Title: Latent-Conditioned Parameterized Quantum Circuits Serve as Universal Approximators for Distributions Over Quantum States

Abstract:

In domains such as quantum simulation, quantum chemistry, and quantum machine learning, there is a growing need to model not just individual quantum states, but entire ensembles that capture the heterogeneity of a target system. Generating these ensembles one state at a time is computationally prohibitive, whether using variational methods or fault-tolerant architectures. To address this challenge, we propose a generative modeling strategy centered on Latent-Conditioned Parameterized Quantum Circuits (LPQCs). This hybrid quantum-classical framework employs classical neural networks to translate latent variables—drawn from a prior distribution—into the parameters governing a parameterized quantum circuit.

We demonstrate that LPQCs function as universal approximators for probability measures defined over density operators, specifically within the $1$-Wasserstein distance. This finding effectively extends classical universal approximation theorems into the realm of quantum distributions. Furthermore, we introduce a multimodal latent prior alongside a mixture-of-experts circuit architecture. Empirical results indicate that this combination helps mitigate the barren plateau problem during the optimization process.

Our numerical experiments validate the framework using two distinct tasks: a synthetic multi-cluster ensemble of mixed quantum states and an ensemble of 3-D molecular structures derived from the QM9 dataset. In both scenarios, LPQCs surpass recent quantum generative baselines and remain competitive with standard classical baselines, despite operating with significantly lower output dimensionality. By harnessing the expressive power of classical neural networks within the latent space, LPQCs provide a practical pathway for quantum generative modeling.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC