Channel-Constrained Markovian Quantum Diffusion Model from Open System Perspective

TL;DR

This paper introduces a channel-constrained Markovian quantum diffusion model that uses open system dynamics and quantum channels to generate high-fidelity quantum states, validated on various quantum systems.

Contribution

It develops a novel framework modeling quantum diffusion as controlled Markov evolution with physically valid quantum channels optimized for high-fidelity state synthesis.

Findings

Achieves fidelities exceeding 0.998 on 7-qubit systems.

Demonstrates high-fidelity state generation under noise conditions.

Validates the model on systems from single qubits to entangled states.

Abstract

We present a channel-constrained Markovian quantum diffusion (CCMQD) model that prepares quantum states by rigorously framing the generative process within the dynamics of open quantum systems. Our model interprets the forward diffusion process as natural decoherence using quantum master equations, whereas the reverse denoising is achieved by learning inverse quantum channels. Our core innovation is a comprehensive channel-constrained framework: we model the diffusion and denoising steps as quantum channels defined by Kraus operators, ensure their physical validity through optimization on the Stiefel manifold, and introduce tailored training strategies and loss functions that leverage this constrained structure for high-fidelity state reconstruction. Experimental validation on systems ranging from single qubits to entangled states $7$ -qubits demonstrates high-fidelity state generation, achieving fidelities exceeding $0.998$ under both random and depolarizing noise conditions. This work confirms that quantum diffusion can be characterized as a controlled Markov evolution, demonstrating that environmental interactions are not limited to being a source of decoherence but can also be utilized to achieve high-fidelity quantum state synthesis.