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

Area of Science:

• Quantum Information Science
• Quantum Computing
• Quantum Machine Learning

Background:

• Mixed quantum states are crucial for describing many quantum systems.
• Generating mixed quantum states is a fundamental but challenging task in quantum information processing.
• Existing diffusion models face difficulties in ensuring physically valid reverse steps.

Purpose of the Study:

• To introduce a novel quantum-mechanical diffusion model for generating mixed quantum states.
• To develop a framework grounded in quantum channel theory for both forward and backward processes.
• To enhance the efficiency and robustness of quantum generative modeling.

Main Methods:

• Developed the Quantum Generative Diffusion Model (QGDM) based on quantum channel theory.
• Implemented a non-unitary forward process transforming target states into mixed states.
• Utilized a trainable backward process with partial trace and shared parameters for state recovery.
• Introduced a resource-efficient version of QGDM and analyzed its denoising design.

Main Results:

• QGDM successfully generates mixed quantum states with physically valid reverse steps.
• The model outperforms quantum generative adversarial networks in pure- and mixed-state generation.
• QGDM exhibits enhanced noise robustness compared to other quantum generative models.
• A resource-efficient version preserves generative capabilities while reducing auxiliary qubits.

Conclusions:

• QGDM provides a robust and efficient channel-based diffusion framework for learning mixed-state targets.
• The model extends quantum generative modeling capabilities for realistic quantum information settings.
• QGDM offers a promising approach for advancing quantum information processing tasks.