Findings & lessons

A plain-English synthesis of what this proof-of-concept actually demonstrated. For the raw per-run numbers see the README result table and results/qpu_runs/; for the concepts behind them see the seven concept primers.

We proved the entire quantum-chemistry pipeline runs end-to-end on real tungsten chemistry on real IBM Quantum hardware — and we measured, transparently, exactly how far today’s machines are from trustworthy chemistry.

The workflow works — and it scales by parameters, not architecture

Three experiments of rising difficulty were validated on real IBM Quantum hardware, each with a saved artifact (job ID, backend, shot count): Bell → H2 → WH−. The full chain runs end-to-end:

pyscf Hamiltonian → active space → qubit mapping → ansatz → VQE → QPU validation

The same code skeleton extends to the real fusion-relevant problem (a W8 vacancy cluster with hydrogen, ~200 logical qubits, ~2029+). What changes between “today” and “future” is geometry, active space, ansatz, and backend — not the architecture. The validated scaffold is the deliverable.

Noise scales steeply with circuit depth — and we quantified it

The same pipeline, run at three depths, traces a clean gradient from a single entangling layer to ~100 two-qubit gates:

0%
Bell state spurious counts — 1 layer (28 / 1024)
0
H2 ΔE, mHa — 2 qubits, shallow
0
WH− ΔE, mHa — 6 qubits, ~100 two-qubit gates
The key observation

H2 and WH− used the same 4096 shots, yet WH−’s error was ~6.5× larger — and that ratio tracks circuit depth, not shot count. That is the empirical fingerprint that the dominant error is systematic gate-error bias, not random shot noise. It is a clean, real-hardware demonstration of the single most important NISQ-era lesson.

On a hard problem today, the noise can exceed the signal

WH−’s unmitigated hardware noise (~200 mHa) exceeded the well depth it was trying to measure (~110 mHa). When the error bar is larger than the quantity itself, the result is physically uninformative as chemistry. This is the crispest possible marker of where current hardware sits relative to a real chemistry target — and it is reported honestly rather than hidden.

Error mitigation helps in magnitude — but isn’t reliable yet, and can overshoot

A Zero-Noise Extrapolation run (ibm_marrakesh, 2026-05-31, job d8e6ucjo3njc73eub3v0) cut the error magnitude ~2× — from +199.8 mHa to −97.9 mHa, dipping under the ~110 mHa well depth. But it overshot: the mitigated energy (−67.5411 Ha) landed ~87 mHa below the exact CASCI ground state (−67.4545 Ha), which is physically impossible for a true expectation value. ZNE over-extrapolated at this circuit depth — trading a too-high bias for a too-low overshoot.

The lesson is not “mitigation failed.” It is that at ~100 two-qubit gates, ZNE buys a magnitude improvement, not a reliability one. Two corollaries:

Two corollaries
  • The variational floor is a free correctness check. A real energy can never fall below the ground state, so the negative result instantly self-flagged as untrustworthy. See the error-mitigation primer.
  • More shots would not have helped — shots fight variance; this is bias.

The real unlock is error correction, not cleverness

Error mitigation buys roughly 2–10×; reaching chemical accuracy (~1.6 mHa) on this problem needs about 100×. No amount of mitigation tuning closes that gap on today’s chips — it is a fault-tolerance (2029+) story. The value of this prototype is that it quantifies the gap precisely instead of hand-waving.

Honest scoping is the product — what this is not

So… did it work?

Yes — as a workflow proof and an honest hardware benchmark. It ran the complete quantum-chemistry pipeline on real tungsten chemistry on real quantum hardware, and it transparently 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 (~2029+). It did not, and was never meant to, produce a trustworthy tungsten binding energy.

Summary in five bullets

  1. The full VQE-on-real-chemistry pipeline runs end-to-end on real IBM hardware, and scales to the production problem by parameters, not architecture.
  2. Noise scales with circuit depth (2.7% → 30.6 → 199.8 mHa); the 6.5× gap at equal shots is the signature of bias, not shot noise.
  3. On WH−, noise (~200) exceeded the signal (~110) — today’s hardware cannot yet see this chemistry.
  4. ZNE halved the error magnitude but overshot the physical floor — mitigation buys magnitude, not reliability, at this depth.
  5. Chemical accuracy needs fault tolerance (~2029+); this POC quantifies the gap honestly rather than overclaiming.

Keep reading

The story-page verdict is the two-minute version; the seven concept primers unpack each idea, and the FAQ answers the questions this POC tends to provoke.