Gradients and training

PennyLane offers seamless integration between classical and quantum computations. Code up quantum circuits in PennyLane, compute gradients of quantum circuits, and connect them easily to the top scientific computing and machine learning libraries.


When creating a QNode, you can specify the differentiation method that PennyLane should use whenever the gradient of that QNode is requested.

@qml.qnode(dev, diff_method="parameter-shift")
def circuit(x):
    qml.RX(x, wires=0)
    return qml.probs(wires=0)

PennyLane currently provides the following differentiation methods for QNodes:

Simulation-based differentiation

The following methods use reverse accumulation to compute gradients; a well-known example of this approach is backpropagation. These methods are not hardware compatible; they are only supported on statevector simulator devices such as default.qubit.

However, for rapid prototyping on simulators, these methods typically out-perform forward-mode accumulators such as the parameter-shift rule and finite-differences. For more details, see the quantum backpropagation demonstration.

  • "backprop": Use standard backpropagation.

    This differentiation method is only allowed on simulator devices that are classically end-to-end differentiable, for example default.qubit. This method does not work on devices that estimate measurement statistics using a finite number of shots; please use the parameter-shift rule instead.

  • "adjoint": Use a form of backpropagation that takes advantage of the unitary or reversible nature of quantum computation.

    The adjoint method reverses through the circuit after a forward pass by iteratively applying the inverse (adjoint) gate. This method is similar to "backprop", but has significantly lower memory usage and a similar runtime.

  • "reversible": Use a form of backpropagation that takes advantage of the unitary or reversible nature of quantum computation.

    This method is similar to the adjoint method, but has a slightly larger time overhead and a similar memory overhead. Compared to the parameter-shift rule, the reversible method can be faster or slower, depending on the density and location of parametrized gates in a circuit.

Hardware-compatible differentiation

The following methods support both quantum hardware and simulators, and are examples of forward accumulation. However, when using a simulator, you may notice that the time required to compute the gradients scales quadratically with the number of trainable circuit parameters.

  • "parameter-shift": Use the analytic parameter-shift rule for all supported quantum operation arguments, with finite-difference as a fallback.

  • "finite-diff": Use numerical finite-differences for all quantum operation arguments.

Device gradients

  • "device": Queries the device directly for the gradient. Only allowed on devices that provide their own gradient computation.


If not specified, the default differentiation method is diff_method="best". PennyLane will attempt to determine the best differentiation method given the device and interface. Typically, PennyLane will prioritize device-provided gradients, backpropagation, parameter-shift rule, and finally finite differences, in that order.

Gradient transforms

In addition to registering the differentiation method of QNodes to be used with autodifferentiation frameworks, PennyLane also provides a library of gradient transforms via the qml.gradients module.

Quantum gradient transforms are strategies for computing the gradient of a quantum circuit that work by transforming the quantum circuit into one or more gradient circuits. They accompany these circuits with a function that post-processes their output. These gradient circuits, once executed and post-processed, return the gradient of the original circuit.

Examples of quantum gradient transforms include finite-difference rules and parameter-shift rules; these can be applied directly to QNodes:

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

def circuit(weights):
    qml.RX(weights[0], wires=0)
    qml.RY(weights[1], wires=1)
    qml.CNOT(wires=[0, 1])
    qml.RX(weights[2], wires=1)
    return qml.probs(wires=1)
>>> weights = np.array([0.1, 0.2, 0.3], requires_grad=True)
>>> circuit(weights)
tensor([0.9658079, 0.0341921], requires_grad=True)
>>> qml.gradients.param_shift(circuit)(weights)
tensor([[-0.04673668, -0.09442394, -0.14409127],
        [ 0.04673668,  0.09442394,  0.14409127]], requires_grad=True)

Note that, while gradient transforms allow quantum gradient rules to be applied directly to QNodes, this is not a replacement — and should not be used instead of — standard training workflows (for example, qml.grad() if using Autograd, loss.backward() for PyTorch, or tape.gradient() for TensorFlow). This is because gradient transforms do not take into account classical processing, and only support gradients of quantum components. For more details on available gradient transforms, as well as learning how to define your own gradient transform, please see the qml.gradients documentation.

Training and interfaces

The bridge between the quantum and classical worlds is provided in PennyLane via interfaces. Currently, there are four built-in interfaces: NumPy, PyTorch, JAX, and TensorFlow. These interfaces make each of these libraries quantum-aware, allowing quantum circuits to be treated just like any other operation.

In PennyLane, an interface is declared when creating a QNode, e.g.,

@qml.qnode(dev, interface="tf")
def my_quantum_circuit(...):


If no interface is specified, PennyLane will default to the NumPy interface (powered by the autograd library).

This will allow native numerical objects of the specified library (NumPy arrays, Torch Tensors, or TensorFlow Tensors) to be passed as parameters to the quantum circuit. It also makes the gradients of the quantum circuit accessible to the classical library, enabling the optimization of arbitrary hybrid circuits.

See the links below for walkthroughs of each specific interface:

In addition to the core interfaces discussed above, PennyLane also provides higher-level classes for converting QNodes into both Keras and torch.nn layers:

pennylane.qnn.KerasLayer(qnode, …)

Converts a QNode() to a Keras Layer.

pennylane.qnn.TorchLayer(qnode, …)

Converts a QNode() to a Torch layer.


QNodes with an interface will always incur a small overhead on evaluation. If you do not need to compute quantum gradients of a QNode, specifying interface=None will remove this overhead and result in a slightly faster evaluation. However, gradients will no longer be available.