vjp(f, params, cotangents, method=None, h=None, argnum=None)[source]

A qjit() compatible Vector-Jacobian product of PennyLane programs.

This function allows the Vector-Jacobian Product of a hybrid quantum-classical function to be computed within the compiled program.


vjp is intended to be used with qjit() only.


When used with qjit(), this function only supports the Catalyst compiler. See catalyst.vjp() for more details.

Please see the Catalyst quickstart guide, as well as the sharp bits and debugging tips page for an overview of the differences between Catalyst and PennyLane.

  • f (Callable) – Function-like object to calculate VJP for

  • params (List[Array]) – List (or a tuple) of arguments for f specifying the point to calculate VJP at. A subset of these parameters are declared as differentiable by listing their indices in the argnum parameter.

  • cotangents (List[Array]) – List (or a tuple) of tangent values to use in VJP. The list size and shapes must match the size and shape of f outputs.

  • method (str) – Differentiation method to use, same as in grad().

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

  • argnum (Union[int, List[int]]) – the params’ indices to differentiate.


Return values of f paired with the VJP values.

Return type


  • TypeError – invalid parameter types

  • ValueError – invalid parameter values

See also

grad(), jvp(), jacobian()


def vjp(params, cotangent):
  def f(x):
      y = [jnp.sin(x[0]), x[1] ** 2, x[0] * x[1]]
      return jnp.stack(y)

  return qml.vjp(f, [params], [cotangent])
>>> x = jnp.array([0.1, 0.2])
>>> dy = jnp.array([-0.5, 0.1, 0.3])
>>> vjp(x, dy)
[array([0.09983342, 0.04      , 0.02      ]),
array([-0.43750208,  0.07000001])]