Code Comparison

Engineering trade-offs between the leading QEC codes for superconducting qubits.

Surface Code	\(\\sim 10^2\\text{--}10^3+\) physical qubits per logical qubit. High threshold \(p_{\\mathrm{th}} \\approx 1\\%\). Compatible with 2D nearest-neighbor planar layouts. Most widely adopted.
Color Code	\(\\sim 10^2\\text{--}10^3+\) physical qubits per logical qubit. Supports more transversal logical gates but requires more complex routing and connectivity.
Bacon-Shor Code	Grid of physical qubits per logical qubit. Requires fewer stabilizer measurements, reducing overhead and making implementation easier.
LDPC Codes	Lower qubit overhead than surface codes. Requires non-local connectivity, which is harder for current planar chip architectures.
GKP / Cat Codes	(1) oscillator mode can encode (1) logical qubit. Highly hardware-efficient but sensitive to energy decay and photon loss in bosonic cavities.