降本量子核训练

中文摘要 AI 辅助

量子核方法在近期量子机器学习中具有前景，但其训练成本受限于Gram矩阵构造的二次方扩展以及估计单个核值的测量成本。在本工作中，我们研究了一类异常检测作为训练非变分量子核模型的资源高效运行机制。使用ULB信用卡欺诈检测数据集，我们评估了三种量子特征映射在不同训练集大小和量子比特数量下的表现。幂律饱和模型显示随着训练数据增加存在强烈的收益递减，500样本模型保留了其拟合渐近平均精度（AP）的约90%至93%。我们进一步观察到在所评估的特征映射和所研究的量子比特范围内没有严重的指数集中现象，从而避免了该机制下指数增长的测量需求。最后，Nyström近似将核构造从$\mathcal{O}(N^2)$减少到$\mathcal{O}(Nm)$次评估，QSVR仅使用五个地标即保留了其精确核AP的94%至97%。对于ZZ-QSVR，将训练样本从4,000个下采样至500个并应用五地标近似，所需核评估次数从约800万减少至2,485次，减少了超过3,200倍，而AP从0.812降至0.737。在本文考虑的最低IonQ定价假设下，这对应于量子核训练成本从约13.4亿美元降至417,480美元的示例性减少。这些结果表明，训练集缩减和低秩近似可以大幅减少训练非变分量子核异常检测器所需的资源，同时保留有意义的异常判别性能。

英文摘要

Quantum kernel methods are promising for near-term quantum machine learning, but their training costs are driven by the quadratic scaling of Gram-matrix construction and the measurement cost of estimating individual kernel values. In this work, we investigate one-class anomaly detection as a resource-efficient operating regime for training non-variational quantum kernel models. Using the ULB Credit Card Fraud Detection dataset, we evaluate three quantum feature maps across training-set sizes and qubit counts. Power-law saturation models reveal strong diminishing returns with increasing training data, with 500-sample models retaining approximately 90--93\% of their fitted asymptotic average precision (AP). We further observe no severe exponential concentration among the evaluated feature maps over the investigated qubit range, thereby avoiding the exponentially increasing measurement requirements associated with that regime. Finally, Nyström approximation reduces kernel construction from $\mathcal{O}(N^2)$ to $\mathcal{O}(Nm)$ evaluations, with QSVR retaining 94--97\% of its exact-kernel AP using only five landmarks. For ZZ-QSVR, downsampling from 4,000 to 500 training samples and applying a five-landmark approximation decreases the number of required kernel evaluations from approximately $8.0$ million to $2,485$, a reduction of more than 3,200-fold, while AP decreases from $0.812$ to $0.737$. Under the minimum IonQ pricing assumption considered here, this corresponds to an illustrative reduction in quantum kernel training cost from approximately \$1.34 billion to \$417{,}480. These results demonstrate that training-set reduction and low-rank approximation can substantially reduce the resources required to train non-variational quantum kernel anomaly detectors while retaining meaningful anomaly-discrimination performance.

发表机构

• North Carolina A&T（北卡罗来纳农业与技术州立大学）
• Montgomery College（蒙哥马利学院）

机构由 AI 辅助整理，请以论文原文为准。