This paper proposes a new procedure called quantum shadow gradient descent
(QSGD) that addresses these key challenges. Our method has the benefits of a
one-shot approach, in not requiring any sample duplication while having a
convergence rate comparable to the ideal update rule using exact gradient
computation. We propose a new technique for generating quantum shadow samples
(QSS), which generates quantum shadows as opposed to classical shadows used in
existing works. With classical shadows, the computations are typically
performed on classical computers and, hence, are prohibitive since the
dimension grows exponentially. Our approach resolves this issue by measurements
of quantum shadows. As the second main contribution, we study more general
non-product ansatz of the form $\exp\{i\sum_j \theta_j A_j\}$ that model
variational Hamiltonians. We prove that the gradient can be written in terms of
the gradient of single-parameter ansatzes that can be easily measured. Our
proof is based on the Suzuki-Trotter approximation; however, our expressions
are exact, unlike prior efforts that approximate non-product operators. As a
result, existing gradient measurement techniques can be applied to more general
VQAs followed by correction terms without any approximation penalty. We provide
theoretical proofs, convergence analysis and verify our results through
numerical experiments.

该论文提出了一种名为量子阴影梯度下降 (QSGD) 的新程序，以解决一次性方法、量子阴影样本生成和非乘积态哈密顿量等相关问题，并通过理论证明、收敛分析和数值实验验证了其结果。

量子影子梯度下降法用于量子学习

Quantum Shadow Gradient Descent for Quantum Learning

The exponential run time of quantum simulators on classical machines and long
queue depths and high costs of real quantum devices present significant
challenges in the effective training of Variational Quantum Algorithms (VQAs)
like Quantum Neural Networks (QNNs), Variational Quantum Eigensolver (VQE) and
Quantum Approximate Optimization Algorithm (QAOA). To address these
limitations, we propose a new approach, WEPRO (Weight Prediction), which
accelerates the convergence of VQAs by exploiting regular trends in the
parameter weights. We introduce two techniques for optimal prediction
performance namely, Naive Prediction (NaP) and Adaptive Prediction (AdaP).
Through extensive experimentation and training of multiple QNN models on
various datasets, we demonstrate that WEPRO offers a speedup of approximately
$2.25\times$ compared to standard training methods, while also providing
improved accuracy (up to $2.3\%$ higher) and loss (up to $6.1\%$ lower) with
low storage and computational overheads. We also evaluate WEPRO's effectiveness
in VQE for molecular ground-state energy estimation and in QAOA for graph
MaxCut. Our results show that WEPRO leads to speed improvements of up to
$3.1\times$ for VQE and $2.91\times$ for QAOA, compared to traditional
optimization techniques, while using up to $3.3\times$ less number of shots
(i.e., repeated circuit executions) per training iteration.

WEPRO 加速了量子神经网络的收敛速度，提供了更高的准确性和更低的损失，并且比传统优化技术提高了 3.1 倍的速度和使用了 3.3 倍少的重复电路执行次数。