Bug Report: Logical Error Rates with PAULI_CHANNEL_2

[rsnegrin]

Description

I had an issue when using PyMatching decoder with circuits that include a PAULI_CHANNEL_2 gate in the Stim framework.

Code

Expand to see the code

import stim
import sinter
import os

p_r = 1e-6
p_cnot = 0.1
p2 = [
    p_cnot,  # p_ix
    0.0,
    0.0,
    0.0,
    0.0,
    0.0,
    0.0,
    0.0,
    0.0,
    0.0,
    0.0,
    0.0,
    0.0,
    0.0,
    0.0,
]

# Circuit with X_ERROR
circ1 = stim.Circuit()
circ1.append("R", range(3))
circ1.append("X_ERROR", range(3), p_r)
circ1.append("TICK")
circ1.append("CX", [0, 1])
circ1.append("X_ERROR", 1, p_cnot)
circ1.append("TICK")
circ1.append("CX", [2, 1])
circ1.append("X_ERROR", 1, p_cnot)
circ1.append("TICK")
circ1.append("M", range(3))

circ1.append("DETECTOR", [stim.target_rec(-3 + 1)], (1, 0))
circ1.append(
    "DETECTOR",
    [stim.target_rec(-3 + 0), stim.target_rec(-3 + 1), stim.target_rec(-3 + 2)],
    (0, 0),
)
circ1.append("OBSERVABLE_INCLUDE", [stim.target_rec(-1)], 0)

# Circuit with PAULI_CHANNEL_2
circ2 = stim.Circuit()
circ2.append("R", range(3))
circ2.append("X_ERROR", range(3), p_r)
circ1.append("TICK")
circ2.append("CX", [0, 1])
circ2.append("PAULI_CHANNEL_2", [0, 1], p2)
circ1.append("TICK")
circ2.append("CX", [2, 1])
circ2.append("PAULI_CHANNEL_2", [2, 1], p2)
circ1.append("TICK")
circ2.append("M", range(3))

circ2.append("DETECTOR", [stim.target_rec(-3 + 1)], (1, 0))
circ2.append(
    "DETECTOR",
    [stim.target_rec(-3 + 0), stim.target_rec(-3 + 1), stim.target_rec(-3 + 2)],
    (0, 0),
)
circ2.append("OBSERVABLE_INCLUDE", [stim.target_rec(-1)], 0)

tasks = [
    sinter.Task(circuit=circ, json_metadata={"i": i})
    for i, circ in enumerate([circ1, circ2])
]
results = sinter.collect(
    num_workers=os.cpu_count(),
    tasks=tasks,
    decoders=["pymatching"],
    max_shots=10_000_000,
    max_errors=None,
)
results.sort(key=lambda x: x.json_metadata["i"])

logical_error_rate1 = results[0].errors / results[0].shots
logical_error_rate2 = results[1].errors / results[1].shots
print(f"Logical error X_ERROR: {logical_error_rate1}")
print(f"Logical error PAULI_CHANNEL_2: {logical_error_rate2}")

Both circuits should be equivalent with the difference that one uses X_ERROR and the other PAULI_CHANNEL_2 to represent the same error.

Output

Here es an example of the output:

• Logical error X_ERROR: 1.5e-06
• Logical error PAULI_CHANNEL_2: 0.1799395

When using PAULI_CHANNEL_2 , I need to set approximate_disjoint_errors=True to be able to run the simulations. Sinter also sets decompose_errors=True as default (details).

Here is the detector error model when using the PAULI_CHANNEL_2:

circ2.detector_error_model(decompose_errors=True, approximate_disjoint_errors=True)

# Output:
stim.DetectorErrorModel('''
    error(1e-06) D0
    error(1e-06) D0 D1
    error(1e-06) D0 L0
    error(0.1) D1 L0 ^ D0 L0
    error(0.1) D1 ^ D0
    detector(1, 0) D0
    detector(0, 0) D1
''')

Other decoders like Fusion Blossom don’t have this problem and give similar results for both circuits. Also, the issue is not limited to X_ERROR, since I initially encountered this with Z_ERROR.

I'm not sure about the exact source of this problem, but it would be good to evaluate.
Thanks !