A VQE proof-of-concept that runs the full quantum-chemistry pipeline on real tungsten chemistry — on real IBM Quantum hardware — then measures exactly how far today’s machines are from trustworthy chemistry.
Why this matters
ITER, DEMO, and every other deuterium–tritium fusion design lines its inner wall with tungsten — the metal with the highest melting point. Hot plasma slams hydrogen and its radioactive isotope tritium into that wall, and some of it gets stuck in microscopic lattice defects.
That trapped tritium is a safety, supply, and licensing problem: it is radioactive, expensive to produce, and regulated. For every reactor design, engineers need one number — how strongly does tritium bind to a tungsten vacancy? That binding energy is just the energy of the trapped atom minus the energy of the free atom. Compute both, subtract.
Millions of degrees. Hydrogen and tritium bombard the tungsten wall continuously.
Atoms lodge in vacancy defects in the tungsten crystal — a growing radioactive inventory.
Predicting the binding energy means computing the energy of electrons around tungsten — one of the hardest problems in computational science.
The number that breaks classical computers
The electrons all repel each other and must stay quantum-mechanically out of each other’s way. The wavefunction of an N-electron system lives in a space of size roughly 2N. For H2 that is trivial. For tungsten it is 274 — about 1022 numbers.
That is more than the number of stars in the observable universe. You cannot store that on any classical computer, ever. Approximate methods (Hartree–Fock, DFT) cope for most chemistry, but break down exactly where transition metals like tungsten live: strong electron correlation.
The algorithm
A quantum computer with N qubits already is a 2N-dimensional state space — it stores wavefunctions natively, for free. The Variational Quantum Eigensolver is the workhorse that uses this for chemistry.
Build a parameterised quantum circuit — a recipe that, given a set of knobs, prepares some quantum state. Measure that state’s energy. A classical optimizer nudges the knobs to lower it. Repeat until the energy stops dropping. The lowest energy you reach is your estimate of the ground state.
A learning ladder
Each notebook stands alone; together they climb from “hello, quantum” to real tungsten chemistry. Every rung was executed end-to-end on real IBM Quantum hardware.
Scales by parameters, not architecture
What changes between the two is geometry, basis, active space, ansatz, and backend — not the architecture. The validated scaffold is the deliverable.
So… did it work?
It ran the complete quantum-chemistry pipeline on real tungsten chemistry on real quantum hardware, and measured how far today’s machines are from trustworthy chemistry: the noise exceeds the signal, mitigation helps but overshoots, and chemical accuracy needs error correction.
The key read H2 and WH− used the same 4096 shots, yet WH−’s error was ~6.5× larger. That ratio tracks circuit depth, not shot count — the fingerprint of systematic gate-error bias, not random noise. On WH−, the ~200 mHa noise exceeded the ~110 mHa well depth it was trying to measure.
The discipline of knowing what a number is — and isn’t — is the difference between a research result and a marketing slide. Three things to keep straight:
The 3.11 eV “well depth” is for the WH− anion, a tractable closed-shell proxy — not the experimental binding energy of neutral WH. Its closeness to literature values is coincidental error cancellation, not physics.
CAS(4,4) is small enough that classical CASCI solves it exactly in milliseconds. This is a workflow demonstration on the smallest meaningful instance, not a classical-beating result.
The result is a validated workflow plus a hardware noise benchmark — demonstration-grade at ~7 kcal/mol error, well above chemical accuracy. It was never meant to be a trustworthy tungsten answer.
Where this goes
| Stage | Qubits | Type | Hardware | Timeline |
|---|---|---|---|---|
| This POC | 6 | circuit | NISQ sim + single-point QPU | Today |
| Larger basis CAS(6,6) | ~10 | circuit | NISQ, more QPU minutes | Today, paid |
| Multi-W cluster | 20–40 | circuit | Late-NISQ + mitigation | ~2027 |
| W8 vacancy + H | 200+ | logical | Fault-tolerant QPU | 2029+ |
Go deeper
Qubits, Hamiltonians, the VQE loop, active spaces, scaling, sim-vs-QPU, error mitigation — ~300 words each, one diagram each.
Start with qubits →The full synthesis of what the prototype demonstrated, and exactly where today’s hardware sits relative to a real chemistry target.
Read the verdict →Did it beat classical? Why WH−? Did you really run it on hardware? The questions this POC tends to provoke.
Browse answers →Three Jupyter notebooks in learning order, on GitHub. Clone, run on the simulator free, validate on a QPU.
Open on GitHub ↗Scripts, result artifacts (job IDs, backends, energies), and the full README. MIT licensed.
View source ↗How the same pipeline bridges the NISQ era and the fault-tolerant future, one parameter swap at a time.
See the roadmap →