qp.qaoa.layers.cost_layer¶

cost_layer(gamma, hamiltonian)[source]¶

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 qp

cost_h = qp.Hamiltonian([1, 1], [qp.Z(0), qp.Z(0) @ qp.Z(1)])

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

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

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

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

    qaoa.cost_layer(gamma, cost_h)

    return [qp.expval(qp.Z(i)) for i in range(2)]

which gives us a circuit of the form:

>>> print(qp.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(qp.draw(circuit, level="device")(0.5))
0: ──H──RZ(1.00)─╭RZZ(1.00)─┤  <Z>
1: ──H───────────╰RZZ(1.00)─┤  <Z>

code/api/pennylane.qaoa.layers.cost_layer

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qp.qaoa.layers.cost_layer¶

Usage Details

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