Directly computes the quantum fidelity |⟨φ(x)|φ(y)⟩|² using the SWAP test. This is the "true" quantum kernel without approximations.
| Property | Value |
|---|
| Category | Machine Learning |
| Difficulty | Advanced |
| Framework | PennyLane |
| Qubits | 5 (2+2+1) |
| Depth | ~15 |
| Gates | H, CSWAP, RY, RZ |
Measures overlap between two quantum states:
|0⟩ ─── H ───●─── H ─── measure
│
|φ(x)⟩ ─────SWAP
│
|φ(y)⟩ ─────SWAP
P(ancilla = 0) = (1 + |⟨φ(x)|φ(y)⟩|²) / 2
Therefore:
┌───┐ ┌───┐
q_0: ┤ H ├──●──┤ H ├──M
└───┘ │ └───┘
│
q_1: ─φ(x)──X──────────
│
q_2: ─φ(x)──X──────────
│
q_3: ─φ(y)──X──────────
│
q_4: ─φ(y)──X──────────
from circuit import run_circuit
result = run_circuit(n_samples=10, n_data_qubits=2)
print(f"Total qubits: {result['total_qubits']}")
print(f"Diagonal mean: {result['diagonal_mean']:.4f}")
print(f"Is PSD: {result['is_psd']}")
| Property | Expected |
|---|
| K(x,x) | 1.0 |
| K(x,y) | [0, 1] |
| Symmetry | K(x,y) = K(y,x) |
| PSD | Always true |
| n_data_qubits | Total Qubits | CSWAP gates |
|---|
| 1 | 3 | 1 |
| 2 | 5 | 2 |
| 4 | 9 | 4 |
| n | 2n+1 | n |
| Method | Qubits | Accuracy | Measurements |
|---|
| Inversion test | n | Exact | O(1/ε²) |
| SWAP test | 2n+1 | Exact | O(1/ε²) |
| Compute-uncompute | n | Exact | O(1/ε²) |
- Kernel methods: Exact quantum similarity
- Quantum state discrimination: Distinguishing states
- Entanglement witness: Detecting entanglement