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In the syndrome measurement circuit constructed using Stim, is there any difference between simulating with the data qubits prepared in the state $|0_L \rangle$ and simulating with data qubits prepared in the state $|0\rangle^{\otimes n}$? For example, when calculating the logical X error rate, when I performed simulations in both cases, the results appeared to be almost the same numerically, but I'm not completely confident whether I'm obtaining exactly the same logical error probability in both cases and why.

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  • $\begingroup$ It's not clear what the distinction you're imagining actually cashes out as, in terms of the circuit. Give the two circuits. $\endgroup$ May 27, 2023 at 16:49

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All qubits starts in the $|0\rangle$ state at the start of the circuit, so operations that noiselessly measure Z observables or stabilizers at the beginning are effectively no-ops.

Operations like MPP X0*X1*X5*X6 that noiselessly measure an X stabilizer can matter, but you aren't actually using the measurement result and it doesn't anticommute with anything else you are doing so those operations also happen to be irrelevant here. If you declared detectors that compared the noisy measurement results to the noiseless measurement results then you would see differences.

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