A purely Quantum Generative Modeling through Unitary Scrambling and Collapse

TL;DR

The paper tackles the bottleneck of classical components in quantum generative modeling by introducing a purely quantum Scrambling–Collapse framework (QGen). It architectures generation as a two-phase process: scrambling disperses information through Gaussian diffusion and unitary delocalization, and collapse reconstructs structured outputs via parameterized quantum circuits, trained with a measurement-based objective to avoid barren plateaus. Empirically, QGen outperforms classical and hybrid baselines under matched parameter budgets and remains robust under finite-shot sampling, demonstrated on MNIST, Fashion-MNIST, and EMNIST. This work provides a scalable, quantum-native approach to generative modeling with potential near-term hardware applicability and a path toward quantum advantage as devices scale.

Abstract

Quantum computing offers fundamentally more expressive mechanisms for generative modeling, yet current approaches remain constrained by classical neural components that bottleneck quantum capability and hardware efficiency. We propose the Quantum Scrambling and Collapse Generative Model (QGen), a purely quantum paradigm that eliminates classical dependencies. QGen implements two coherent processes: scrambling, which interleaves Gaussian diffusion channels with unitary delocalization to disperse information globally while avoiding collapse into uninformative states; and collapse, where parameterized quantum circuits refocus scrambled distributions into structured outputs, achieving distributional reconstruction under coherent evolution. To enable scalability, we introduce a measurement-based training principle that decomposes learning into tractable subproblems, mitigating barren plateaus. Empirically, QGen outperforms classical and hybrid baselines under matched parameter budget, while maintaining robustness under finite-shot sampling, demonstrating strong feasibility for near-term hardware.

Figures (28)

• Figure 1: Schematic of the proposed quantum generative model. The model disperses information by injecting local perturbations through a Gaussian channel, which are then coherently propagated across the Hilbert space via unitary evolution and quantum interference. In the collapse stage, PQCs leverages the established entanglement to refocus the delocalized states into structured distributions, with quantum measurement yielding reconstructions faithful to the original data.
• Figure 2: The Purely Quantum Scrambling-Collapse Generative Framework. (a) Forward Scrambling Process (left): an initial data sample $x_0 \sim q(x_0)$ progressively transformed by alternating Gaussian diffusion channels $\mathcal{N}_{\beta_t}$ and unitary delocalization operators $U_{\theta_t}$, dispersing local information into global quantum correlations and yielding a scrambled state $\rho_T$ whose measurement statistics converge to a Gaussian-like prior; (b) Reverse Collapse Process (right): A parameterized collapse operator $\mathcal{C}_\phi$ is trained to iteratively refocus the scrambled information, reversing the dynamics to reconstruct the target data distribution from the simple prior.
• Figure 3: Visualization of scrambling strategies. Left: Comparison of noise scheduling strategies: U-Fixed (purely unitary), U-Sched (unitary with variance scheduling), G-only (Gaussian channel only), and Ours. Pure unitary dynamics induce progressive entropy homogenization, driving the system toward the maximally mixed state. Introducing variance scheduling or Gaussian noise regulates entropy growth and preserves recoverable structure. Right: Log-scaled measurement distributions across timesteps $t$, showing that the joint action of noise injection and unitary scrambling drives smooth convergence toward a Gaussian-like prior, thereby ensuring statistical tractability and reversible dynamics.
• Figure 4: Effect of normalization and loss design. (a) Log-scaled probability distributions of quantum states across timesteps with and without normalization. Normalization compensates for exponentially small probabilities, often spanning several orders of magnitude, thereby alleviating sparsity issues induced by the exponentially large state space. (b) Reconstructed samples under different training losses, highlighting the trade-off between diversity and fidelity.
• Figure 5: Comparison of generated samples under different scrambling strategies.