Nadarasa · v0.4.0 · External hook
Quantum collision models as a PQP rewriter axis
Ferreira, Topel, Fromholz & Wootton (Moth Quantum, June 2026) reinterpret light-matter scattering as a sequence of symmetry-constrained unitary collisions, precompute reflectance/transmittance tables on a quantum simulator, and bake them into a Blender shader. Four pieces of their construction touch our scaffolding directly — one of them suggests a concrete new residue rule for the 2q rewriter.
arXiv:2606.29989 · Rendering Coherent Scattering via Quantum Collision Models
João S. Ferreira, Spencer S. Topel, Pierre Fromholz, James R. Wootton. Acknowledges Konstantinos Meichanetzidis — same ZX/DisCoCat lineage we already cite via PQP Ch. 14.
Four touch-points
1.Symmetry-constrained U
Ferreira et al. eq. (8)Collision unitaries decompose as U = ⊕ₙ Uₙ on the Fock space and commute with the total-excitation number N = Σⱼ bⱼ†bⱼ. This is a new conserved quantity our PQP rewriter does not yet exploit — directly analogous to rule (M)'s matrix-canonical residue, but block-diagonal in number sectors and therefore cheaper to canonicalise.
2.LUT precompute → real-time shader
Ferreira et al. §4Precompute reflectance/transmittance on a 60-point parameter grid using a slow quantum sampler, bake the result into a shader, render in real time. This is exactly the workflow we already operate: Selene → JSON dump → React route. Strong external validation that decoupling sampler latency from frontend latency is the right architecture, not a workaround.
3.Sector reduction → closed form
Ferreira et al. App. BIn the single-photon sector the full collision circuit collapses to the classical thin-film Airy summation. Same shape as our AQFT_k1 vs QFT_full story — full quantum machinery reduces to a stripped classical kernel inside a conserved sector. The rewriter could in principle exhibit this collapse mechanically.
4.Near-term hardware-ready
Ferreira et al. §6Largest configuration (Nₗ=4, Nᵣ=10) uses 24 qubits with modest depth — explicitly flagged as future work for execution on real Quantinuum-class hardware. A Selene-side smoke test on a 2-mode collision unitary would slot directly into our existing tomography harness.
Candidate rule (P) · particle-number-preserving residue
On the 2-qubit computational basis the number operator is N = |01⟩⟨01| + |10⟩⟨10| + 2·|11⟩⟨11|. Our existing alphabet splits cleanly:
- Number-preserving:
CZ,S⊗I,I⊗S(alsoCNOT,iSWAP,√iSWAP— not in our alphabet). - NOT number-preserving:
H⊗I,I⊗H.
For any sequence built from the preserving sub-alphabet, the canonical residue can be computed sector-by-sector — extract M₀ = ⟨00|M|00⟩ (1×1), M₁ = M↾span{|01⟩,|10⟩} (2×2), M₂ = ⟨11|M|11⟩ (1×1), and canonicalise each block. Sound by construction ([U, N] = 0 ⇒ block-diagonal in the sector basis), cheaper than full 4×4 canonicalisation, and orthogonal to rule (M).
Deferred to v0.4.2: a sound rule (P) implementation needs a restricted-alphabet enumerator and a fresh promotion table. Acceptance would be ≥1 conjecture rule (P) closes that rule (M) leaves open on the preserving sub-alphabet — honest negative is acceptable.