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mindquantum.core.circuit.qfi

mindquantum.core.circuit.qfi(circuit: Circuit, backend='mqvector')

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

$$A_{i,j}=\frac{\partial ⟨\psi |}{\partial x_i}\frac{\partial |\psi ⟩}{\partial x_j}$$

and

$$B_{i,j}=\frac{\partial ⟨\psi |}{\partial x_i}|\psi ⟩⟨\psi |\frac{\partial |\psi ⟩}{\partial x_j}$$

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]])