Scalable Quantum Error Mitigation with Neighbor-Informed Learning

TL;DR

This paper introduces neighbor-informed learning (NIL), a scalable quantum error mitigation framework that improves accuracy and efficiency by learning from structurally related circuits, unifying existing methods and enabling large-scale quantum computations.

Contribution

The paper presents NIL, a novel scalable QEM method that unifies and enhances existing techniques, with a new 2-design training approach and logarithmic training set scaling.

Findings

NIL outperforms traditional QEM methods in accuracy and efficiency.

The training set size scales logarithmically with neighbor circuits.

Theoretical and numerical evidence supports NIL's effectiveness.

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.