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arXiv:2607.21675

Hash-QNeRF: Multiresolution Hash Encoding for Quantum Neural Radiance Fields

Digonto Biswas, Tana Ballove, Anjan Bandyopadhyay, Sutanu Mangal, Arun Kumar Pati

quant-phcs.CVSubmitted Jul 23, 2026• Announced Jul 24, 2026• 0 citations
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Abstract

Neural Radiance Fields (NeRF) have revolutionized novel view synthesis, yet their classical implementations remain computationally intensive for high-fidelity rendering. QNeRF recently demonstrated the feasibility of training NeRF on gate-based quantum computers by combining amplitude embedding, parameterized quantum circuits (PQCs), parity-based measurements, and volumetric rendering. However, QNeRF relies on classical sinusoidal positional encoding for spatial coordinates, which scales poorly with scene complexity and resolution. In this work, we replace the sinusoidal positional encoding for spatial coordinates with the multiresolution hash encoding from Instant-NGP while keeping the view-direction encoding, amplitude MLP, quantum circuit, parity measurement, output scaling, and volumetric rendering pipeline unchanged. This hybrid design, Hash-QNeRF, retains the quantum radiance prediction step while benefiting from the fast convergence and memory efficiency of learnable hash grids. On a synthetic Blender scene, we achieve a final training loss of 0.003534, corresponding to approximately 24.5 dB PSNR on the fitted batch. Noise resilience experiments using Qiskit FakeKyiv and FakeTorino backends yield state fidelities of 0.93 to 0.98, indicating that hash encoding does not degrade the quantum circuit's noise tolerance.

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Implicit neural representations (INRs) have become a powerful paradigm for continuous signal modeling and 3D scene reconstruction, yet classical networks suffer from a well-known spectral bias that limits their ability to capture high-frequency details. Quantum Implicit Representation Networks (QIREN) mitigate this limitation by employing parameterized quantum circuits with inherent Fourier structures, enabling compact and expressive frequency modeling beyond classical MLPs. In this paper, we present Quantum Neural Radiance Fields (Q-NeRF), the first hybrid quantum-classical framework for neural radiance field rendering. Q-NeRF integrates QIREN modules into the Nerfacto backbone, preserving its efficient sampling, pose refinement, and volumetric rendering strategies while replacing selected density and radiance prediction components with quantum-enhanced counterparts. We systematically evaluate three hybrid configurations on standard multi-view indoor datasets, comparing them to classical baselines using PSNR, SSIM, and LPIPS metrics. Results show that hybrid quantum-classical models achieve competitive reconstruction quality under limited computational resources, with quantum modules particularly effective in representing fine-scale, view-dependent appearance. Although current implementations rely on quantum circuit simulators constrained to few-qubit regimes, the results highlight the potential of quantum encodings to alleviate spectral bias in implicit representations. Q-NeRF provides a foundational step toward scalable quantum-enabled 3D scene reconstruction and a baseline for future quantum neural rendering research.

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Recent advances in neural rendering, particularly 3D Gaussian Splatting (3DGS), have enabled real-time rendering of complex scenes. However, standard 3DGS relies on spherical harmonics, which often struggle to accurately capture high-frequency view-dependent effects such as sharp reflections and transparency. While hybrid approaches like Viewing Direction Gaussian Splatting (VDGS) mitigate this limitation using classical Multi-Layer Perceptrons (MLPs), they remain limited by the expressivity of classical networks in low-parameter regimes. In this paper, we introduce QuantumGS, a novel hybrid framework that integrates Variational Quantum Circuits (VQC) into the Gaussian Splatting pipeline. We propose a unique encoding strategy that maps the viewing direction directly onto the Bloch sphere, leveraging the natural geometry of qubits to represent 3D directional data. By replacing classical color-modulating networks with quantum circuits generated via a hypernetwork or conditioning mechanism, we achieve higher expressivity and better generalization. Source code is available in the supplementary material. Code is available at https://github.com/gwilczynski95/QuantumGS

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A central challenge in quantum machine learning is the state preparation bottleneck that describes the prohibitive computational cost of loading high-dimensional classical data into a quantum state. Although amplitude encoding can represent $2^n$-dimensional data using only $n$ qubits in principle, preparing arbitrary states remains computationally expensive, typically requiring variational optimization of a parameterized quantum circuit for each individual data instance. In this work, we propose a method that avoids iterative optimization by training a classical neural network to map input data directly to the continuous parameters of a fixed quantum circuit. We demonstrate the generation of quantum image states with high fidelity on data not seen during training. Since all optimization is performed once during training, the resulting model encodes new inputs in a single inference step, providing a scalable pathway for data loading in near-term quantum algorithms. We validate our method on the MNIST and Fashion-MNIST datasets, achieving fidelities up to 0.992 on unseen images and reducing the per-data-instance runtime by more than 5000-fold.

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Quantum neural networks (QNNs), represented by parameterized quantum circuits, can be trained in the paradigm of supervised learning to map input data to predictions. Much work has focused on theoretically analyzing the expressive power of QNNs. However, in almost all literature, QNNs' expressive power is numerically validated using only simple univariate functions. We surprisingly discover that state-of-the-art QNNs with strong expressive power can have poor performance in approximating even just a simple sinusoidal function. To fill the gap, we propose four expressibility-enhancing strategies for QNNs: Sinusoidal-friendly embedding, redundant measurement, post-measurement function, and random training data. We analyze the effectiveness of these strategies via mathematical analysis and/or numerical studies including learning complex sinusoidal-based functions. Our results from comparative experiments validate that the four strategies can significantly increase the QNNs' performance in approximating complex multivariable functions and reduce the quantum circuit depth and qubits required.

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End-to-End QGAN-Based Image Synthesis via Neural Noise Encoding and Intensity Calibration

Xue Yang, Rigui Zhou, Shizheng Jia +5 more

Quantum Generative Adversarial Networks (QGANs) offer a promising path for learning data distributions on near-term quantum devices. However, existing QGANs for image synthesis avoid direct full-image generation, relying on classical post-processing or patch-based methods. These approaches dilute the quantum generator's role and struggle to capture global image semantics. To address this, we propose ReQGAN, an end-to-end framework that synthesizes an entire N=2^D-pixel image using a single D-qubit quantum circuit. ReQGAN overcomes two fundamental bottlenecks hindering direct pixel generation: (1) the rigid classical-to-quantum noise interface and (2) the output mismatch between normalized quantum statistics and the desired pixel-intensity space. We introduce a learnable Neural Noise Encoder for adaptive state preparation and a differentiable Intensity Calibration module to map measurements to a stable, visually meaningful pixel domain. Experiments on MNIST and Fashion-MNIST demonstrate that ReQGAN achieves stable training and effective image synthesis under stringent qubit budgets, with ablation studies verifying the contribution of each component.

quant-pharXiv:2603.18554•Mar 20, 2026•0 citations
Neural Radiance Fields (NeRF) have revolutionized novel view synthesis, yet their classical implementations remain computationally intensive for high-fidelity rendering. QNeRF recently demonstrated the feasibility of training NeRF on gate-based quantum computers by combining amplitude embedding, parameterized quantum circuits (PQCs), parity-based measurements, and volumetric rendering. However, QNeRF relies on classical sinusoidal positional encoding for spatial coordinates, which scales poorly with scene complexity and resolution.
In this work, we replace the sinusoidal positional encoding for spatial coordinates with the multiresolution hash encoding from Instant-NGP while keeping the view-direction encoding, amplitude MLP, quantum circuit, parity measurement, output scaling, and volumetric rendering pipeline unchanged. This hybrid design, Hash-QNeRF, retains the quantum radiance prediction step while benefiting from the fast convergence and memory efficiency of learnable hash grids. On a synthetic Blender scene, we achieve a final training loss of 0.003534, corresponding to approximately 24.5 dB PSNR on the fitted batch. Noise resilience experiments using Qiskit FakeKyiv and FakeTorino backends yield state fidelities of 0.93 to 0.98, indicating that hash encoding does not degrade the quantum circuit's noise tolerance.
Implicit neural representations (INRs) have become a powerful paradigm for continuous signal modeling and 3D scene reconstruction, yet classical networks suffer from a well-known spectral bias that limits their ability to capture high-frequency details. Quantum Implicit Representation Networks (QIREN) mitigate this limitation by employing parameterized quantum circuits with inherent Fourier structures, enabling compact and expressive frequency modeling beyond classical MLPs. In this paper, we present Quantum Neural Radiance Fields (Q-NeRF), the first hybrid quantum-classical framework for neural radiance field rendering. Q-NeRF integrates QIREN modules into the Nerfacto backbone, preserving its efficient sampling, pose refinement, and volumetric rendering strategies while replacing selected density and radiance prediction components with quantum-enhanced counterparts. We systematically evaluate three hybrid configurations on standard multi-view indoor datasets, comparing them to classical baselines using PSNR, SSIM, and LPIPS metrics. Results show that hybrid quantum-classical models achieve competitive reconstruction quality under limited computational resources, with quantum modules particularly effective in representing fine-scale, view-dependent appearance. Although current implementations rely on quantum circuit simulators constrained to few-qubit regimes, the results highlight the potential of quantum encodings to alleviate spectral bias in implicit representations. Q-NeRF provides a foundational step toward scalable quantum-enabled 3D scene reconstruction and a baseline for future quantum neural rendering research.
Recent advances in neural rendering, particularly 3D Gaussian Splatting (3DGS), have enabled real-time rendering of complex scenes. However, standard 3DGS relies on spherical harmonics, which often struggle to accurately capture high-frequency view-dependent effects such as sharp reflections and transparency. While hybrid approaches like Viewing Direction Gaussian Splatting (VDGS) mitigate this limitation using classical Multi-Layer Perceptrons (MLPs), they remain limited by the expressivity of classical networks in low-parameter regimes. In this paper, we introduce QuantumGS, a novel hybrid framework that integrates Variational Quantum Circuits (VQC) into the Gaussian Splatting pipeline. We propose a unique encoding strategy that maps the viewing direction directly onto the Bloch sphere, leveraging the natural geometry of qubits to represent 3D directional data. By replacing classical color-modulating networks with quantum circuits generated via a hypernetwork or conditioning mechanism, we achieve higher expressivity and better generalization. Source code is available in the supplementary material. Code is available at https://github.com/gwilczynski95/QuantumGS
Quantum implicit neural representations have recently emerged as compact function approximators for continuous visual signals. In parallel, Neural Radiance Fields (NeRFs) have become a dominant framework for novel-view synthesis by recovering continuous volumetric scene representations from posed 2D images, but often require substantial model capacity and intensive optimisation. We introduce 3D Quantum Implicit Scene Representation (3D-QISR), the first hybrid quantum-classical radiance-field model for novel-view synthesis from 2D observations. 3D-QISR replaces the classical NeRF backbone with parameterised quantum circuits that encode spatial and view-dependent information through quantum state transformations, enabling compact quantum-enhanced implicit representations while preserving compatibility with standard volumetric rendering. We propose two architectures: Full 3D-QISR, which maximises the representational role of a unified quantum state, and Dual-Branch 3D-QISR, which separates spatial and view-dependent quantum embeddings to introduce a task-aligned inductive bias, reduce state-preparation complexity, and improve scalability and hardware compatibility. Experiments on moderate-resolution novel-view synthesis benchmarks show that 3D-QISR executed on simulated quantum hardware matches or outperforms classical baselines while using fewer than half the trainable parameters. These results position quantum neural networks as compact and competitive building blocks for continuous volumetric scene representation, opening a new direction for quantum-enhanced implicit neural rendering.
A central challenge in quantum machine learning is the state preparation bottleneck that describes the prohibitive computational cost of loading high-dimensional classical data into a quantum state. Although amplitude encoding can represent 2n2^n2n-dimensional data using only nnn qubits in principle, preparing arbitrary states remains computationally expensive, typically requiring variational optimization of a parameterized quantum circuit for each individual data instance. In this work, we propose a method that avoids iterative optimization by training a classical neural network to map input data directly to the continuous parameters of a fixed quantum circuit. We demonstrate the generation of quantum image states with high fidelity on data not seen during training. Since all optimization is performed once during training, the resulting model encodes new inputs in a single inference step, providing a scalable pathway for data loading in near-term quantum algorithms. We validate our method on the MNIST and Fashion-MNIST datasets, achieving fidelities up to 0.992 on unseen images and reducing the per-data-instance runtime by more than 5000-fold.
Quantum neural networks (QNNs), represented by parameterized quantum circuits, can be trained in the paradigm of supervised learning to map input data to predictions. Much work has focused on theoretically analyzing the expressive power of QNNs. However, in almost all literature, QNNs' expressive power is numerically validated using only simple univariate functions. We surprisingly discover that state-of-the-art QNNs with strong expressive power can have poor performance in approximating even just a simple sinusoidal function. To fill the gap, we propose four expressibility-enhancing strategies for QNNs: Sinusoidal-friendly embedding, redundant measurement, post-measurement function, and random training data. We analyze the effectiveness of these strategies via mathematical analysis and/or numerical studies including learning complex sinusoidal-based functions. Our results from comparative experiments validate that the four strategies can significantly increase the QNNs' performance in approximating complex multivariable functions and reduce the quantum circuit depth and qubits required.
Quantum Generative Adversarial Networks (QGANs) offer a promising path for learning data distributions on near-term quantum devices. However, existing QGANs for image synthesis avoid direct full-image generation, relying on classical post-processing or patch-based methods. These approaches dilute the quantum generator's role and struggle to capture global image semantics. To address this, we propose ReQGAN, an end-to-end framework that synthesizes an entire N=2^D-pixel image using a single D-qubit quantum circuit. ReQGAN overcomes two fundamental bottlenecks hindering direct pixel generation: (1) the rigid classical-to-quantum noise interface and (2) the output mismatch between normalized quantum statistics and the desired pixel-intensity space. We introduce a learnable Neural Noise Encoder for adaptive state preparation and a differentiable Intensity Calibration module to map measurements to a stable, visually meaningful pixel domain. Experiments on MNIST and Fashion-MNIST demonstrate that ReQGAN achieves stable training and effective image synthesis under stringent qubit budgets, with ablation studies verifying the contribution of each component.