The SWAP Test

The SWAP test estimates how similar two quantum states are — the overlap |⟨ψ|φ⟩|² — using a controlled-SWAP and a single measured qubit.

Output

|⟨ψ|φ⟩|² from measurement statistics

Gate

controlled-SWAP (Fredkin)

Use

quantum kernels, fingerprinting

What it does

An ancilla in superposition controls a SWAP between the two states; a Hadamard and measurement on the ancilla yield a 0-probability that encodes the overlap. It never reveals the states — only their similarity.

Circuit sketch

Where it's used

Quantum kernel methods and classifiers, state comparison, and entanglement diagnostics.

In code (Qiskit)

qc=QuantumCircuit(3,1)
qc.h(0); qc.cswap(0,1,2); qc.h(0); qc.measure(0,0)