Jacob S. Nelson, Andrew J. Landahl, Andrew D. Baczewski (Jul 29 2025).

Abstract: We present an architecture for early fault-tolerant quantum computers based on the smallest interesting colour code (Earl Campbell, 2016). It realizes a universal logical gate set consisting of single-qubit measurements and preparations in the X and Z bases, single- qubit Hadamard (H) gates, and three-qubit controlled-controlled-Z (CCZ) gates. State teleportations between [[4, 2, 2]] (2D) and [[8, 3, 2]] (3D) error-detecting color codes allow one to make use of the respective transversal H and CCZ gates that these codes possess. As such, minimizing the number of logical quantum teleportation operations, not the number of logical quantum non-Clifford gates, is the relevant optimization goal. To help hardware developers characterize this architecture, we also provide an experimental protocol tailored to testing logical quantum circuits expressed in it.

Arxiv: https://arxiv.org/abs/2507.20387