Surface code

The surface code is a quantum error-correcting code that encodes one logical qubit in a two-dimensional lattice of physical Qubits, using repeated parity measurements on neighboring qubits to detect and locate errors without disturbing the stored information. It is the leading approach to fault-tolerant quantum computing because it needs only local, nearest-neighbor connections and tolerates a relatively high physical error rate.

#How it works

Data qubits sit on a grid while measurement qubits check stabilizers, the local parity conditions whose violations flag bit-flip and phase-flip errors. A classical decoder infers the most likely error from the pattern of flagged checks and applies a correction. Increasing the grid size (the code distance) suppresses the logical error rate exponentially, provided the physical error rate is below a threshold near one percent.

#Overhead

Reaching cryptographically useful reliability takes on the order of 1,000 physical qubits per surface code logical qubit at realistic error rates. In 2024 a Google experiment demonstrated a surface-code memory whose logical error rate fell as the grid grew, crossing below the threshold. This overhead is a main reason a quantum computer able to run Shor's algorithm against real key sizes remains distant.