jacobian(f: Union[catalyst.jax_tracer.Function, pennylane.workflow.qnode.QNode, Callable, catalyst.jit.QJIT], *, method=None, h=None, argnum=None)[source]

A qjit() compatible Jacobian transformation for PennyLane/Catalyst.

This function allows the Jacobian of a hybrid quantum-classical function to be computed within the compiled program. Outside of a compiled function, this function will simply dispatch to its JAX counterpart jax.jacobian. The function f can return any pytree-like shape.

  • f (Callable) – a function or a function object to differentiate

  • method (str) –

    The method used for differentiation, which can be any of ["auto", "fd"], where:

    • "auto" represents deferring the quantum differentiation to the method specified by the QNode, while the classical computation is differentiated using traditional auto-diff. Catalyst supports "parameter-shift" and "adjoint" on internal QNodes. Notably, QNodes with diff_method="finite-diff" is not supported with "auto".

    • "fd" represents first-order finite-differences for the entire hybrid function.

  • h (float) – the step-size value for the finite-difference ("fd") method

  • argnum (Tuple[int, List[int]]) – the argument indices to differentiate


A callable object that computes the Jacobian of the wrapped function for the given


Return type



ValueError – Invalid method or step size parameters.


Any JAX-compatible optimization library, such as JAXopt, can be used alongside jacobian for JIT-compatible variational workflows. See the Quick Start for examples.

See also



dev = qml.device("lightning.qubit", wires=1)

def workflow(x):
    def circuit(x):
        qml.RX(jnp.pi * x[0], wires=0)
        qml.RY(x[1], wires=0)
        return qml.probs()

    g = jacobian(circuit)
    return g(x)
>>> workflow(jnp.array([2.0, 1.0]))
array([[ 3.48786850e-16 -4.20735492e-01]
       [-8.71967125e-17  4.20735492e-01]])