backend services. If not provided, a default client will be used.	None
*args	Any	Additional arguments that will be passed to the solver or client.	()
**kwargs	Any	Additional keyword parameters for configuration or customization.	{}

Returns:

Type	Description
SolveJob	The job object containing the information about the solve process.