Quantum Grand Challenges

Troyer Utility-Scale Filters

Every problem is evaluated against Dr. Matthias Troyer's utility-scale filters. Only problems that pass all six are classified as active candidates for quantum advantage.

Proven speedup?

VQE/QAOA fail

I/O survives?

O(N) loading erases gain

QEC survives?

Overhead kills quadratic

Naturally quantum?

Feynman criterion

Crossover feasible?

Realistic problem size

Guiding state preparable?

Single-reference: coupled cluster already wins

Search problems by name, algorithm, status or description

Active Problems9 pass all Troyer filters

Hubbard Model

QPE

QPE for the two-site Hubbard model (4 qubits, 10 phase bits). 595k physical qubits, 40 logical. Any speedup is over exact diagonalization and depends on preparing a good initial state; none is demonstrated.

Catalysis Simulation

QPE

QPE for H₂ (STO-3G, 10 phase bits). 423k physical qubits, 35 logical. Reproduces the full-CI energy in simulation, for a molecule classical methods solve instantly.

Drug Discovery

QPE

QPE for an illustrative two-qubit binding Hamiltonian (10 phase bits). 423k physical qubits, 35 logical. The Hamiltonian is not derived from a molecule.

Factorization

Calibrated

Shor's algorithm for N = 15 (8 qubits): order finding for a = 7, with modular multipliers and an inverse QFT checked against exact results. 20-run calibration ensemble. 61k physical qubits, 25 logical, 9 T-gates.

Materials Discovery

QPE

QPE band gap of a toy tight-binding dimer (10 phase bits). 755k physical qubits, 35 logical. A two-level model, not a real material.

Error Correction

Calibrated

3-qubit repetition code with 20-run calibration ensemble. 100% correction rate. 1.8k physical qubits.

Nuclear Physics

QPE

QPE for the deuteron (pionless EFT, two-state basis, 10 phase bits). 667k physical qubits, 35 logical. Reproduces the published -1.749 MeV; the basis is too small to reach the experimental -2.224 MeV.

Photovoltaics

Calibrated

Quantum walk exciton transport with 20-run calibration ensemble. 47k physical qubits, 12 logical.

Quantum Chromodynamics

Calibrated

Trotterized transverse-field Ising chain, a spin-chain stand-in for lattice gauge dynamics (no gauge fields yet). 20-run ensemble: Z-parity 0.46 ± 0.05 (95% CI; exact 0.487). 55k physical qubits, 9 logical.

Active problems

120+

Azure Quantum runs

Resource estimates

Algorithms indexed

Troyer filters

Methodology Paper

Covers the maturity gate model, Troyer utility-scale filters, 9 algorithm families, automated CI validation, and Azure Quantum integration.

Read Paper →

Cite This Work

@software{rall2026quantum,
  author = {Rall, Werner},
  title = {Quantum Grand Challenges},
  year = {2026},
  doi = {10.5281/zenodo.19222020}
}

Quick Start

Problems run offline with nothing but Python. Evaluating a problem queries a knowledge-base index, so it needs either access to ours or your own Azure AI Search and OpenAI resources.

Setupgit clone https://github.com/WernerRall147/quantum-grand-challenges.git
cd quantum-grand-challenges
pip install qdk numpy scipy matplotlib

Run a Problemcd problems/01_hubbard
make classical   # baseline
make build       # Q# compilation
make run         # execute

Evaluatepip install azure-identity azure-search-documents openai
az login
python agents/orchestrator/evaluate.py \
  "Simulate ground state of a 50-atom catalyst"

Run the App Yourselfexport SEARCH_ENDPOINT="https://<your>.search.windows.net"
export AZURE_OPENAI_ENDPOINT="https://<your>.openai.azure.com/"
python knowledge/seed_knowledge_base.py

uvicorn agents.api.main:app --reload --port 8000
docker run --rm -p 8000:8000 qgc-eval-api:local
cd website && npm install && npm run dev