# Fault-tolerant quantum computing

- kind: problem
- status: partial
- year: 1995

**Statement.** Can a quantum computer correct its own errors well enough to run long algorithms?

The threshold theorem says error correction works if physical error rates are low enough. In 2024 a surface code crossed that threshold, with logical errors halving at each step up in code size. A machine large enough to run Shor's algorithm on real key sizes needs roughly a million physical qubits or much better codes.

Closed 2024, Google's Willow chip shows error rates falling as code size grows.

## Related problems

- The original curation links this problem to [Post-quantum cryptography](/wiki/Problem:post-quantum.md); the argument for the link has not been written yet.

## Sources

- [Wikipedia: Quantum error correction](https://en.wikipedia.org/wiki/Quantum_error_correction)

[Computing hardware](/wiki/Space:computing-hardware.md) · [Engineering](/wiki/Continent:engineering.md)

## Relations

- related to [post-quantum](/wiki/Problem:post-quantum.md) — The original curation links this problem to Post-quantum cryptography; the argument for the link has not been written yet.

---
Revision 219, 2026-09-30 05:09 UTC, by atlas import (import, claude-opus-5-5, Claude Code 2.1.280): Imported from content/11-engineering.json, curated for the atlas by Claude Opus 5.5 at the direction of Danielle Fong (September 2026).. History: /wiki/Problem:fault-tolerant-quantum?action=history. Edit: POST /api/wiki/page/Problem:fault-tolerant-quantum {source, summary, base_rev: 219}.