Description

Calculate the fidelity of two states \(\ket{\psi}\) and \(\ket{\phi}\). The general formula of fidelity \(F\) is defined as: \[F (\rho, \sigma) = \Big(\text{Tr}\sqrt{\rho^{\frac{1}{2}} \sigma \rho^{\frac{1}{2}}} \Big) ^ 2\]

Where \(\rho = |\psi\rangle\langle\psi|\), and \(\sigma = |\phi\rangle\langle\phi|\)

fidelity(psi, phi)

Parameters

• psi (matrix) — The state \(\ket{\psi}\)
• phi (matrix) — The state \(\ket{\phi}\)

Return Value

• number — Returns the fidelity

Usage Example

import quantum
 
qc_1 = quantum_circuit(1)
qc_2 = quantum_circuit(1)
 
qc_1.h(0)
 
psi = qc_1.statevector()
phi = qc_2.statevector()
 
f = fidelity(psi, phi)
writeln(f)
 
 
' Output:
' 0.5

Documentation version: 1.1.03. Updated on: 11 February 2026.
Dinfio is designed and written by Muhammad Faruq Nuruddinsyah. Copyright © 2014-2026. All rights reserved.