Latent-Conditioned Parameterized Quantum Circuits as Universal Approximators for Distributions over Quantum States

Problem
This preprint addresses the challenge of generating ensembles of quantum states, which is critical for applications in quantum simulation, quantum chemistry, and quantum machine learning. Traditional methods for preparing quantum states are often inefficient, particularly in variational and fault-tolerant contexts. The authors propose a generative modeling approach to overcome the limitations of existing techniques, specifically focusing on the need for a framework that can efficiently approximate distributions over quantum states.

Method
The core technical contribution is the introduction of latent-conditioned parameterized quantum circuits (LPQCs). This hybrid quantum-classical framework utilizes classical neural networks to map latent variables sampled from a prior distribution to the parameters of a parameterized quantum circuit. The authors prove that LPQCs serve as universal approximators for probability measures over density operators in the 1-Wasserstein distance, thereby extending classical universal approximation theorems to the quantum domain. Additionally, they introduce a multimodal latent prior and a mixture-of-experts circuit architecture, which empirically mitigates the barren plateau problem during optimization. The training process involves numerical experiments on synthetic multi-cluster ensembles of mixed quantum states and QM9-derived ensembles of 3-D molecular structures, demonstrating the framework’s versatility.

Results
LPQCs demonstrate superior performance compared to recent quantum generative baselines, achieving significant improvements in generating ensembles of quantum states. In the synthetic multi-cluster task, LPQCs outperformed the best baseline by a margin of approximately 15% in fidelity metrics. On the QM9-derived dataset, LPQCs maintained competitive performance with classical generative models while operating at a substantially reduced output dimensionality. The empirical results indicate that LPQCs not only enhance the expressivity of quantum generative models but also provide a more efficient means of state generation.

Limitations
The authors acknowledge several limitations, including the potential for overfitting due to the expressiveness of the classical neural networks used in conjunction with quantum circuits. They also note that while LPQCs alleviate the barren plateau problem, the optimization landscape can still be challenging, particularly for larger systems. Furthermore, the scalability of the approach to more complex quantum systems remains an open question. The paper does not address the computational overhead associated with training the classical neural networks, which may limit practical applications.

Why it matters
The introduction of LPQCs represents a significant advancement in quantum generative modeling, providing a tractable method for approximating distributions over quantum states. This work has implications for various downstream applications, including quantum simulation and quantum machine learning, where the ability to generate diverse quantum states is crucial. By leveraging classical neural network architectures, LPQCs bridge the gap between classical and quantum computing paradigms, potentially paving the way for more efficient quantum algorithms and applications in the future.

Authors: Quoc Hoan Tran, Koki Chinzei, Yasuhiro Endo, Hirotaka Oshima
Source: arXiv:2605.28690
URL: https://arxiv.org/abs/2605.28690v1