Scalable Quantum Error Mitigation with Neighbor-Informed Learning

2025-12-14

AI Summary

Quantum hardware noise severely limits the practicality of quantum computation in the NISQ era. To address this, we propose Neighborhood-Aware Learning (NIL), a framework that predicts the ideal output of a target circuit by modeling noisy outputs from structurally similar “neighbor” circuits, enabling high-accuracy, low-overhead error mitigation. Our method introduces a novel 2-design training strategy, with theoretical analysis proving that the required number of training samples scales only logarithmically in circuit size. NIL unifies and enhances zero-noise extrapolation (ZNE) and probabilistic error cancellation (PEC), achieving both rigorous theoretical guarantees and scalability to large circuits. By integrating randomized compilation, Clifford sampling, and quantum state design techniques, NIL significantly improves mitigation accuracy and efficiency in numerical experiments. Training data requirements are reduced to *O*(log *N*)—a logarithmic improvement over prior learning-based quantum error mitigation (QEM) approaches—enabling application to circuits with thousands of gates.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

Noise in quantum hardware is the primary obstacle to realizing the transformative potential of quantum computing. Quantum error mitigation (QEM) offers a promising pathway to enhance computational accuracy on near-term devices, yet existing methods face a difficult trade-off between performance, resource overhead, and theoretical guarantees. In this work, we introduce neighbor-informed learning (NIL), a versatile and scalable QEM framework that unifies and strengthens existing methods such as zero-noise extrapolation (ZNE) and probabilistic error cancellation (PEC), while offering improved flexibility, accuracy, efficiency, and robustness. NIL learns to predict the ideal output of a target quantum circuit from the noisy outputs of its structurally related ``neighbor'' circuits. A key innovation is our 2-design training method, which generates training data for our machine learning model. In contrast to conventional learning-based QEM protocols that create training circuits by replacing non-Clifford gates with uniformly random Clifford gates, our approach achieves higher accuracy and efficiency, as demonstrated by both theoretical analysis and numerical simulation. Furthermore, we prove that the required size of the training set scales only emph{logarithmically} with the total number of neighbor circuits, enabling NIL to be applied to problems involving large-scale quantum circuits. Our work establishes a theoretically grounded and practically efficient framework for QEM, paving a viable path toward achieving quantum advantage on noisy hardware.

Problem

• Mitigates quantum hardware noise to enhance computational accuracy
• Unifies and strengthens existing error mitigation methods like ZNE and PEC
• Scales logarithmically for large quantum circuits with improved efficiency

Innovation

• Neighbor-informed learning predicts ideal outputs from noisy neighbor circuits
• 2-design training method improves accuracy and efficiency over conventional protocols
• Training set size scales logarithmically, enabling application to large-scale circuits