Quick answers to the questions this POC tends to provoke. Skim it for the parts that interest you; nothing builds on anything else.
If a question you have isn’t covered, the full story or the concept primers are likely the right next read.
No, and it shouldn’t be expected to. The active space we use — CAS(4, 4) — is small enough that classical CASCI computes the exact ground state in milliseconds. This POC isn’t a quantum-advantage demonstration; it’s a workflow demonstration on the smallest meaningful instance. Quantum advantage for chemistry is a 2029+ fault-tolerant story — see the scaling-roadmap primer.
Methodology readiness. The same code in 03_wh_binding.ipynb scales — by changing parameters, not architecture — to the active spaces that fault-tolerant hardware will unlock. Whoever picks up this repo in 2029 with 200 logical qubits can swap the geometry, basis, active space, and backend without rewriting the pipeline.
Three notebooks form a learning ladder.
01_hello_quantum.ipynb — Bell state. Smallest non-trivial quantum circuit. Validates the toolchain.02_h2_binding.ipynb — H2 at the STO-3G level. Smallest non-trivial quantum chemistry problem. Has a known exact answer (FCI) to compare against.03_wh_binding.ipynb — WH− via pyscf. The smallest tungsten-hydrogen system that fits a 6-qubit budget while still containing real transition-metal correlation physics.pyscf does the classical part — Hartree-Fock reference, integral generation, FCIDump export. VQE then finds the correlated ground state by optimizing a quantum circuit. At this size pyscf could do the whole calculation classically (it’s CASCI at CAS(4,4)) — the point is that the scaffold extends to active spaces pyscf can’t handle on its own.
WH− is a closed-shell singlet (16 valence electrons, all paired) — qiskit-nature’s ActiveSpaceTransformer handles it cleanly. Neutral WH is a 6Σ+ sextet (5 unpaired electrons), which ActiveSpaceTransformer in qiskit-nature 0.7 can’t slice properly. WH− keeps the W–H σ-bond physics while fitting the qubit budget. Important caveat: the “well depth” we compute is for WH−, not the experimental binding energy of WH — those are different quantities. The 3.11 eV number landing close to literature WH values is coincidental error cancellation, not validation. We document this explicitly in the notebook.
UCCSD is chemistry-aware and would give higher accuracy. But at 6 qubits with our integrals it takes ~24 minutes per cost-function call — that’s days for a full VQE convergence. EfficientSU2 is hardware-efficient: shallow, fast, robust. It gets us to ~11 mHa accuracy in minutes. For a methodology demonstration that’s the right tradeoff. For production work, UCCSD or its successors.
For H2: ~2.45 nanohartree from the FCI reference — essentially exact within the chosen basis. For WH−: 11.3 mHa from the CASCI reference, which is roughly 300 meV or 7 kcal/mol. That is well above chemical accuracy (1 kcal/mol). This is demonstration-grade, not production-grade. The error budget would shrink with UCCSD or deeper EfficientSU2 — and could be driven to whatever precision you like with QPE on fault-tolerant hardware, within the chosen basis and active space (the basis-set and active-space limitations remain).
Yes — all three notebooks have been executed on real IBM Quantum hardware end-to-end as of 2026-05-28.
01_hello_quantum.ipynb): submitted to ibm_marrakesh on 2026-05-27. Counts showed the expected entanglement signature (~50% 00, ~50% 11) plus a ~2.7% error from spurious 01/10 outcomes that violate perfect correlation. Job ID d8bccr4e6kns73aasfi0. Full record in results/qpu_runs/bell_marrakesh_2026-05-27.json ↗.ibm_marrakesh on 2026-05-28. ΔE = Eqpu − Esim ≈ +30.6 mHa = +834 meV (no mitigation). Job ID d8cd09j8amns73bjcan0.ibm_fez on 2026-05-28. ΔE ≈ +199.8 mHa = +5,438 meV (no mitigation). Important read: this ΔE exceeds the ~110 mHa well depth the simulator computed, which means the unmitigated QPU energy at θ* sits above the dissociation asymptote and is physically uninformative as a binding-energy estimate. The value of this measurement is as a noise-scaling data point, not a chemistry result. Job ID d8cd4hajki0s73ar3jj0.The two single-point ΔE values together quantify how noise scales with circuit depth on this generation of hardware — see the README’s “H2 and WH− single-point QPU validation” section.
Math: a 6-qubit VQE with ~60 parameters takes ~2000 cost-function evaluations to converge. At ~10 sec per QPU call, that’s 5.5 hours of hardware time. IBM Open plan gives 10 minutes per month. The pattern that does fit — train on simulator, validate single-point on QPU — is covered in the simulator-vs-QPU primer.
Yes — and we did. qiskit-ibm-runtime’s EstimatorV2 exposes ZNE (zero-noise extrapolation) plus twirled readout mitigation. The WH− validation script supports it via --mitigation zne, and a real run on 2026-05-31 (ibm_marrakesh) is documented in the error-mitigation primer: ZNE roughly halved the error magnitude but overshot the variational floor — a methodology data point, not a trustworthy chemistry result, exactly as expected at this circuit depth. The baseline notebook runs are kept unmitigated on purpose, to show the raw NISQ cost. Each mitigation level costs more shots, so deeper tuning fits a paid plan.
Circuit depth. EfficientSU2(reps=4, full entanglement) on 6 qubits gives a circuit ~30 layers deep with on the order of 100 two-qubit gates after transpilation. Every two-qubit gate has ~0.5% error and they compound. H2’s EfficientSU2(reps=2, linear) on 2 qubits is dramatically shallower — only a handful of two-qubit gates — so the noise budget is much smaller. The measured ΔE ratio (199.8 / 30.6 ≈ 6.5×) is the empirical version of this scaling. Fault tolerance is what removes this entirely.
Tritium retention in tungsten plasma-facing walls is a quantitative problem: predicting binding energies of hydrogen isotopes in defective tungsten lattices requires accurate electronic structure for transition metal systems. Classical methods struggle (DFT functionals disagree with experiment by 30+% on these systems; coupled cluster doesn’t scale to defect-cluster geometries). It’s one of the canonical “useful chemistry that quantum computers should eventually be able to do.”
When fault-tolerant quantum hardware exists at the ~200 logical qubit scale. That’s plausibly 2029+ for first useful demonstrations, mid-2030s for routine production use. The roadmap details are in the scaling-roadmap primer. This POC is the workflow scaffold for that future.
Yes — and the disagreement between predicted and measured tritium retention is a known source of operational uncertainty. Better electronic-structure methods would reduce uncertainty in tritium inventory projections, which matters for safety case modelling, fuel cycle design, and regulatory approval. Improving the precision is the value proposition, not enabling something that’s currently impossible.
pyscf has no Windows wheels and its source build fails on Windows out of the box. Notebook 03 needs pyscf; notebooks 01 and 02 don’t. So notebook 03 runs in a WSL2 Ubuntu venv while 01 and 02 run in a Windows venv. The launcher (setup/start-wh-jupyter.cmd) bridges the two by starting Jupyter inside WSL while pointing at the Windows-side notebook folder.
Earlier items are now done — single-point QPU validation (2026-05-28) and a first WH− ZNE run (2026-05-31, see the error-mitigation primer). Remaining, in order of cost/value:
The repo is built private-first so we can audit it before flipping to public. Specifically we’ve checked: no leaked API tokens (env-var pattern, never in code); no proprietary data; no overclaiming in any narrative; MIT licence; all numbers reproducible from the notebooks.
Three substantive gaps a reader should know about: