ExpvalCost(ansatz, hamiltonian, device, interface='autograd', diff_method='best', optimize=False, **kwargs)¶
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.
ansatz (callable) –
The ansatz for the circuit before the final measurement step. Note that the ansatz must have the following signature:
paramsare the trainable weights of the variational circuit, and
kwargsare 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
diff_method (str, None) – The method of differentiation to use with the created cost function. Supports all differentiation methods supported by the
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.
a cost function with signature
cost_fn(params, **kwargs)that evaluates the expectation of the Hamiltonian on the provided device(s)
- Return type
To construct an
ExpvalCostcost 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), qml.PauliZ(0) @ qml.Hadamard(2) ] H = qml.Hamiltonian(coeffs, obs)
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.
optimize=Truecan 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
groupingmodule. These groups can be executed together on a single qnode, resulting in a lower device overhead:
commuting_obs = [qml.PauliX(0), qml.PauliX(0) @ qml.PauliZ(1)] H = qml.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