Extracting information efficiently from quantum systems is a major component
of quantum information processing tasks. Randomized measurements, or classical
shadows, enable predicting many properties of arbitrary quantum states using
few measurements. While random single qubit measurements are experimentally
friendly and suitable for learning low-weight Pauli observables, they perform
poorly for nonlocal observables. Prepending a shallow random quantum circuit
before measurements maintains this experimental friendliness, but also has
favorable sample complexities for observables beyond low-weight Paulis,
including high-weight Paulis and global low-rank properties such as fidelity.
However, in realistic scenarios, quantum noise accumulated with each additional
layer of the shallow circuit biases the results. To address these challenges,
we propose the robust shallow shadows protocol. Our protocol uses Bayesian
inference to learn the experimentally relevant noise model and mitigate it in
postprocessing. This mitigation introduces a bias-variance trade-off:
correcting for noise-induced bias comes at the cost of a larger estimator
variance. Despite this increased variance, as we demonstrate on a
superconducting quantum processor, our protocol correctly recovers state
properties such as expectation values, fidelity, and entanglement entropy,
while maintaining a lower sample complexity compared to the random single qubit
measurement scheme. We also theoretically analyze the effects of noise on
sample complexity and show how the optimal choice of the shallow shadow depth
varies with noise strength. This combined theoretical and experimental analysis
positions the robust shallow shadow protocol as a scalable, robust, and
sample-efficient protocol for characterizing quantum states on current quantum
computing platforms.

我们提出了鲁棒的浅阴影协议，在实验中正确恢复了状态属性，如期望值、保真度和纠缠熵，同时维持了比随机单量子比特测量方案更低的样本复杂性。

基于浅影的稳健高效量子属性学习演示

Demonstration of Robust and Efficient Quantum Property Learning with  Shallow Shadows

Quantum computing, with its potential to enhance various machine learning
tasks, allows significant advancements in kernel calculation and model
precision. Utilizing the one-class Support Vector Machine alongside a quantum
kernel, known for its classically challenging representational capacity,
notable improvements in average precision compared to classical counterparts
were observed in previous studies. Conventional calculations of these kernels,
however, present a quadratic time complexity concerning data size, posing
challenges in practical applications. To mitigate this, we explore two distinct
approaches: utilizing randomized measurements to evaluate the quantum kernel
and implementing the variable subsampling ensemble method, both targeting
linear time complexity. Experimental results demonstrate a substantial
reduction in training and inference times by up to 95\% and 25\% respectively,
employing these methods. Although unstable, the average precision of randomized
measurements discernibly surpasses that of the classical Radial Basis Function
kernel, suggesting a promising direction for further research in scalable,
efficient quantum computing applications in machine learning.

量子计算在机器学习任务中的潜力使得核计算和模型精度得到显著提高。通过使用一类支持向量机和量子核，相对于经典对照方法，先前研究观察到了显着的平均精度改进。然而，传统计算这些核的方法对于数据大小具有二次时间复杂度，这在实际应用中带来了挑战。为了缓解这个问题，我们探索了两种不同的方法：利用随机测量来评估量子核以及实施可变子采样集合方法，这两种方法都针对线性时间复杂度。实验结果表明，采用这些方法的训练和推断时间大大减少，分别达到了 95% 和 25%，同时随机测量的平均精度明显优于经典径向基函数核，为进一步研究可扩展、高效的量子计算在机器学习中的应用方向提供了有希望的线索。