Metrics: comparing distributions

Every target's outcome distribution q is compared with the ideal statevector distribution p.

TVD (p, q) = \frac{1}{2} x \sum ∣ p (x) - q (x) ∣

Total variation distance: 0 = identical, 1 = no overlap. The most intuitive 'how wrong' number.

F_{H} (p, q) = (x \sum p (x) q (x))^{2}, D_{H} = 1 - F_{H}

Hellinger fidelity (1 = identical) and distance. Matches qiskit.quantum_info.hellinger_fidelity.

Success probability is the probability the target assigns to the ideal most likely bitstring: the number you care about for algorithms with one right answer (Grover, Bernstein–Vazirani).

p	q	TVD	Hellinger fidelity
{00: .5, 11: .5}	same	0	1
{00: .5, 11: .5}	{00: .5, 01: .5}	0.5	0.25

← Previous

Simulators, noise, T1/T2 and fake backends

Q-sphere and Bloch spheres