Surface Code
The leading quantum error correction code for practical systems
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Shor's Error Correction Code
Introduction to Surface Code
The surface code is the most promising quantum error correction code for near-term quantum computers. It uses a 2D lattice of qubits with local interactions, making it hardware-friendly.
Key Properties:
ā¢ 2D planar layout
ā¢ Nearest-neighbor interactions only
ā¢ High threshold (~1% error rate)
ā¢ Scalable architecture
Why Surface Code?
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Hardware Friendly
Only nearest-neighbor qubit interactions required
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High Threshold
Tolerates ~1% physical error rate
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Local Operations
All stabilizer measurements are local
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Scalable
Grows to arbitrary size on 2D lattice
vs Other Codes
| Code | Qubits | Connectivity | Practical? |
|---|---|---|---|
| Bit Flip | 3 | All-to-all | No (X only) |
| Shor's Code | 9 | Complex | No (overhead) |
| Surface Code | dĀ² + (d-1)Ā² | 2D nearest | Yes! ā |
Code Parameters
Distance d
3, 5, 7...
Must be odd
Data Qubits
dĀ²
Physical qubits
Measurement
dĀ²-1
Ancilla qubits
Logical
1
Per patch