Quantum-inspired Multi-dimensional Visual Fields with Learnable Energy Representations
Shuteng Wang, Christian Theobalt, Vladislav Golyanik
Implicit representations with parametrized quantum circuits for gate-based quantum systems emerged as a promising paradigm for efficient learning, but still with many challenges. However, an optimal strategy for incorporating such circuits remains unclear, owing to limited understanding of different ways to leverage quantum-mechanical properties in representation learning. Existing works face problems such as: 1) reliance on heavy post-processing that overshadows quantum-mechanical effects, and 2) worse performance compared to classical modules. We introduce QVFs ($\textbf{Q}$uantum $\textbf{V}$isual $\textbf{F}$ields), a complete learnable quantum circuit without classical post-processing inspired by gate-based quantum system evolution. QVF integrates Hamiltonian-driven trainable neural operators with unitary quantum dynamics, regulating information flow through quantum conservation laws while employing projective measurement for feature extraction. Notably, our framework naturally inherits quantum-mechanical properties, including: (1) Fourier-spectral interpretability and (2) stable, reversible unitary evolution that ensures numerical stability—properties rigorously established in literature as critical for robust, bias-free learning. We evaluate QVF's properties, including expressiveness and robustness, with up to six qubits against existing methods on representing 2D images and 3D geometries. A benchmark study is performed against established quantum circuit architectures. Our results demonstrate that QVF, as a complete quantum circuit, can (1) efficiently learn high-fidelity multi-dimensional visual fields and (2) consistently outperform existing widely-used baselines across metrics such as learning speed, even at scale, therefore highlighting its practical potential.