qml.qaoa.layers.cost_layer

cost_layer(gamma, hamiltonian)

Applies the QAOA cost layer corresponding to a cost Hamiltonian.

For the cost Hamiltonian \(H_C\), this is defined as the following unitary:

\[U_C \ = \ e^{-i \gamma H_C}\]

where \(\gamma\) is a variational parameter.

Parameters

• gamma (int or float) – The variational parameter passed into the cost layer

• hamiltonian (Hamiltonian) – The cost Hamiltonian

Raises

ValueError – if the terms of the supplied cost Hamiltonian are not exclusively products of diagonal Pauli gates

Usage Details

We first define a cost Hamiltonian:

from pennylane import qaoa
import pennylane as qml

cost_h = qml.Hamiltonian([1, 1], [qml.PauliZ(0), qml.PauliZ(0) @ qml.PauliZ(1)])

We can then pass it into qaoa.cost_layer, within a quantum circuit:

dev = qml.device('default.qubit', wires=2)

@qml.qnode(dev)
def circuit(gamma):

    for i in range(2):
        qml.Hadamard(wires=i)

    cost_layer(gamma, cost_h)

    return [qml.expval(qml.PauliZ(wires=i)) for i in range(2)]

which gives us a circuit of the form:

>>> print(qml.draw(circuit)(0.5))
0: ──H─╭ApproxTimeEvolution(1.00,1.00,0.50)─┤  <Z>
1: ──H─╰ApproxTimeEvolution(1.00,1.00,0.50)─┤  <Z>
>>> print(qml.draw(circuit, expansion_strategy="device")(0.5))
0: ──H──MultiRZ(1.00)─╭MultiRZ(1.00)─┤  <Z>
1: ──H────────────────╰MultiRZ(1.00)─┤  <Z>

code/api/pennylane.qaoa.layers.cost_layer

 

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