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mindquantum.simulator.fidelity

mindquantum.simulator.fidelity(rho: np.ndarray, sigma: np.ndarray)

Calculate the fidelity of two quantum states.

Definition of quantum state fidelity shown as below.

$$F(\rho ,\sigma )={\left(\text{tr}\sqrt{\sqrt{\rho }\sigma \sqrt{\rho }}\right)}^2$$

where $\rho$ and $\sigma$ are density matrices.

If both $\rho$ and $\sigma$ are pure, $\rho =|{\psi }_{\rho }⟩⟨{\psi }_{\rho }|$ and $\sigma =|{\psi }_{\sigma }⟩⟨{\psi }_{\sigma }|$, then

$$F(\rho ,\sigma )={\left|⟨{\psi }_{\rho }|{\psi }_{\sigma }⟩\right|}^2$$

Besides, mixing state vector with density matrix as input is also supported.

Parameters

• rho (np.ndarray) – One of the quantum state. Support both state vector and density matrix.

• sigma (np.ndarray) – Another quantum state. Support both state vector and density matrix.

Returns

numbers.Number, the fidelity of two quantum states.

Examples

>>> from mindquantum.core.circuit import Circuit
>>> from mindquantum.simulator import Simulator, fidelity
>>> circ = Circuit().h(0).x(1, 0)
>>> sim = Simulator('mqmatrix', 2)
>>> sim.apply_circuit(circ)
>>> rho = sim.get_qs()
>>> sim.reset()
>>> sigma = sim.get_qs()
>>> fidelity(rho, sigma)
0.5000000000000001