|q⟩ Bad Qubits

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Predict the output
On the seeded simulator (seed 1366), this circuit runs for 1024 shots. About how many come out |001⟩? Estimate P(|001⟩) × 1024 and pick the closest option.
⚛ 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 counts of |001⟩ over 1024 shots — then run it.