Jeongbin Jo

Jeongbin Jo

Backward diffusion is a prototype ill-posed evolution: high spatial frequencies grow exponentially in time, so mesh-based time marching without explicit regularization is quickly overwhelmed by noise. Schrödingerization embeds the semidiscrete generator into Hermitian dynamics on an extended space; we ask whether McLachlan projection onto a fixed low-dimensional frame supplies a structured regularizer whose error budget can be read from a projection defect that separates full lifted propagation from the reduced trajectory. We prove uniqueness of the reduced flow, Gram-norm conservation, a lifted--reduced gap bound in terms of that defect, and perturbation estimates that highlight overlap-matrix conditioning when matrix elements are estimated statistically. We also spell out a fair classical baseline -- spectral low-pass or Tikhonov filtering on the same semidiscrete model, with bandwidth or ridge strength matched to the information content of the chosen frame -- so numerical contrasts isolate the Schrödingerized reduced pipeline rather than an unregularized Crank--Nicolson march that mainly showcases blow-up. A calibrated one-dimensional benchmark pairs a spectrally truncated reference with snapshot-built subspace evolution and finite-shot Qiskit Aer estimation, illustrating how lift, projection, and sampling layers contribute differently to the overall error.

Jeongbin Jo, Santanam Wishal, Shah Md Khalil Ullah et al.

Quantum generative models offer a novel approach to exploring high-dimensional Hilbert spaces but face significant challenges in scalability and expressibility when applied to multi-modal distributions. In this study, we explore a Hybrid Quantum-Classical U-Net architecture integrated with Adaptive Non-Local Observables (ANO) as a potential solution to these hurdles. By compressing classical data into a dense quantum latent space and utilizing trainable observables, our model aims to extract non-local features that complement classical processing. We also investigate the role of Skip Connections in preserving semantic information during the reverse diffusion process. Experimental results on the full MNIST dataset (digits 0-9) demonstrate that the proposed architecture is capable of generating structurally coherent and recognizable images for all digit classes. While hardware constraints still impose limitations on resolution, our findings suggest that hybrid architectures with adaptive measurements provide a feasible pathway for mitigating mode collapse and enhancing generative capabilities in the NISQ era.