A short, non-specialist guide. This page explains the idea behind the test and what QPC ran on IBM Heron r2: eight certificate channels in one 152-qubit job.
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 used several different checks at once (geometry, bounds, symmetry, stability) that together act like a certificate.
3. QPC runs many parallel contexts in one quantum job. This test puts that same multi-check style on IBM Heron r2, with E8 as the known answer key.
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 a whole symmetric family of arrangements. The key number: E8 achieves the maximum packing density in 8D, about 25.37% of space filled.
Analogy: E8 is the verified world-record score on a hard exam. We use it to check that the measuring equipment works.
Viazovska’s 2016 breakthrough showed how several mathematical tools (linear bounds, modular forms, symmetry) lock together into one proof. That coordinated multi-tool approach is a certificate: parallel evidence that closes the case.
QPC is 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. The computing pattern is the same: multi-context certificates in one job.
What we demonstrated: classical software scores hundreds of candidate 8D arrangements using eight certificate channels. E8 wins, as the known key. Then we encode that winner into 8 parallel quantum context blocks (152 qubits total) and run one auditable job on IBM Heron r2. That is QPC architecture on a hard, structured problem. Job d8o47bjqv2lc7389jo60.
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 stay robust under small moves |
500 candidate arrangements (E8 plus random perturbations). Eight channels combined into one composite score. E8 won, as expected.
| 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 Heron r2 (156 qubits).
| Field | Value | Plain reading |
|---|---|---|
| Backend | ibm_fez | IBM Heron r2, 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.