mindquantum.core.circuit.qfi

mindquantum.core.circuit.qfi(circuit: Circuit, backend='mqvector')[source]

Calculate the quantum fisher information of the given parameterized circuit with given parameters.

The quantum fisher information of a parameterized circuit is defined as:

\[\text{QFI}_{i,j} = 4\text{Re}(A_{i,j} - B_{i,j})\]

where

\[A_{i,j} = \frac{\partial \left<\psi\right| }{\partial x_{i}} \frac{\partial \left|\psi\right> }{\partial x_{j}}\]

and

\[B_{i,j} = \frac{\partial \left<\psi\right| }{\partial x_i}\left|\psi\right> \left<\psi\right|\frac{\partial \left|\psi\right> }{\partial x_{j}}\]

Parameters

circuit (Circuit) – A parameterized quantum circuit.
backend (str) – A supported simulator backend. Please refer description of Simulator. Default: 'mqvector'.

Returns

Function, a function that can calculate quantum fisher information.

Examples

>>> import numpy as np
>>> from mindquantum.core.circuit import qfi, Circuit
>>> circ = Circuit().rx('a', 0).ry('b', 0).rz('c', 0)
>>> qfi_ops = qfi(circ)
>>> qfi_ops(np.array([1, 2, 3]))
array([[ 1.        ,  0.        , -0.90929743],
       [ 0.        ,  0.29192658, -0.18920062],
       [-0.90929743, -0.18920062,  0.94944468]])