Paper ID: 2401.07039

Quantum Generative Diffusion Model: A Fully Quantum-Mechanical Model for Generating Quantum State Ensemble

Chuangtao Chen, Qinglin Zhao, MengChu Zhou, Zhimin He, Zhili Sun, Haozhen Situ

Classical diffusion models have shown superior generative results and have been applied to many problems. Exploring these models in the quantum domain can advance the field of quantum generative learning. In this paper, we introduce the Quantum Generative Diffusion Model (QGDM), a simple and elegant quantum counterpart of classical diffusion models. The core idea of QGDM is that any target quantum state can be transformed into a completely mixed state, which has the highest entropy and maximum uncertainty about the system, through a non-unitary forward process. Subsequently, a trainable backward process can be used to recover the target state from the completely mixed state. The design requirements for QGDM's backward process include ensuring non-unitarity while maintaining a low number of parameters. To achieve this, we introduce partial trace operations in the backward process to enforce non-unitary. Additionally, we control the number of trainable parameters by using a parameter-sharing strategy and incorporating temporal information as an input in the backward process. Furthermore, we introduce a resource-efficient version of QGDM, which reduces the number of auxiliary qubits while preserving impressive generative capabilities. Our proposed models exhibit better convergence performance than Quantum Generative Adversarial Networks (QGANs) because our models optimize a convex distance function using gradient descent. Comparative results with QGANs demonstrate the effectiveness of our models in generating both pure and mixed quantum states. Notably, our models achieve 53.03% higher fidelity in mixed-state generation tasks compared to QGANs. These results highlight the potential of the proposed models to tackle challenging quantum generation tasks.

Submitted: Jan 13, 2024