Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 1 1 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 1 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 1 0
Final-round detectors: 0 0 1 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 1
Final-round detectors: 0 0 1 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 1 1 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]


Prompt:
You are an expert quantum error correction decoder. Your job is to identify which data qubits experienced errors based on syndrome measurements.

A surface code protects 1 logical qubit using 9 data qubits arranged in a 3x3 grid. Stabilizer measurements detect errors: a '1' means that stabilizer fired (detected something wrong nearby); a '0' means it looks fine. Errors must be deduced from the pattern of stabilizers that fired.

Code distance: 3
Number of stabilizer rounds: 1
Physical error rate: 0.0005
X-stabilizer count per round: 0
Z-stabilizer count per round: 4

Round 1 X-stabilizers:
Round 1 Z-stabilizers: 0 0 0 0
Final-round detectors: 0 0 0 0

Identify which data qubits (numbered 0-8) had X-errors and Z-errors. Most syndromes have 0-2 errors; an empty list means no errors of that type.

Output exactly ONE line and nothing else. Do not write reasoning, markdown, bullets, analysis, or explanations. Your entire response must match this exact format:
X_ERRORS=[qubit_ids] Z_ERRORS=[qubit_ids]

Valid one-line examples:
X_ERRORS=[] Z_ERRORS=[]
X_ERRORS=[] Z_ERRORS=[4]
X_ERRORS=[2] Z_ERRORS=[5,6]