A Constant Rate Quantum Computer on a Line
Quantum Physics
2025-02-25 v1
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.
Cite
@article{arxiv.2502.16132,
title = {A Constant Rate Quantum Computer on a Line},
author = {Craig Gidney and Thiago Bergamaschi},
journal= {arXiv preprint arXiv:2502.16132},
year = {2025}
}