Surface Code

3×3 grid of data qubits — X and Z stabilizers detect errors without disturbing logical qubit

SURFACE CODE — click data qubit to inject error
Data qubit (clean)
X error (bit flip)
Z error (phase flip)
Both X&Z
X-stabilizer (plaquette)
Z-stabilizer (vertex)
HOW IT WORKS
The surface code encodes 1 logical qubit in 9 physical data qubits.

X-stabilizers (plaquettes): measure XXXX on 4 neighboring data qubits. A −1 eigenvalue reveals Z errors nearby.

Z-stabilizers (vertices): measure ZZZZ. A −1 eigenvalue reveals X errors nearby.

The syndrome (pattern of −1 stabilizers) tells us where errors occurred — without measuring the logical state!
SYNDROME MEASUREMENT
ERROR LOG
No errors injected.