# qml.layer¶

layer(template, depth, *args, **kwargs)[source]

Repeatedly applies a unitary a given number of times.

Parameters
• template (callable) – The sequence of quantum gates that is being repeated. This could be a single gate, a function of gates, or a “registered” PennyLane template.

• depth (int) – The number of times the unitary is repeatedly applied.

• *args – Dynamic parameters that are passed into the unitary each time it is repeated. Each dynamic argument must be a list of first dimension equal to depth. The $$j$$-th element of the list is the value of the argument the $$j$$-th time the unitary is applied.

• **kwargs – Static parameters that are passed into the unitary each time it is repeated.

Layering Gates

The layering function can be used to repeatedly apply a function containing quantum operations, a template, or a quantum gate.

For example, we can define the following subroutine:

import pennylane as qml
import numpy as np

def subroutine():
qml.CNOT(wires=[0, 1])
qml.PauliX(wires=)


and then pass it into the qml.layer function. In this instance, we repeat subroutine three times:

dev = qml.device('default.qubit', wires=3)

@qml.qnode(dev)
def circuit():
qml.layer(subroutine, 3)
return [qml.expval(qml.PauliZ(0)), qml.expval(qml.PauliZ(1))]


This creates the following circuit:

>>> circuit()
>>> print(circuit.draw())
0: ──H──╭C──X──H──╭C──X──H──╭C──X──┤ ⟨Z⟩
1: ─────╰X────────╰X────────╰X─────┤ ⟨Z⟩


Static Arguments

Static arguments are arguments passed into template that don’t change with each repetition. Static parameters are always passed as keyword arguments into qml.layer. For example, consider the following subroutine:

def subroutine(wires):
qml.CNOT(wires=wires)
qml.PauliX(wires=wires)


We wish to repeat this gate sequence three times on wires 1 and 2. Since the wires on which the subroutine acts don’t change with each repetition, the wires parameter is passed as a keyword argument. Therefore, we define a circuit as:

@qml.qnode(dev)
def circuit():
qml.layer(subroutine, 3, wires=[1, 2])
return [qml.expval(qml.PauliZ(1)), qml.expval(qml.PauliZ(2))]


which yields the following circuit:

>>> circuit()
>>> print(circuit.draw())
1: ──H──╭C──X──H──╭C──X──H──╭C──X──┤ ⟨Z⟩
2: ─────╰X────────╰X────────╰X─────┤ ⟨Z⟩


Dynamic Arguments

In addition to passing static arguments to template, we can also pass dynamic arguments. These are arguments that change with each repetition of the unitary. They are passed as non-keyword arguments to qml.layer, after template and depth. Each dynamic parameter must be a list of length equal to depth. The $$j$$-th element of the list represents the value of the argument used for the $$j$$-th repetition.

For example, let us define the following variational ansatz:

def ansatz(params):
qml.RX(params, wires=)
qml.MultiRZ(params, wires=[0, 1])
qml.RY(params, wires=)


We wish to repeat this ansatz two times, with each layer having different params:

@qml.qnode(dev)
def circuit(params):
qml.layer(ansatz, 2, params)
return [qml.expval(qml.PauliZ(0)), qml.expval(qml.PauliZ(1))]


Since we only have one dynamic argument, params, we pass an array of first-dimension two, for the two layers of the repeated ansatz. We can also see that the params argument supplies three different parameters to three different gates. We therefore supply an array of size (2, 3) as an argument to qml.layer:

params = np.array([[0.5, 0.5, 0.5], [0.4, 0.4, 0.4]])


which yields the following circuit:

>>> circuit(params)
>>> print(circuit.draw())
0: ──RX(0.5)──╭RZ(0.5)──RX(0.4)──╭RZ(0.4)──RX(0.3)──╭RZ(0.3)───────────┤ ⟨Z⟩
1: ───────────╰RZ(0.5)──RY(0.5)──╰RZ(0.4)──RY(0.4)──╰RZ(0.3)──RY(0.3)──┤ ⟨Z⟩


Passing Multiple Static and Dynamic Arguments

It is also possible to pass multiple static and dynamic arguments into the same unitary. Dynamic arguments must be ordered in qml.layer in the same order in which they are passed into the template.

Consider the following ansatz:

def ansatz(param1, param2, wires, var):
qml.RX(param1, wires=wires)
qml.MultiRZ(param2, wires=wires)

if var:


This circuit can be repeated as:

@qml.qnode(dev)
def circuit(param1, param2):
qml.layer(ansatz, 2, param1, param2, wires=[1, 2], var=True)
return [qml.expval(qml.PauliZ(1)), qml.expval(qml.PauliZ(2))]


We can then run the circuit with a given set of parameters (note that the parameters are of size (2, 1), as the circuit is repeated twice, and for each repetition, both param1 and param2 are simply real numbers):

param1 = np.array([0.1, 0.2])
param2 = np.array([0.3, 0.4])


This gives us the following circuit:

>>> circuit(parm1, param2)
>>> print(circuit.draw())
1: ──RX(0.1)──╭RZ(0.3)──RX(0.2)──╭RZ(0.4)─────┤ ⟨Z⟩
2: ───────────╰RZ(0.3)──H────────╰RZ(0.4)──H──┤ ⟨Z⟩