TL;DR: The surface code is the leading quantum error correction scheme. It arranges physical qubits on a 2D lattice where each logical qubit requires d² physical qubits for code distance d. Google's Willow d
The surface code is the leading quantum error correction scheme. It arranges physical qubits on a 2D lattice where each logical qubit requires d² physical qubits for code distance d. Google's Willow demonstrated below-threshold error correction with the surface code in 2024. At ~1,000 physical qubits per logical qubit, a million-qubit machine could support ~1,000 logical qubits.
Complexity
O(d²) physical qubits per logical qubit (d = code distance)
Application
Enabling fault-tolerant quantum computation