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I am attempting to compute the circuit for the syndrome extraction of the [[144, 12, 12]] code using stim so as to consider circuit-level noise. Unfortunately, when trying to obtain the detector error model, there is an error in which it says that the circuit contains non-deterministic detectors. That should not be, since all measurements within the Z-basis should be determined.

The logic of the circuit goes as follows (it follows the process of the figure from Fowler et al, but with 6 data qubits):

  1. Initialize all data qubits and checks to the |0> state.
  2. Make z-checks (Hx generators) to undergo a Hadamard gate.
  3. Apply CNOTs from data qubit to x-check and from z-check to data qubit in an ordered manner as described in Bravyi et al.
  4. Make z-checks to undergo a Hadamard gate.
  5. Measure all checks in the Z base.

The CNOT schedule makes n/2 data qubits interact first with the x-checks while the other n/2 interact first with the z-checks. It is when the data qubits interact with the other half of checks that detection error model cannot be computed. I have trying to compute it both with depolarizing 1 qubit gate and 2 qubit gate errors and with perfect gates and both fail. Is there a significant point that I am missing?

The code follows the structure:

    full_circuit = stim.Circuit()
    circuit = stim.Circuit()

    ldatas = [i for i in range(self.Hz.shape[1]//2)]
    rdatas = [ldatas[-1] + 1 + i for i in range(self.Hz.shape[1]//2)]
    xchecks = [rdatas[-1] + 1 + i for i in range(self.Hx.shape[0])]
    zchecks = [xchecks[-1] + 1 + i for i in range(self.Hz.shape[0])]
    
    full_circuit.append_operation("R", ldatas + rdatas + xchecks + zchecks)
    full_circuit.append_operation("M", xchecks + zchecks)

    circuit.append_operation("R", xchecks + zchecks)
    circuit.append_operation("H", zchecks)

    As = [A1, A2, A3, B1.T, B2.T, B3.T]
    Bs = [A1.T, A2.T, A3.T, B1, B2, B3]
    # A and B are the polynomials used to make the parity check matrix.        

    for j in range(len(As)//2):
        A = As[j]
        B = Bs[j]
        for i in range(len(xchecks)):
            index_data = np.where(A[i] == 1)[0][0]
            circuit.append_operation("CNOT", (zchecks[i],ldatas[index_data]))
            circuit.append_operation("DEPOLARIZE2", (zchecks[i], ldatas[index_data]), p)
            index_data = np.where(B[i] == 1)[0][0]
            circuit.append_operation("CNOT", (rdatas[index_data], xchecks[i]))
            circuit.append_operation("DEPOLARIZE2", (rdatas[index_data], xchecks[i]), p)

    for j in range(len(As)//2, len(As)):
            A = As[j]
            B = Bs[j]
            for i in range(len(xchecks)):
                index_data = np.where(A[i] == 1)[0][0]
                circuit.append_operation("CNOT", (zchecks[i],rdatas[index_data]))
                circuit.append_operation("DEPOLARIZE2", (zchecks[i], rdatas[index_data]), p)
                index_data = np.where(B[i] == 1)[0][0]
                circuit.append_operation("CNOT", (ldatas[index_data], xchecks[i]))
                circuit.append_operation("DEPOLARIZE2", (ldatas[index_data], xchecks[i]), p)
    
    circuit.append_operation("H", zchecks)
    circuit.append_operation("M", xchecks + zchecks)

    #  I only record parity of detectors susceptible to X-noise.
    for i in range(len(xchecks)):
        circuit.append_operation("DETECTOR", [stim.target_rec(i-(4*self.Hz.shape[0])), stim.target_rec(i-(2*self.Hz.shape[0]))])
    
    full_circuit += circuit * (rounds -1)

The first CNOT loop can be computed and the detector error model successfully extracted, nevertheless, upon applying the second for loop (with or without DEPOLARIZE2 errors), I reach a stack trace error.

A simplified version of the circuit can be found in the last figure.

enter image description here enter image description here

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  • $\begingroup$ It's not possible to debug the problem if you don't share the actual stim circuit. But the most likely issue is that you did the operations in a bad order. $\endgroup$ Nov 3, 2023 at 22:27
  • $\begingroup$ Try only measuring one stabilizer and get that working, then add the operations for a second, and so forth until the error comes back. That will tell you specifically which operation is in the wrong place. $\endgroup$ Nov 3, 2023 at 22:37
  • $\begingroup$ I have updated the question so as to include the circuit, apologies for that. If I compute only x-check circuit or z-check circuit the circuit works fine (or even if I only compute the first for loop within the stim circuit). Otherwise I face an error. $\endgroup$ Nov 5, 2023 at 9:49
  • $\begingroup$ You didn't include the full circuit, you included code that generates the circuit. And you didn't include the dependencies of that code, so no one can run it. $\endgroup$ Nov 5, 2023 at 11:18
  • $\begingroup$ I have now included a figure of a code which undergoes the same error. The top 4 qubits are data qubits, the qubits 4 and 5 are X detectors and the bottom ones are Z-detectors. Upon finding the detector error model I get the error. $\endgroup$ Nov 6, 2023 at 20:28

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