# qml.ExpvalCost¶

class ExpvalCost(ansatz, hamiltonian, device, interface='autograd', diff_method='best', optimize=False, **kwargs)[source]

Bases: object

Create a cost function that gives the expectation value of an input Hamiltonian.

This cost function is useful for a range of problems including VQE and QAOA.

Parameters
• ansatz (callable) –

The ansatz for the circuit before the final measurement step. Note that the ansatz must have the following signature:

ansatz(params, **kwargs)


where params are the trainable weights of the variational circuit, and kwargs are any additional keyword arguments that need to be passed to the template.

• hamiltonian (Hamiltonian) – Hamiltonian operator whose expectation value should be measured

• device (Device, Sequence[Device]) – Corresponding device(s) where the resulting cost function should be executed. This can either be a single device, or a list of devices of length matching the number of terms in the Hamiltonian.

• interface (str, None) – Which interface to use. This affects the types of objects that can be passed to/returned to the cost function. Supports all interfaces supported by the qnode() decorator.

• diff_method (str, None) – The method of differentiation to use with the created cost function. Supports all differentiation methods supported by the qnode() decorator.

• optimize (bool) – Whether to optimize the observables composing the Hamiltonian by separating them into qubit-wise commuting groups. Each group can then be executed within a single QNode, resulting in fewer QNodes to evaluate.

Returns

a cost function with signature cost_fn(params, **kwargs) that evaluates the expectation of the Hamiltonian on the provided device(s)

Return type

callable

Hamiltonian, generate_hamiltonian(), map(), dot()

Example:

To construct an ExpvalCost cost function, we require a Hamiltonian to measure, and an ansatz for our variational circuit.

We can construct a Hamiltonian manually,

coeffs = [0.2, -0.543]
obs = [
qml.PauliX(0) @ qml.PauliZ(1) @ qml.PauliY(3),
]
H = qml.vqe.Hamiltonian(coeffs, obs)


Alternatively, the molecular_hamiltonian() function from the Quantum Chemistry module can be used to generate a molecular Hamiltonian.

Once we have our Hamiltonian, we can select an ansatz and construct the cost function.

>>> ansatz = qml.templates.StronglyEntanglingLayers
>>> dev = qml.device("default.qubit", wires=4)
>>> cost = qml.ExpvalCost(ansatz, H, dev, interface="torch")
>>> params = torch.rand([2, 4, 3])
>>> cost(params)
tensor(-0.2316, dtype=torch.float64)


The cost function can then be minimized using any gradient descent-based optimizer.

Optimizing observables:

Setting optimize=True can be used to decrease the number of device executions. The observables composing the Hamiltonian can be separated into groups that are qubit-wise commuting using the grouping module. These groups can be executed together on a single qnode, resulting in a lower device overhead:

qml.enable_tape()
commuting_obs = [qml.PauliX(0), qml.PauliX(0) @ qml.PauliZ(1)]
H = qml.vqe.Hamiltonian([1, 1], commuting_obs)

dev = qml.device("default.qubit", wires=2)
ansatz = qml.templates.StronglyEntanglingLayers

cost_opt = qml.ExpvalCost(ansatz, H, dev, optimize=True)
cost_no_opt = qml.ExpvalCost(ansatz, H, dev, optimize=False)

params = qml.init.strong_ent_layers_uniform(3, 2)


Grouping these commuting observables leads to fewer device executions:

>>> cost_opt(params)
>>> ex_opt = dev.num_executions
>>> cost_no_opt(params)
>>> ex_no_opt = dev.num_executions - ex_opt
>>> print("Number of executions:", ex_no_opt)
Number of executions: 2
>>> print("Number of executions (optimized):", ex_opt)
Number of executions (optimized): 1


Note that this feature is only available in tape mode.

 __call__(*args, **kwargs) Call self as a function. metric_tensor(args[, kwargs, diag_approx, …]) Evaluate the value of the metric tensor.
__call__(*args, **kwargs)[source]

Call self as a function.

metric_tensor(args, kwargs=None, diag_approx=False, only_construct=False)[source]

Evaluate the value of the metric tensor.

Parameters
• args (tuple[Any]) – positional (differentiable) arguments

• kwargs (dict[str, Any]) – auxiliary arguments

• diag_approx (bool) – iff True, use the diagonal approximation

• only_construct (bool) – Iff True, construct the circuits used for computing the metric tensor but do not execute them, and return None.

Returns

metric tensor

Return type

array[float]