Color-Code Logical Qubit

Description

Color-code logical qubits are encoded in 2D or 3D topological stabilizer codes defined on trivalent, three-colorable lattices. Relative to surface code, color codes can offer transversal implementation of a larger Clifford gate set, reducing some lattice-surgery overheads.

Figure

Hamiltonian / Stabilizers

For each face $f$ in a colorable lattice:

$S_f^X={\prod }_{i\in f}{X}_i,S_f^Z={\prod }_{i\in f}{Z}_i$

Code space is the +1 eigenspace of all face stabilizers. Logical operators correspond to colored string operators connecting boundaries.

Why it matters

Color codes are a leading alternative to surface code when gate-transversality and decoding tradeoffs favor reduced compilation overhead, especially for Clifford-heavy workloads.

Key Metrics

Metric	Value	Notes	Fidelity reference
Threshold	~0.1–1%	Decoder/noise model dependent	—
Transversal Clifford support	Yes	Major architectural advantage	—
Qubit overhead	Comparable order to surface code	Constants depend on layout	—
Experimental status	Early-scale demonstrations	Not yet full fault-tolerant stack	—

Linked Papers

• bombin-2006-color-codes

Related Entries

• surface-code-logical-qubit
• transmon
• trapped-ion-qubit