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Rendering Coherent Scattering via Quantum Collision Models

This paper introduces a novel rendering framework that integrates classical ray-tracing with quantum collision models to simulate dynamic, coherent light-matter interactions and chaotic optical responses, utilizing near-term quantum computers to pre-compute bidirectional scattering distribution functions (BSDFs) for physically accurate, physics-inspired materials.

Original authors: João S. Ferreira, Spencer S. Topel, Pierre Fromholz, James R. Wootton

Published 2026-06-30

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CC BY 4.0

Original authors: João S. Ferreira, Spencer S. Topel, Pierre Fromholz, James R. Wootton

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to paint a picture of a shiny, magical statue. Usually, computer graphics programs treat light like a stream of tiny, independent marbles bouncing off surfaces. They calculate how much light bounces back (reflection), how much goes through (transmission), and how much gets "lost" (absorption) as if these were separate, static events.

This paper proposes a completely different way to think about light. The authors, from a company called Moth Quantum, suggest that instead of treating light as simple marbles, we should treat it like a quantum dance where light and the material it hits are constantly changing each other.

Here is a simple breakdown of their ideas:

1. The "Memory" of the Material

In traditional computer graphics, if a ray of light hits a wall, the wall doesn't "remember" the hit. It just reflects the light and moves on.

The authors imagine a material that remembers. They propose a model where light and the material's surface are like partners in a dance. When a ray of light (a "dancer") hits the surface, they bump into each other in a specific, rule-bound way called a "Quantum Collision."

The Analogy: Imagine a billiard table where the balls aren't just hard spheres. When two balls hit, they briefly merge, swap energy, and change the table's surface before bouncing apart. The surface "remembers" the hit and changes how it reacts to the next ball.

2. The "Collision" Rules

The authors created a set of mathematical rules (called a "Unitary Operator") that governs these collisions.

Conservation: Just like in real life, energy can't be created or destroyed. If a light particle hits the surface, it must either bounce back, go through, or be absorbed by the surface (making the surface vibrate).
Superposition: In the quantum world, a particle can be in two places at once. The authors use this to say that a single ray of light can be reflected, transmitted, and absorbed simultaneously until we look at the final result. This creates complex interference patterns, like the swirling colors you see on a soap bubble or a peacock feather.

3. Building a "Quantum Shader"

The paper describes a new tool for artists and programmers called a "shader."

The Process: Instead of calculating light one bounce at a time, this tool simulates a sequence of these quantum collisions.
The Layers: They imagine stacking many thin layers of material (like sheets of paper or graphene). As light bounces between these layers, it collides with the surface of each layer.
The Result: Because the light is "remembering" all its previous collisions and interfering with itself, the final image has a much richer, deeper, and more complex look than standard computer graphics can produce. It creates colors and textures that shift and change in ways that feel "alive."

4. Why Use Quantum Computers?

Simulating these quantum dances is incredibly hard for normal computers because the number of possibilities explodes very quickly.

The Solution: The authors suggest using quantum computers to do the heavy lifting. These computers are naturally good at simulating quantum physics.
The Workflow: They plan to use a quantum computer to pre-calculate the "rules" of how light behaves on these special materials. Once calculated, these rules can be turned into a standard file (a Look-Up Table) that any regular computer can use to render the beautiful, complex images in real-time.

Summary

In short, this paper is about teaching computers to see light as a quantum interaction rather than a simple bounce.

By treating light and matter as partners in a complex, memory-filled dance, the authors have created a new way to render materials that look like they are made of "living" light. They demonstrated this by creating images of a jade statue coated in a new, imaginary material that shows deep, shifting colors and complex patterns, proving that this "quantum collision" approach can create visual effects that traditional methods simply cannot achieve.

Technical Summary: Rendering Coherent Scattering via Quantum Collision Models

Problem Statement

Traditional rendering techniques rely on geometric optics and statistical approximations that treat optical properties as static and absorption as incoherent energy loss. These assumptions fail for emerging meta-materials and strongly coupled quantum systems where optical appearance is governed by coherent propagation, strong light-matter coupling, and the coherent history of photons traversing an adaptive medium. Current methods cannot accurately model:

Coherent Absorption: Where absorption acts as a coherent amplitude rather than simple energy loss.
Non-linear Interactions: Interactions between light modes that are essential for reproducing the behavior of strongly coupled quantum materials.
Dynamic Evolution: Materials whose properties evolve in response to incident illumination, retaining a "memory" of previous interactions.

Methodology

The authors propose a rendering framework based on Quantum Collision Models (QCMs) that bridges macroscopic ray tracing and microscopic wave solvers. The core approach reinterprets propagating rays and material excitations as quantum particles interacting locally in space and time.

Formalism

Second Quantization: The system is described using Fock states $|n_\gamma\rangle$ , where excitations correspond to photons (EM field) and surface modes (polaritons/excitons).
Unitary Collisions: Light-matter interaction is modeled as a discrete sequence of elastic scattering events governed by a symmetry-constrained unitary operator $U$ $U$ .
- Single Collision: An incident ray $|e\rangle$ interacts with a surface, splitting into reflected ( $r$ ), transmitted ( $t$ ), and surface ( $s$ ) modes. The transformation $|F\rangle = U|I\rangle$ is encoded in a scattering matrix derived from a collision Hamiltonian $H_c$ .
- Symmetry Constraints: $U$ must satisfy invariance under reflection/transmission swaps and conserve the total number of excitations (block-diagonal in the excitation-number basis).
Hamiltonian Construction: The unitary is generated via $U = e^{-iH_c}$ $U = e^{- i H_{c}}$ .
- Linear Regime: Terms $H_0$ through $H_3$ describe linear scattering, reflection, transmission, and absorption/emission.
- Non-linear Regime: Higher-order terms ( $H_{\geq 4}$ ) introduce non-linear interactions, such as coupling between multiple rays or mode-dependent hopping amplitudes. The authors treat these non-linear terms as "artistic tools" to generate distinct optical signatures, parameterized by an interaction strength $h_i$ .

Implementation Strategy

Hardware Truncation: To ensure computational tractability on current quantum hardware (and classical simulation thereof), the Fock space is truncated to a maximum of one excitation per mode. This reduces each mode to a single qubit, allowing the simulation of collision circuits using 3-qubit gates.
Pre-computation: The optical properties (BSDFs) are pre-computed using quantum circuits (simulated classically for this work) and stored in multidimensional Look-Up Tables (LUTs) based on microscopic parameters (layer count, ray count, interaction strength).
Multi-Layer Setup: The framework models stacks of 2D materials (inspired by Van der Waals materials like graphite). Rays accumulate phase shifts as they propagate between layers, and surface modes retain memory of previous collisions, enabling complex interference patterns.

Key Contributions

Collision-Based Interaction Model: A novel extension of ray tracing that incorporates coherent absorption and non-linear light-matter effects by treating interactions as quantum collisions.
Symmetry-Constrained Unitary Operators: The derivation of specific unitary operators suitable for simulating 2D material interfaces, ensuring physical consistency (energy/momentum conservation) while allowing for non-integrable dynamics.
Multilayer Interaction Framework: A system that generates iridescence and rich optical responses through repeated collisions and phase accumulation across multiple layers, capturing effects that scale with the number of layers ( $N_l$ ) and rays ( $N_r$ ).
Production-Ready Shader: A practical implementation demonstrating how these pre-computed quantum-derived BSDFs can be integrated into standard rendering pipelines to render new, physics-inspired materials.

Results

The paper demonstrates the framework's capabilities through several visualizations and quantitative analyses:

Single Layer Absorption: Simulations show that as the number of rays ( $N_r$ ) increases, the surface mode occupation decays exponentially, and the material becomes more translucent.
Multi-Layer Interference: In a stack of $N_l$ layers, the reflectance ( $R$ ) and transmittance ( $T$ ) exhibit complex oscillations dependent on the phase difference $\xi$ and the number of layers.
Non-Linear Effects: By introducing non-zero interaction strength ( $h_i \neq 0$ ), the system generates optical signatures distinct from classical thin-film interference. The paper shows that increasing $N_l$ and $N_r$ creates "richer scenes with deeper color contrast" due to quantum interactions.
Visual Output: The framework successfully renders an opaque jade statue coated with a novel material node, where the visual appearance changes dynamically based on the quantum collision parameters, producing effects not achievable with traditional geometric optics.

Significance and Claims

The paper claims to offer a novel shading framework that unifies classical ray tracing with quantum mechanics to explore coherent light-matter interactions. Its significance lies in:

Bridging Scales: It connects macroscopic rendering with microscopic wave physics without requiring full-wave solvers for every pixel, instead offloading the complex physics to pre-computed quantum simulations.
New Material Synthesis: It enables the generation of materials with "distinct optical signatures" driven by non-linear quantum effects, expanding the palette of achievable appearances in computer graphics.
Feasibility on Near-Term Hardware: The approach is designed to be viable on current quantum hardware by restricting calculations to the single-excitation sector, making it a practical step toward quantum-accelerated rendering.
Physical Motivation: Unlike purely procedural approaches, the visual effects are grounded in physical principles of coherent scattering, symmetry constraints, and multi-layer interference.

The authors explicitly state that their goal is not to render physically accurate specific 2D materials (like exact graphene properties) but to use the physics of these systems as a foundation for creating new, physically motivated artistic controls and materials.