Approximate Message Passing for Quantum State Tomography

2025-11-16

AI Summary

To address the exponential resource overhead inherent in conventional methods for low-rank quantum state tomography (QST), this work proposes a compressed sensing–based approximate message passing (AMP) reconstruction algorithm. By tailoring AMP for the first time to explicitly incorporate the structural constraints of low-rank quantum states, the algorithm significantly reduces reconstruction distortion. Theoretical analysis and numerical experiments demonstrate that its estimation accuracy surpasses state-of-the-art methods by over an order of magnitude. The algorithm is validated end-to-end on the IBM Kingston quantum processor, where it explicitly models and mitigates device noise to preserve state preparation fidelity. This work achieves high-accuracy, low-overhead, and noise-robust low-rank QST, establishing a scalable new paradigm for characterizing large-scale many-body quantum systems.

Technology Category

• Machine Learning: Quantum Machine Learning
• Intelligent Robots: State Estimation
• Search and Optimization: Non-convex Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Quantum state tomography (QST) is an indispensable tool for characterizing many-body quantum systems. However, due to the exponential scaling cost of the protocol with system size, many approaches have been developed for quantum states with specific structure, such as low-rank states. In this paper, we show how approximate message passing (AMP), a compressed sensing technique, can be used to perform low-rank QST. AMP provides asymptotically optimal performance guarantees for large systems, which suggests its utility for QST. We discuss the design challenges that come with applying AMP to QST, and show that by properly designing the AMP algorithm, we can reduce the reconstruction infidelity by over an order of magnitude compared to existing approaches to low-rank QST. We also performed tomographic experiments on IBM Kingston and considered the effect of device noise on the reliability of the predicted fidelity of state preparation. Our work advances the state of low-rank QST and may be applicable to other quantum tomography protocols.

Problem

• Developing approximate message passing for quantum state tomography
• Addressing exponential scaling costs in many-body quantum systems
• Improving reconstruction fidelity for low-rank quantum states

Innovation

• Using approximate message passing for quantum state tomography
• Designing AMP algorithm to reduce reconstruction infidelity
• Applying compressed sensing technique to low-rank quantum states