Trainable Photonic Measurement for Physics-Informed PDE Learning

2026-06-17

AI Summary

Traditional methods struggle to preserve phase, frequency, and derivative structures when solving highly challenging nonsmooth or strongly nonlinear partial differential equations (PDEs), leading to limited accuracy. This work proposes a photonic quantum neural field approach that encodes spatial coordinates into trainable optical phases, mixes information via multiphoton Fock-state interference, and decodes solutions from photon-number measurements. Leveraging programmable photonic circuits as differentiable function representations, the method enables end-to-end training within a physics-informed residual framework. Notably, it introduces photon-number measurement itself as a learnable representation mechanism—rather than a fixed mapping or mere hardware accelerator—for the first time. Evaluated across seven benchmark PDE classes—including elliptic, wave, nonlinear dispersive, and inverse problems—the approach achieves the lowest errors in the most difficult regimes, improving accuracy by nearly an order of magnitude over classical methods while using only about one-quarter of the trainable parameters.

Abstract

Photonic quantum machine learning offers a route to trainable physical representations built from phase, interference and measurement. However, its role in scientific machine learning remains largely unexplored. Physics-informed neural fields provide a natural setting, because differential equations require trial spaces that preserve phase, frequency and derivative structure. Here we introduce a photonic quantum neural field in which coordinates become trainable optical phases, are mixed by multi-photon Fock-space interference and are decoded from photon-number measurements. The photonic circuit is optimized as the neural-field representation itself, not as a fixed feature map or hardware accelerator. Photonic measurement is therefore a trainable representation on which the physics-informed residual is minimized. Across seven elliptic, wave, nonlinear dispersive and inverse PDE benchmarks, we observe a phase-complexity transition: classical coordinate and Fourier-feature networks suffice in smooth regimes, whereas the photonic field is most accurate when residual derivatives amplify phase mismatch. In the hardest regimes it gives the lowest errors, with margins reaching an order of magnitude and about one quarter of the trainable parameters of classical baselines. Frozen and shuffled controls, together with noise stress tests, attribute this gain to learned interference and stable Fock-probability readout under compound perturbations. These results identify photonic quantum measurement as a representation-learning principle for scientific machine learning.

Problem

• physics-informed PDE learning
• photonic quantum measurement
• neural fields
• phase mismatch
• scientific machine learning

Innovation

• photonic quantum neural field
• trainable photonic measurement
• physics-informed PDE learning
• Fock-space interference
• optical phase encoding