|q⟩ Bad Qubits

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Predict the output
This circuit is sampled for 1024 shots on the seeded simulator (seed 1233). How many of the shots come out |0000⟩? Estimate P(|0000⟩) × 1024 and pick the closest option.
⚛ The apparatus
const c = circuit(4);
// 1 & 2: two elementary Bell pairs
c.h(0); c.cx(0, 1);
c.h(2); c.cx(2, 3);
// 3: Bell-state measurement on the repeater qubits (inverse entangler)
c.cx(1, 2);
c.h(1);
// 4: feed-forward corrections onto Bob's qubit (deferred-measurement form)
c.cx(2, 3);   // X correction conditioned on q2
c.cz(1, 3);   // Z correction conditioned on q1
// 5
c.measure();
return c;

Commit your prediction for counts of |0000⟩ over 1024 shots — then run it.