Quantum Computing
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Quantum Fidelity

Measures how close two quantum states are — 1 means identical, 0 means orthogonal.

Formula

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

Variables

FFidelity
\rho, \sigmaDensity matrices of the two states
\text{tr}Trace

Example

Fidelity = 0.99 → 99 % match to the ideal state

Did You Know?

Current leading quantum processors achieve single-gate fidelities above 99.9 % — but errors compound fast across thousands of gates.

quantumfidelityerrorverification

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Qubit Superposition State

Intermediate

General state of a single qubit as a superposition of the computational basis states.

Normalisation Constraint

Basic

The squared amplitudes of a qubit must sum to 1, ensuring total probability is 100 %.

Hadamard Gate

Intermediate

Puts a qubit into an equal superposition — the most common single-qubit gate.

Pauli-X Gate (Quantum NOT)

Basic

Flips |0⟩ to |1⟩ and vice versa — the quantum equivalent of a classical NOT gate.

CNOT Gate

Intermediate

Two-qubit gate that flips the target qubit only when the control qubit is |1⟩.

Bell State (EPR Pair)

Intermediate

Maximally entangled two-qubit state — measuring one qubit instantly determines the other.