Hawkynt

Topological Surface Code

Classical simulation of topological surface code, a 2D lattice quantum error correction code with stabilizer measurements. Educational implementation demonstrating syndrome extraction and error correction principles from Kitaev’s fault-tolerant quantum computing framework.

Properties

Property	Value
Category	Error Correction
Sub-category	Quantum Code
Security status	🧪 Experimental
Complexity	Expert
Inventor	Alexei Kitaev
Year	1997
Origin	🇷🇺 Russia
Source	algorithms/ecc/surface-code.js

Security

Status: 🧪 Experimental

Known vulnerabilities

Issue	Description	Mitigation
Quantum Hardware Required	Surface codes require quantum hardware with physical qubits. Classical simulation is exponentially expensive.	—
Threshold Requirements	Requires physical error rates below ~1% threshold for effective error correction. Above threshold, logical error rates increase.	—
Resource Overhead	Distance-3 code requires 17 physical qubits per logical qubit. Distance-5 requires 49 qubits. Overhead grows quadratically.	—

Documentation

• Kitaev’s Original Paper (1997)
• Topological Quantum Memory (2002)
• Error Correction Zoo - Surface Code
• Google Quantum AI - Surface Code
• IBM Qiskit Surface Codes

References

• Fault-tolerant quantum computation by anyons
• Dennis, Kitaev, Landahl, Preskill - Topological quantum memory
• Google Willow Surface Code
• Surface codes: Towards practical large-scale quantum computation

Test vectors

7 vectors ship with this algorithm and run in the test suite. Byte values are hexadecimal.

Vector 1 — Distance-3 planar surface code - no errors

Field	Value
distance	3
input	0000000000000000000000000000000000
expected	0000000000000000000000000000000000

Vector 2 — Distance-3 planar surface code - X error detection via stabilizers

Field	Value
distance	3
input	0001000000000000000000000000000000
expected	0000000000000000000000000000000000

Vector 3 — Distance-3 planar surface code - Z error detection via stabilizers

Field	Value
distance	3
errorType	Z
input	0001000000000000000000000000000000
expected	0000000000000000000000000000000000

Vector 4 — [Encode logical

0> state in distance-3 surface code](https://errorcorrectionzoo.org/c/surface)

Field	Value
distance	3
logicalState	0
input	00
expected	0000000000000000000000000000000000

Vector 5 — [Encode logical

1> state in distance-3 surface code](https://errorcorrectionzoo.org/c/surface)

Field	Value
distance	3
logicalState	1
input	01
expected	0101010101010101010101010101010101

Vector 6 — Distance-5 planar surface code - no errors

Field	Value
distance	5
input	00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00
expected	00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00

Vector 7 — Syndrome extraction for X stabilizer violation

Field	Value
distance	3
syndromeExtraction	Yes
input	0000010000000000000000000000000000
expected	0001010000000000

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