Mixed-State Quantum Denoising Diffusion Probabilistic Model

TL;DR

This paper introduces MSQuDDPM, a novel quantum generative model that removes the need for complex unitaries, improving near-term implementability and performance in quantum state generation tasks.

Contribution

The paper proposes MSQuDDPM, a mixed-state quantum diffusion model that replaces scrambling unitaries with noise channels and measurement-based circuits, enhancing practicality and convergence.

Findings

Successful quantum ensemble generation demonstrated

Elimination of high-fidelity scrambling unitaries

Improved convergence with superfidelity-based cost functions

Abstract

Generative quantum machine learning has gained significant attention for its ability to produce quantum states with desired distributions. Among various quantum generative models, quantum denoising diffusion probabilistic models (QuDDPMs) [Phys. Rev. Lett. 132, 100602 (2024)] provide a promising approach with stepwise learning that resolves the training issues. However, the requirement of high-fidelity scrambling unitaries in QuDDPM poses a challenge in near-term implementation. We propose the \textit{mixed-state quantum denoising diffusion probabilistic model} (MSQuDDPM) to eliminate the need for scrambling unitaries. Our approach focuses on adapting the quantum noise channels to the model architecture, which integrates depolarizing noise channels in the forward diffusion process and parameterized quantum circuits with projective measurements in the backward denoising steps. We also introduce several techniques to improve MSQuDDPM, including a cosine-exponent schedule of noise interpolation, the use of single-qubit random ancilla, and superfidelity-based cost functions to enhance the convergence. We evaluate MSQuDDPM on quantum ensemble generation tasks, demonstrating its successful performance.