Two qubits can be in a state that is not one state for each: the *Bell state*

(|00⟩ + |11⟩)/√2.

Measured, it gives 00 or 11, each half the time, and never 01 or 10. Each qubit on its own looks like a fair coin, yet the two always agree. No pair of separate one-qubit states gives this; the qubits are *entangled*.

The gate that entangles here is the controlled-NOT, `cx control, target`. It flips the target exactly when the control is |1⟩. On a control in superposition it acts on both parts at once.

The engine runs a circuit of `h`, `cx` and the other Clifford gates on the *stabilizer tableau*, which follows thousands of qubits exactly without writing out 2ⁿ amplitudes. Try `wai-quantum plan` on your solution to see it chosen.