[abstract]Abstract: We prove by construction that the Bravyi-Poulin-Terhal bound on the spatial density of
stabilizer codes does not generalize to stabilizer circuits. To do so, we construct a fault tolerant quantum computer with a coding rate above 5$\%$ and quasi-polylog time overhead, out of a line of qubits with nearest-neighbor connectivity, and prove it has a threshold. The construction is based on modifications to the tower of Hamming codes of Yamasaki and Koashi (Nature Physics, 2024), with operators measured using a variant of Shor’s measurement gadget.
