qml.math.fidelity_statevector¶
-
fidelity_statevector(state0, state1, check_state=False, c_dtype='complex128')[source]¶ Compute the fidelity for two states (given as state vectors) acting on quantum systems with the same size.
The fidelity for two pure states given by state vectors \(\ket{\psi}\) and \(\ket{\phi}\) is defined as
\[F( \ket{\psi} , \ket{\phi}) = \left|\braket{\psi, \phi}\right|^2\]This is faster than calling
pennylane.math.fidelity()on the density matrix representation of pure states.Note
It supports all interfaces (NumPy, Autograd, Torch, TensorFlow and Jax). The second state is coerced to the type and dtype of the first state. The fidelity is returned in the type of the interface of the first state.
- Parameters
state0 (tensor_like) –
(2**N)or(batch_dim, 2**N)state vector.state1 (tensor_like) –
(2**N)or(batch_dim, 2**N)state vector.check_state (bool) – If True, the function will check the validity of both states; that is, the shape and the norm
c_dtype (str) – Complex floating point precision type.
- Returns
Fidelity between the two quantum states.
- Return type
float
Example
Two state vectors can be used as arguments and the fidelity (overlap) is returned, e.g.:
>>> state0 = [0.98753537-0.14925137j, 0.00746879-0.04941796j] >>> state1 = [0.99500417+0.j, 0.09983342+0.j] >>> qml.math.fidelity_statevector(state0, state1) 0.9905158135644924