A Constant Rate Quantum Computer on a Line

TL;DR

This paper demonstrates a fault-tolerant quantum computer on a line of qubits with a high coding rate and low overhead, challenging previous bounds on spatial density for stabilizer codes.

Contribution

It constructs a linear, fault-tolerant quantum computer with a coding rate above 5% and quasi-polylogarithmic time overhead, proving the Bravyi-Poulin-Terhal bound does not extend to stabilizer circuits.

Findings

Achieves a coding rate above 5% on a linear qubit array.

Proves the existence of a threshold for the constructed quantum computer.

Shows the bound on spatial density does not apply to stabilizer circuits.

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.