|q⟩ Bad Qubits

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Multiple choice
After running this circuit, what is the probability of measuring |001⟩?
⚛ The apparatus
const c = circuit(3);
// 1. Encode |+_L>.
c.h(0);
c.cx(0, 1);
c.cx(0, 2);
// 2. Inject an X error on qubit 2.
c.x(2);
// 3. Decode (CNOT is self-inverse).
c.cx(0, 1);
c.cx(0, 2);
// 4. Coherent majority correction onto the data qubit.
c.ccx(2, 1, 0);
return c;

Commit your prediction for P(|001⟩) — then run it.