Q-Embroidery: A Study on Weaving Quantum Error Correction into the Fabric of Quantum Classifiers

TL;DR

This paper tackles the challenge of protecting quantum classifiers from noise by integrating quantum error correction codes (QECCs) into classifier circuits. It systematically evaluates the Steane code and distance-3 and distance-5 surface codes on 1-qubit and 2-qubit classifiers trained on synthetic 2D and 4D data, across depolarizing, bit-flip, and phase-flip error models. The key finding is that the distance-5 surface code generally provides the strongest resilience, while the Steane code offers smaller gains and can outperform some surface-code configurations under certain noise patterns; importantly, QECCs mitigate degradation rather than inherently improving nominal accuracy. The results emphasize that QECC choice should consider error type, resource constraints, and target accuracy, providing practical guidance for deploying QECC-enhanced quantum classifiers in noisy devices and laying groundwork for scalable quantum ML architectures.

Abstract

Quantum computing holds transformative potential for various fields, yet its practical application is hindered by the susceptibility to errors. This study makes a pioneering contribution by applying quantum error correction codes (QECCs) for complex, multi-qubit classification tasks. We implement 1-qubit and 2-qubit quantum classifiers with QECCs, specifically the Steane code, and the distance 3 & 5 surface codes to analyze 2-dimensional and 4-dimensional datasets. This research uniquely evaluates the performance of these QECCs in enhancing the robustness and accuracy of quantum classifiers against various physical errors, including bit-flip, phase-flip, and depolarizing errors. The results emphasize that the effectiveness of a QECC in practical scenarios depends on various factors, including qubit availability, desired accuracy, and the specific types and levels of physical errors, rather than solely on theoretical superiority.

Figures (8)

• Figure 1: Classical datasets for quantum classification: The left figure shows a two-dimensional dataset in magenta and cyan for the one-qubit classifier. The right figure presents a four-dimensional dataset in red, blue, green, and yellow for the two-qubit classifier, simplified to three dimensions using Principal Component Analysis (PCA) for visualization.
• Figure 2: Overview of quantum classifier circuits: The left figure shows a one-qubit classifier circuit for a two-dimensional dataset (Fig. \ref{['fig:dataset']} left), while the right figure depicts a two-qubit classifier circuit for a four-dimensional dataset (Fig. \ref{['fig:dataset']} right).
• Figure 3: Overhead analysis post-QECC application: This figure illustrates the average increase in qubit count (left) and gate count (right) required for the classifiers after the integration of QECCs.
• Figure 4: Comparative performance of QECCs under physical noise: This figure displays QECC performance for 1-qubit and 2-qubit classifiers under 'D', 'BP', and 'BPD' error modes as physical noise increases. With six subfigures, it compares resilience between classifiers, highlighting the distance $5$ surface code's superior improvement and the Steane code's minimal gain across noise levels.
• Figure 5: Heatmap analysis of quantum classifier resilience: This figure presents a heatmap comparison of 1-qubit (left) and 2-qubit (right) classifiers, showing how physical noise affects their performance. The 2-qubit classifier shows a sharper drop in successful trial probability (PST) with higher noise levels, particularly under BPD and least with D.