Fault-tolerant quantum computation with constant overhead for general noise

TL;DR

This paper proves that fault-tolerant quantum computation with constant qubit overhead is possible under very general noise models, including realistic non-stochastic noise, by using specialized quantum codes and error correction schemes.

Contribution

It extends fault-tolerance results to general noise models using QLDPC codes, demonstrating constant overhead feasibility beyond stochastic noise assumptions.

Findings

Constant qubit overhead achievable under general noise

Development of fault-tolerant error correction for non-stochastic noise

Implementation of logical gates under broad noise conditions

Abstract

Fault-tolerant quantum computation traditionally incurs substantial resource overhead, with both qubit and time overheads scaling polylogarithmically with the size of the computation. While prior work by Gottesman showed that constant qubit overhead is achievable under stochastic noise using quantum low-density parity-check (QLDPC) codes, it has remained an open question whether similar guarantees hold under more general, non-stochastic noise models. In this work, we address this question by considering a general circuit-level noise model defined via the diamond norm, which captures both stochastic and non-stochastic noise, including coherent and amplitude damping noise. We prove that constant qubit overhead fault-tolerant quantum computation is achievable in this general setting, using QLDPC codes with constant rate and linear minimum distance. To establish our result, we develop a fault-tolerant error correction scheme and a method for implementing logic gates under general circuit noise. These results extend the theoretical foundations of fault-tolerant quantum computation and offer new directions for fault-tolerant architectures under realistic noise models.