Quantum circuits¶

In PennyLane, quantum computations are represented as quantum node objects. A quantum node is used to declare the quantum circuit, and also ties the computation to a specific device that executes it. Quantum nodes can be easily created by using the qnode decorator.

QNodes can interface with any of the supported numerical and machine learning libraries—NumPy, PyTorch, TensorFlow, and JAX—indicated by providing an optional interface argument when creating a QNode. Each interface allows the quantum circuit to integrate seamlessly with library-specific data structures (e.g., NumPy arrays, or Pytorch/TensorFlow tensors) and optimizers.

By default, QNodes use the NumPy interface. The other PennyLane interfaces are introduced in more detail in the section on interfaces.

Quantum functions¶

A quantum circuit is constructed as a special Python function, a quantum circuit function, or quantum function in short. For example:

import pennylane as qml

def my_quantum_function(x, y):
    qml.RZ(x, wires=0)
    qml.CNOT(wires=[0,1])
    qml.RY(y, wires=1)
    return qml.expval(qml.PauliZ(1))

Note

PennyLane uses the term wires to refer to a quantum subsystem—for most devices, this corresponds to a qubit. For continuous-variable devices, a wire corresponds to a quantum mode.

Quantum functions are a restricted subset of Python functions, adhering to the following constraints:

The quantum function accepts classical inputs, and consists of quantum operations or sequences of operations called Templates, using one instruction per line.
The function can contain classical flow control structures such as for loops, but in general they must not depend on the parameters of the function.
The quantum function must always return either a single or a tuple of measured observable values, by applying a measurement function to a qubit observable or continuous-value observable.

Note

Measured observables must come after all other operations at the end of the circuit function as part of the return statement, and cannot appear in the middle.

Note

Quantum functions can only be evaluated on a device from within a QNode.

Defining a device¶

To run—and later optimize—a quantum circuit, one needs to first specify a computational device.

The device is an instance of the Device class, and can represent either a simulator or hardware device. They can be instantiated using the device loader.

dev = qml.device('default.qubit', wires=2, shots=1000)

PennyLane offers some basic devices such as the 'default.qubit' and 'default.gaussian' simulators; additional devices can be installed as plugins (see available plugins for more details). Note that the choice of a device significantly determines the speed of your computation, as well as the available options that can be passed to the device loader.

Device options¶

When loading a device, the name of the device must always be specified. Further options can then be passed as keyword arguments; these options can differ based on the device. For the in-built 'default.qubit' and 'default.gaussian' devices, the options are:

wires (int or Iterable): Number of subsystems represented by the device, or iterable that contains unique labels for the subsystems as numbers (i.e., [-1, 0, 2]) and/or strings (['ancilla', 'q1', 'q2']).
shots (None or int or list[int]): How many times the circuit should be evaluated (or sampled) to estimate statistical quantities. On some supported simulator devices, shots=None indicates to compute measurement statistics exactly. Note that this argument can be temporarily overwritten when a QNode is called. For example, my_qnode(shots=3) will temporarily evaluate my_qnode using three shots.

For a plugin device, refer to the plugin documentation for available device options.

Shot batches¶

Batches of shots can be specified by passing a list, allowing measurement statistics to be course-grained with a single QNode evaluation.

Consider

>>> shots_list = [5, 10, 1000]
>>> dev = qml.device("default.qubit", wires=2, shots=shots_list)

When QNodes are executed on this device, a single execution of 1015 shots will be submitted. However, three sets of measurement statistics will be returned; using the first 5 shots, second set of 10 shots, and final 1000 shots, separately.

For example:

@qml.qnode(dev)
def circuit(x):
  qml.RX(x, wires=0)
  qml.CNOT(wires=[0, 1])
  return qml.expval(qml.PauliZ(0) @ qml.PauliX(1)), qml.expval(qml.PauliZ(0))

Executing this, we will get an output of size (3, 2):

>>> circuit(0.5)
tensor([[ 1.   ,  1.   ],
        [ 0.2  ,  1.   ],
        [-0.022,  0.876]], requires_grad=True)

Custom wire labels¶

When you create a device by passing an integer to the wires argument, the integer defines the number of wires that you can address by consecutive integer labels 0, 1, 2, ....

But you can define your own wire labels instead, which may be handy if wires have “meanings” like an ancilla or garbage register, if they are arranged in a non-linear fashion like a grid, or if there are wires that you want to skip because they do not work on a hardware device.

This is done by passing an iterable of wire labels to the wires argument:

dev = qml.device('default.qubit', wires=['wire1', 'wire2'])

In the quantum function you can now use your own labels to address wires:

def my_quantum_function(x, y):
    qml.RZ(x, wires='wire1')
    qml.CNOT(wires=['wire1' ,'wire2'])
    qml.RY(y, wires='wire2')
    return qml.expval(qml.PauliZ('wire2'))

Allowed wire labels can be of the following types:

strings like wires=['a', 'd', 'b', ...] or wires=['auxiliary', 'q1', 'q2', ...],
integers like wires=[0, 4, 7] or even wires=[-1, 0, 4]
floats and other numbers like wires=[1., 2., 4.]
mixed types like wires=['auxiliary', -1, 0, 'q3']

Note

Some devices, such as hardware chips, may have a fixed number of wires. The iterable of labels passed to the device’s wires argument must match this expected number of wires.

Creating a quantum node¶

Together, a quantum function and a device are used to create a quantum node or QNode object, which wraps the quantum function and binds it to the device.

A QNode can be explicitly created as follows:

circuit = qml.QNode(my_quantum_function, dev)

The QNode can be used to compute the result of a quantum circuit as if it was a standard Python function. It takes the same arguments as the original quantum function:

>>> circuit(np.pi/4, 0.7)
tensor(0.764, requires_grad=True)

To view the quantum circuit given specific parameter values, we can use the draw() transform:

>>> print(qml.draw(circuit)(np.pi/4, 0.7))
 wire1: ──RZ(0.785)──╭C───────────┤
 wire2: ─────────────╰X──RY(0.7)──┤ ⟨Z⟩

The QNode decorator¶

A more convenient—and in fact the recommended—way for creating QNodes is the provided qnode decorator. This decorator converts a Python function containing PennyLane quantum operations to a QNode circuit that will run on a quantum device.

Note

The decorator completely replaces the Python-based quantum function with a QNode of the same name—as such, the original function is no longer accessible.

For example:

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

@qml.qnode(dev)
def circuit(x):
    qml.RZ(x, wires=0)
    qml.CNOT(wires=[0,1])
    qml.RY(x, wires=1)
    return qml.expval(qml.PauliZ(1))

result = circuit(0.543)

Collections of QNodes¶

Sometimes you may need multiple QNodes that only differ in the measurement observable (like in VQE), or in the device they are run on (for example, if you benchmark different devices), or even the quantum circuit that is evaluated. While these QNodes can be defined manually “by hand”, PennyLane offers QNode collections as a convenient way to define and run families of QNodes.

QNode collections are a sequence of QNodes that:

Have the same function signature, and
Can be evaluated independently (that is, the input of any QNode in the collection does not depend on the output of another).

Consider the following two quantum nodes:

@qml.qnode(dev1)
def x_rotations(params):
    qml.RX(params[0], wires=0)
    qml.RX(params[1], wires=1)
    qml.CNOT(wires=[0, 1])
    return qml.expval(qml.PauliZ(0))

@qml.qnode(dev2)
def y_rotations(params):
    qml.RY(params[0], wires=0)
    qml.RY(params[1], wires=1)
    qml.CNOT(wires=[0, 1])
    return qml.expval(qml.Hadamard(0))

As the QNodes in the collection have the same signature, and we can can construct a QNodeCollection and therefore feed them the same parameters:

>>> qnodes = qml.QNodeCollection([x_rotations, y_rotations])
>>> len(qnodes)
2
>>> qnodes([0.2, 0.1])
array([0.98006658, 0.70703636])

PennyLane also provides some high-level tools for creating and evaluating QNode collections. For example, map() allows a single function of quantum operations (or template) to be mapped across multiple observables or devices.

For example, consider the following quantum function ansatz:

def my_ansatz(params, **kwargs):
    qml.RX(params[0], wires=0)
    qml.RX(params[1], wires=1)
    qml.CNOT(wires=[0, 1])

We can define a list of observables, and two devices:

>>> obs_list = [qml.PauliX(0) @ qml.PauliZ(1), qml.PauliZ(0) @ qml.PauliX(1)]
>>> qpu1 = qml.device("forest.qvm", device="Aspen-4-4Q-D") # requires PennyLane-Forest
>>> qpu2 = qml.device("forest.qvm", device="Aspen-7-4Q-B") # requires PennyLane-Forest

Note

The two devices above require the PennyLane-Forest plugin be installed, as well as the Forest QVM. You can also try replacing them with alternate devices.

Mapping the template across the observables and devices creates a QNodeCollection:

>>> qnodes = qml.map(my_ansatz, obs_list, [qpu1, qpu2], measure="expval")
>>> type(qnodes)
pennylane.collections.qnode_collection.QNodeCollection
>>> params = [0.54, 0.12]
>>> qnodes(params)
array([-0.02854835  0.99280864])
Functions are available to process QNode collections, including :func:`~.pennylane.collections.dot`,
:func:`~.pennylane.collections.sum`, and :func:`~.pennylane.collections.apply`:

>>> cost_fn = qml.sum(qnodes)
>>> cost_fn(params)
0.906

Note

QNode collections support an experimental parallel execution mode. See the QNodeCollection documentation for more details.

Importing circuits from other frameworks¶

PennyLane supports creating customized PennyLane templates imported from other frameworks. By loading your existing quantum code as a PennyLane template, you add the ability to perform analytic differentiation, and interface with machine learning libraries such as PyTorch and TensorFlow. Currently, QuantumCircuit objects from Qiskit, OpenQASM files, pyQuil programs, and Quil files can be loaded by using the following functions:

`from_qiskit`	Loads Qiskit QuantumCircuit objects by using the converter in the PennyLane-Qiskit plugin.
`from_qasm`	Loads quantum circuits from a QASM string using the converter in the PennyLane-Qiskit plugin.
`from_qasm_file`	Loads quantum circuits from a QASM file using the converter in the PennyLane-Qiskit plugin.
`from_pyquil`	Loads pyQuil Program objects by using the converter in the PennyLane-Forest plugin.
`from_quil`	Loads quantum circuits from a Quil string using the converter in the PennyLane-Forest plugin.
`from_quil_file`	Loads quantum circuits from a Quil file using the converter in the PennyLane-Forest plugin.

Note

To use these conversion functions, the latest version of the PennyLane-Qiskit and PennyLane-Forest plugins need to be installed.

Objects for quantum circuits can be loaded outside or directly inside of a QNode. Circuits that contain unbound parameters are also supported. Parameter binding may happen by passing a dictionary containing the parameter-value pairs.

Once a PennyLane template has been created from such a quantum circuit, it can be used similarly to other templates in PennyLane. One important thing to note is that custom templates must always be executed within a QNode (similar to pre-defined templates).

Note

Certain instructions that are specific to the external frameworks might be ignored when loading an external quantum circuit. Warning messages will be emitted for ignored instructions.

The following is an example of loading and calling a parametrized Qiskit QuantumCircuit object while using the QNode decorator:

from qiskit import QuantumCircuit
from qiskit.circuit import Parameter
import numpy as np

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

theta = Parameter('θ')

qc = QuantumCircuit(2)
qc.rz(theta, [0])
qc.rx(theta, [0])
qc.cx(0, 1)

@qml.qnode(dev)
def quantum_circuit_with_loaded_subcircuit(x):
    qml.from_qiskit(qc)({theta: x})
    return qml.expval(qml.PauliZ(0))

angle = np.pi/2
result = quantum_circuit_with_loaded_subcircuit(angle)

Furthermore, loaded templates can be used with any supported device, any number of times. For instance, in the following example a template is loaded from a QASM string, and then used multiple times on the forest.qpu device provided by PennyLane-Forest:

import pennylane as qml

dev = qml.device('forest.qpu', wires=2)

hadamard_qasm = 'OPENQASM 2.0;' \
                'include "qelib1.inc";' \
                'qreg q[1];' \
                'h q[0];'

apply_hadamard = qml.from_qasm(hadamard_qasm)

@qml.qnode(dev)
def circuit_with_hadamards():
    apply_hadamard(wires=[0])
    apply_hadamard(wires=[1])
    qml.Hadamard(wires=[1])
    return qml.expval(qml.PauliX(0)), qml.expval(qml.PauliX(1))

result = circuit_with_hadamards()

Quantum circuits¶

Quantum functions¶

Defining a device¶

Device options¶

Shot batches¶

Custom wire labels¶

Creating a quantum node¶

The QNode decorator¶

Collections of QNodes¶

Importing circuits from other frameworks¶

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