This run was recorded in April 2026 against a VQE kernel that has since been replaced by phase estimation. The shot distribution below is a real measurement, but it is a measurement of a program that no longer exists in this repository, and it has not been re-run against the current kernel.

Upgraded to QPE for molecular Hamiltonians. Hoefler, Häner and Troyer see 'a huge potential in material science and chemistry'. QPE is exponentially cheaper than FCI once a state with good ground-state overlap is prepared, but coupled cluster, DMRG and selected CI already treat many large molecules accurately, and no generic exponential advantage over them has been established (Lee et al., Nat. Commun. 14, 1952, 2023). The case rests on strongly correlated systems such as FeMoco. The current H₂ instance is pedagogical.

02. Quantum Catalysis Challenge

This problem explores quantum simulation of catalytic reaction mechanisms, comparing classical and quantum approaches for estimating reaction rates and energy barriers. The goal is to establish analytical baselines and prepare for quantum algorithm implementation.

Roadmap

• [x] Scaffold directory structure
• [x] Implement classical analytical baseline (Arrhenius model)
• [x] Implement Q# analytical baseline (matching classical results)
• [x] Generate parameter instances (small/medium/large)
• [x] Validate outputs and plots
• [ ] Update documentation and website status

Quickstart

cd problems/02_catalysis
make classical      # Run classical baseline analysis
make analyze        # Generate plots
make build          # Build Q# project (uses modern QDK  qsharp Python package)
make run            # Run quantum simulation

Outputs

• `estimates/classical_baseline.json`: Structured Arrhenius rates for each instance
• `plots/rate_vs_temperature.png`: Visualization of reaction rates vs. temperature
• `qsharp/src/Main.qs`: Q# baseline source, compiled on-the-fly by the modern QDK (no DLL artifact)

Current Results

Running python python/classical_baseline.py produces the following reaction rates:

| Instance | Catalyst | Temperature (K) | Rate (s^-1) |

|----------|----------|-----------------|-------------|

| small | Pt | 300 | 0.8727 |

| medium | Fe | 500 | 5.94×10^2 |

| large | Cu | 700 | 2.92×10^5 |

The Q# entry point RunAnalyticalCatalysisBaseline reports the same values, confirming parity between classical and quantum-friendly baselines.

References

• Quantum simulation of chemical catalysis
• Analytical models for reaction rates
• Q# quantum chemistry libraries

Objective Maturity Gate

• **Current gate**: **Stage C complete** (hardware-aware validation evidence in place: QPE chemistry kernel runnable, calibration ensemble across runs, backend assumptions documented, estimator profile produced for both ns-e3 superconducting and surface-code-generic models).
• **Next gate target**: **Stage D** (advantage evidence package hardening: fairness review against best-known classical baseline, residual risks quantified, claim category locked).

Stage C evidence references for this problem:

• Calibration ensemble: `estimates/quantum_calibration_ensemble.json` and `estimates/calibration_evidence.json`.
• Backend assumptions: `estimates/backend_assumptions.md`.
• Estimator profile (ns-e3 + surface-code-generic): `estimates/estimator_profile_summary.md`, `estimates/latest_qubit_gate_ns_e3.json`, `estimates/latest_surface_code_generic_v1.json`.
• Azure smoke validation: `estimates/azure_smoke_report_small_d1.md`, `estimates/azure_job_manifest_small_d1.json`.
• Reproducible quantum kernel: `qsharp/src/Main.qs` runnable via `qsharp.run('Main.RunCatalysisAnalysis()', 1)`.

DiVincenzo Readiness (Stage C/D Overlay)

| Criterion | Status | Evidence / Notes |

|---|---|---|

| Scalable qubit system | partial | Current results validate analytical parity; scalable chemistry-kernel resource projections are pending Stage C implementation. |

| Initialization | partial | Reaction-parameter initialization is defined for analytical baselines; quantum state-loading fidelity work remains open. |

| Coherence vs gate time | not-yet | Backend-specific coherence and depth/runtime evidence has not yet been produced. |

| Universal gate set | partial | Q# baseline build path is validated, but gate-basis decomposition for a chemistry kernel is not finalized yet. |

| Qubit-specific measurement | partial | Output observables are defined for baseline workflows; hardware readout assumptions and uncertainty bands are pending. |

Advantage Claim Contract

• **Claim category (current)**: `theoretical`.
• **Problem class and regime**: Problem-specific challenge instances defined in this directory.
• **Fair baseline**: Problem-local classical baseline in `python/` outputs.
• **Quantum resource scaling claim**: Expected asymptotic advantage depends on algorithm family and implementation assumptions; no hardware-demonstrated speedup claim yet.
• **Data-loading and I/O assumptions**: Must be documented alongside future advantage claims.
• **Noise/error model assumptions**: Backend-specific model and calibration assumptions to be added at Stage C.
• **Confidence/uncertainty method**: To be reported using shot-based confidence intervals or equivalent statistical bounds.
• **Residual risks**: Oracle/state-preparation/transpilation overhead may dominate for near-term instance sizes.