# Quantum Algorithms & Quantum Advantage: State of the Field (October 2026)

Research dossier · v1 · updated 2026-10-30 · 4,010 words · 31 sources · 28 claims · verification: verified

Covers random circuit sampling and the classical simulation counterattack, noise-based hardness results, verifiable advantage proposals, factoring and chemistry resource estimates, and variational methods as of October 2026. The main takeaway: sampling advantage claims remain contested by classical re-simulation and noise analysis, and the estimated cost of factoring RSA-2048 has fallen to under one million noisy qubits, a resource estimate rather than a demonstration.

## Contents

- Executive summary
- Background and core concepts
- Timeline of key milestones
- State of the art
  - Random circuit sampling: supremacy experiments and classical responses
  - Noise and the hardness boundary
  - Verifiable and certified advantage
  - Factoring and resource estimates
  - Chemistry and simulation algorithms
  - Variational and optimization algorithms
  - Quantitative benchmarks
- Open problems and active debates
- Major programs and players
- Outlook: what to watch (next 12-18 months)
- Key papers
- Glossary

## Sample findings

- Google's 2019 Sycamore experiment on a 53-qubit processor was reported to complete a random circuit sampling task in about 200 seconds, against an estimate of about 10,000 years on Summit.
- Huang et al. estimate that a tensor-network simulator could complete the same sampling task in under 20 days on a Summit-comparable cluster.

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