Quantum Grand Challenges

Troyer Utility-Scale Filters

Every problem is evaluated against Dr. Matthias Troyer's 5 filters. Only problems that pass all five 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

Active Problems9 pass all Troyer filters

Hubbard Model

QPE

QPE for 2-site Hubbard ground state. 132k physical qubits, 18 logical. Exponential speedup for strongly-correlated systems. Naturally quantum.

Catalysis Simulation

QPE

QPE for H₂ molecular ground state (STO-3G). 132k physical qubits, 18 logical. Exponential speedup for quantum chemistry.

Drug Discovery

QPE

QPE for molecular binding energy. 130k physical qubits, 18 logical. Exponential speedup for pharmaceutical Hamiltonians.

Factorization

Calibrated

Shor's algorithm (8 qubits) with 20-run calibration ensemble. Period=7.0 ± 1.96 (95% CI). 77k physical qubits, 25 logical, 6 T-gates.

Materials Discovery

QPE

QPE for band gap estimation via tight-binding Hamiltonian. 132k physical qubits, 18 logical. Exponential speedup for correlated materials.

Error Correction

Calibrated

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

Nuclear Physics

QPE

QPE for deuteron binding energy via EFT Hamiltonian. 132k physical qubits, 18 logical. Exponential speedup for nuclear many-body systems.

Photovoltaics

Calibrated

Quantum walk exciton transport with 20-run calibration ensemble. 138k physical qubits, 12 logical.

Quantum Chromodynamics

Calibrated

Trotter lattice gauge with 20-run ensemble (Wilson=0.47 ± 0.066, 95% CI). 131k physical qubits, 9 logical.

Active problems

120+

Azure Quantum runs

160

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.19222021}
}

Quick Start

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

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

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