Continuous-variable Quantum Diffusion Model for State Generation and Restoration

TL;DR

This paper presents a novel continuous-variable quantum diffusion framework that uses quantum neural networks for high-fidelity quantum state generation and restoration, effectively combating environmental noise in CV quantum systems.

Contribution

It introduces a new CV quantum diffusion model combining physical diffusion processes with neural network-based denoising for state generation and restoration.

Findings

Achieves over 99% fidelity in generating Gaussian and non-Gaussian states.

Demonstrates effective restoration of quantum states from thermal noise.

Shows the framework's efficiency and scalability in simulations.

Abstract

The generation and preservation of complex quantum states against environmental noise are paramount challenges in advancing continuous-variable (CV) quantum information processing. This paper introduces a novel framework based on continuous-variable quantum diffusion principles, synergizing them with CV quantum neural networks (CVQNNs) to address these dual challenges. For the task of state generation, our Continuous-Variable Quantum Diffusion Generative model (CVQD-G) employs a physically driven forward diffusion process using a thermal loss channel, which is then inverted by a learnable, parameter-efficient backward denoising process based on a CVQNN with time-embedding. This framework's capability is further extended for state recovery by the Continuous-Variable Quantum Diffusion Restoration model (CVQD-R), a specialized variant designed to restore quantum states, particularly coherent states with unknown parameters, from thermal degradation. Extensive numerical simulations validate these dual capabilities, demonstrating the high-fidelity generation of diverse Gaussian (coherent, squeezed) and non-Gaussian (Fock, cat) states, typically with fidelities exceeding 99%, and confirming the model's ability to robustly restore corrupted states. Furthermore, a comprehensive complexity analysis reveals favorable training and inference costs, highlighting the framework's efficiency, scalability, and its potential as a robust tool for quantum state engineering and noise mitigation in realistic CV quantum systems.