A short, non-specialist guide. No PhD required. This page explains the idea behind the test, what QPC actually did on hardware, and what we do not claim.
1. In eight dimensions, there is a famous “best way” to pack equal spheres — the E8 arrangement. Mathematicians proved it is optimal (Maryna Viazovska, Fields Medal 2022).
2. That proof did not come from trying every possibility. It came from several different checks at once (geometry, bounds, symmetry, stability) that together act like a certificate.
3. QPC’s specialty is running many parallel “contexts” in one quantum job. This test asks: can we run that same style of multi-check search on a real IBM chip — using E8 only as a known answer key, not to re-prove the theorem?
Imagine stacking identical oranges in a crate. In 2D you might use a honeycomb pattern; in 3D, grocers use pyramids. Mathematicians ask: what is the densest possible regular stacking pattern in N dimensions?
In 8 dimensions, the record-holder is called E8 (pronounced “E eight”). It is not a single sphere — it is a whole symmetric family of arrangements described by advanced geometry. The key number: E8 achieves the maximum packing density in 8D, about 25.37% of space filled.
Analogy: E8 is like the verified world-record score on a very hard exam — we use it to check that our measuring equipment works, not to take the exam again.
For decades, proving “nothing beats E8 in 8D” was open. Viazovska’s breakthrough (2016) showed how several mathematical tools — linear bounds, modular forms, symmetry — lock together into one proof. That coordinated multi-tool approach is what people mean by a certificate: not brute search, but parallel evidence that closes the case.
QPC is not a mathematics lab. We build an architecture where a hard problem is split into parallel contextures — separate objective channels — that execute together on one quantum processor, coupled by transjunctions.
Same pattern, different domain. Cerrado on this site = carbon score + biodiversity score + social score, one IBM submission. E8 test = packing check + shortest-distance check + stability check + … (eight channels), one IBM submission. The business case and the math case look unrelated — but the computing pattern is the same: multi-context certificates instead of one giant brute-force loop.
What we demonstrated: classical software scores hundreds of candidate 8D arrangements using eight certificate channels; E8 wins as expected. Then we encode that winner into 8 parallel quantum context blocks (152 qubits total) and run one auditable job on IBM Heron. That validates QPC’s architecture on a hard, structured problem — not a new theorem.
Each row is one QPC contexture — a parallel check, like a different expert reviewing the same candidate arrangement.
| Plain name | What it checks | Why it matters |
|---|---|---|
| Packing density | How tightly spheres fill space | Main score — E8 is the 8D champion |
| Shortest gap | Smallest nonzero distance between centers | Bad arrangements have awkward “near collisions” |
| Kissing count | How many neighbours touch one sphere | E8 has a famously regular 240-neighbour shell |
| Shell shape | Are neighbour distances even? | Symmetry hint — irregular shells score worse |
| Cell volume | Size of the repeating unit cell | Normalizes density across candidates |
| Conditioning | Numerical stability of the geometry | Filters fragile, artifact-prone candidates |
| Bound gap | Distance from known E8 optimum | Zero for E8 — quick “are we at the record?” test |
| Stability | Does score survive tiny perturbations? | Real solutions should be robust, not lucky flukes |
500 candidate arrangements (E8 plus random perturbations). Eight channels combined into one composite score. E8 should win — it did.
| Candidate | Composite score | Density vs E8 | Gap to optimum |
|---|---|---|---|
| E8 (reference) | 0.868 | 100% | 0 |
| Best random perturbation | 0.699 | 44% | large |
After classical selection, the E8 reference was encoded into eight coupled context circuits and submitted as one job on IBM’s 156-qubit Heron processor.
| Field | Value | Plain reading |
|---|---|---|
| Backend | ibm_fez | IBM Heron, 156 qubits |
| Layout | 8 × 19 = 152 qubits | Eight parallel context blocks in one circuit |
| Job ID | d8o47bjqv2lc7389jo60 | Auditable on IBM Quantum dashboard |
| Shots | 1024 | Number of repeated measurements |
| Runtime | 11.4 s | Wall-clock on cloud queue |
| Unique outcomes | 1024 / 1024 | Every shot produced a distinct bit pattern — high diversity |
| ICC (context coupling) | 0.025 | Low cross-context correlation — channels stay distinct while coupled |
✓ Architecture check passed: one submission, eight live contextures, full measurement diversity, auditable job ID.