A hybrid quantum-classical neural network learns to identify phases of matter by combining quantum measurements with classical deep learning, enabling machines to detect topological order from experimental data.
Drag the slider to adjust the field strength h and observe how topological entanglement entropy S_topo and stabilizer expectation values change. The dashed line marks the phase transition near h = 0.3.
Synthetic data for illustration only. The sharp drop in S_topo signals the transition from topological to trivial phase.
Consider a 4-qubit system in a topological state. After the parameterized quantum circuit, we measure the Z-basis expectation values for each qubit. The classical neural network then processes these measurements to classify the phase.
| Qubit | Z expectation | Weight | Contribution |
|---|---|---|---|
| q0 | +0.82 | 0.45 | +0.37 |
| q1 | -0.63 | 0.32 | -0.20 |
| q2 | +0.91 | 0.28 | +0.25 |
| q3 | -0.74 | 0.35 | -0.26 |
The weighted sum is +0.16, which after a sigmoid activation gives a probability of 0.54 for the topological phase. The network correctly identifies the state as topological (above the 0.5 threshold).