Quantum Visual Fields with Neural Amplitude Encoding

Quantum Implicit Neural Representations (QINRs) include components for learning and execution on gate-based quantum computers. While QINRs recently emerged as a promising new paradigm, many challenges concerning their architecture and ansatz design, the utility of quantum-mechanical properties, training efficiency and the interplay with classical modules remain. This paper advances the field by introducing a new type of QINR for 2D image and 3D geometric field learning, which we collectively refer to as Quantum Visual Field (QVF). QVF encodes classical data into quantum statevectors using neural amplitude encoding grounded in a learnable energy manifold, ensuring meaningful Hilbert space embeddings. Our ansatz follows a fully entangled design of learnable parametrised quantum circuits, with quantum (unitary) operations performed in the real Hilbert space, resulting in numerically stable training with fast convergence. QVF does not rely on classical post-processing -- in contrast to the previous QINR learning approach -- and directly employs projective measurement to extract learned signals encoded in the ansatz. Experiments on a quantum hardware simulator demonstrate that QVF outperforms the existing quantum approach and widely used classical foundational baselines in terms of visual representation accuracy across various metrics and model characteristics, such as learning of high-frequency details. We also show applications of QVF in 2D and 3D field completion and 3D shape interpolation, highlighting its practical potential.