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Research dossier · version 1 · updated Oct 30, 2026

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

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.

4,010 words31 sources28 evidence-mapped claims14 benchmarks18 timeline events✓ citation-verified Oct 30, 2026

AI-assisted synthesis of the cited literature, independently fact-checked against its sources; not peer reviewed.

Contents

  1. Executive summary
  2. Background and core concepts
  3. Timeline of key milestones
  4. State of the art
  5. Random circuit sampling: supremacy experiments and classical responses
  6. Noise and the hardness boundary
  7. Verifiable and certified advantage
  8. Factoring and resource estimates
  9. Chemistry and simulation algorithms
  10. Variational and optimization algorithms
  11. Quantitative benchmarks
  12. Open problems and active debates
  13. Major programs and players
  14. Outlook: what to watch (next 12-18 months)
  15. Key papers
  16. 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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