arXiv:2412.07915quant-phcs.LG2024-12被引 12

解决量子核方法在真实数据上的指数集中问题,实现超150量子比特的高精度分类。

Mitigating exponential concentration in covariant quantum kernels for subspace and real-world data

  • 针对未知群结构数据,设计可抗噪声的保真度量子核方法。
  • 40+量子比特下纠错后准确率达80%,未纠错仅为33%。
  • 适用于大规模量子机器学习实验,尤其适合电力车队调度等实际场景。

保真度量子核在分类任务中表现优异,尤其当数据具有可利用的群结构时。然而其实际应用面临双重挑战:一是真实数据中群结构未知且近似,二是超过100量子比特时受指数集中效应影响。本文将保真度核应用于真实世界中的电动车辆调度数据及子空间并集生成的合成数据,提出专为保真度核设计的位翻转容错(BFT)误差缓解策略,以应对大规模实验中的指数集中问题。多类分类在156量子比特上达到与经典支持向量机相当的精度,创下当前基于IBM设备的最大规模量子机器学习实验记录。真实数据实验中,40+量子比特时纠正后准确率达80%,无纠正仅33%。在156量子比特的合成数据集上,纠正后准确率80%,优于未纠正量子模型的37%,接近经典模型的83%(测试集有限)。

原文摘要 · Abstract (English)

Fidelity quantum kernels have shown promise in classification tasks, particularly when a group structure in the data can be identified and exploited through a covariant feature map. In fact, there exist classification problems on which covariant kernels provide a provable advantage, thus establishing a separation between quantum and classical learners. However, their practical application poses two challenges: on one side, the group structure may be unknown and approximate in real-world data, and on the other side, scaling to the `utility' regime (above 100 qubits) is affected by exponential concentration. In this work, we address said challenges by applying fidelity kernels to real-world data with unknown structure, related to the scheduling of a fleet of electric vehicles, and to synthetic data generated from the union of subspaces, which is then close to many relevant real-world datasets. Furthermore, we propose a novel error mitigation strategy specifically tailored for fidelity kernels, called Bit Flip Tolerance (BFT), to alleviate the exponential concentration in our utility-scale experiments. Our multiclass classification reaches accuracies comparable to classical SVCs up to 156 qubits, thus constituting the largest experimental demonstration of quantum machine learning on IBM devices to date. For the real-world data experiments, the effect of the proposed BFT becomes manifest on 40+ qubits, where mitigated accuracies reach 80%, in line with classical, compared to 33% without BFT. Through the union-of-subspace synthetic dataset with 156 qubits, we demonstrate a mitigated accuracy of 80%, compared to 83% of classical models, and 37% of unmitigated quantum, using a test set of limited size.

量子机器学习误差缓解保真度核大规模量子

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