QNeRF: Neural Radiance Fields on a Simulated Gate-Based Quantum Computer

TL;DR

QNeRF introduces a gate-based quantum–classical architecture for novel-view synthesis by embedding coordinates into a quantum state, processing with a variational quantum circuit, and decoding via classical rendering. It offers two variants, Full QNeRF and Dual-Branch QNeRF, to balance expressivity and hardware practicality, aided by parity-based measurements and an output-scaling (de-concentration) mechanism. On Blender and LLFF datasets, Full QNeRF yields higher PSNR with fewer parameters than a classical NeRF, while Dual-Branch demonstrates superior noise resilience and scalability in near-term devices. Together, these findings provide a foundational step toward quantum-augmented 3D vision, highlighting both potential gains and the practical challenges of deploying quantum-enhanced representations for continuous signal learning.

Abstract

Recently, Quantum Visual Fields (QVFs) have shown promising improvements in model compactness and convergence speed for learning the provided 2D or 3D signals. Meanwhile, novel-view synthesis has seen major advances with Neural Radiance Fields (NeRFs), where models learn a compact representation from 2D images to render 3D scenes, albeit at the cost of larger models and intensive training. In this work, we extend the approach of QVFs by introducing QNeRF, the first hybrid quantum-classical model designed for novel-view synthesis from 2D images. QNeRF leverages parameterised quantum circuits to encode spatial and view-dependent information via quantum superposition and entanglement, resulting in more compact models compared to the classical counterpart. We present two architectural variants. Full QNeRF maximally exploits all quantum amplitudes to enhance representational capabilities. In contrast, Dual-Branch QNeRF introduces a task-informed inductive bias by branching spatial and view-dependent quantum state preparations, drastically reducing the complexity of this operation and ensuring scalability and potential hardware compatibility. Our experiments demonstrate that -- when trained on images of moderate resolution -- QNeRF matches or outperforms classical NeRF baselines while using less than half the number of parameters. These results suggest that quantum machine learning can serve as a competitive alternative for continuous signal representation in mid-level tasks in computer vision, such as 3D representation learning from 2D observations.

Figures (33)

• Figure 1: \ref{['fig:teaser_psnr']}: Comparison between model complexity as number of parameters (dot size) and number of amplitudes encoded with PSNR. \ref{['fig:teaser_fidelity']}: average fidelity on noisy simulated hardware for the proposed models. \ref{['fig:teaser_recon']}: example reconstruction with PSNR of the highlighted box. Zoom recommended.
• Figure 2: Scheme of the proposed models for $n=6$ qubits, and $\ell=2$ repetitions. Positional and view-dependent coordinates (shown in teal and magenta, respectively) are first encoded into quantum amplitudes by one (a) or two (b) MLPs, processed by a PQC (dashed box). Each gate is coloured according to the information that is processed (purple, if the information depends on both positional and view-dependent features, or blue or magenta if it depends only on positional or view-dependent features). The multi-qubit purple gates in (a) and (b) represent a dense entangling layer (see Fig. \ref{['fig:partial_layer']}, top), while the multi-coloured one in (b) is a partial entangling layer (see Fig. \ref{['fig:partial_layer']}, bottom). Then, the state is converted to classical information through a parity-based measurement, and finally processed with a scaling layer to reconstruct the output view.
• Figure 3: Dense entangling layer (top) and a partial entangling layer (bottom), for $n=4$.
• Figure 4: Visualisation of the effect of output scaling for a Full QNeRF, after $50$ epochs (PSNR reported in brackets). "GT" stands for ground truth.
• Figure 5: State fidelity for random parameter initialisations, evaluated over 50 runs for different 8-qubit ansatz and noise models. The red marks (corresponding to $\ell=0$) indicate the fidelity of the amplitude state preparation.