AI 中文总结
研究基于量子硬件发展构建二维成对量子电路假设，通过与一维假设对比，探讨其在固定16量子比特系统中的可表达性与可训练性，发现二维假设在浅层有优势，且在不同层数下梯度方差有差异。
AI 中文摘要
参数化量子电路（PQCs）是变分量子算法（VQAs）和量子机器学习（QML）方法的核心组成部分。现有假设设计常采用与硬件无关或简化的1D链/环纠缠模式。随着量子硬件发展，原生2D连接模式如平面超导量子比特架构愈发重要。受此启发，构建原生2D成对假设并与代表性1D假设在相同层深度下比较其可表达性和可训练性。对于固定的16量子比特系统，2D假设在L = 1和2时具有最小KL散度，其二阶框架势在浅层时比三个1D假设更快接近理论下限。还评估了泡利-Z串期望值〈Z0⊗⋯⊗Z15〉相对于第一个Ry角的梯度方差，在L = 1 - 4时，2D电路的梯度方差较小，L = 5时差异缩小，L = 6时四个假设产生统计上兼容的方差。
英文摘要
Parameterized quantum circuits~(PQCs) constitute a central building block of variational quantum algorithms~(VQAs) and quantum machine learning~(QML) methods. Existing ansatz designs often adopt hardware-agnostic or simplified 1D chain/ring entanglement patterns. However, as quantum hardware continues to develop, native 2D connectivity patterns, such as planar superconducting-qubit architectures, are becoming increasingly important. Inspired by this hardware structure, we construct a native 2D pairwise ansatz and compare its expressibility and trainability with representative 1D ansatze at identical layer depths, despite their different circuit depths. For the fixed 16-qubit system, the 2D ansatz has the smallest KL divergence at $L=1$ and $2$, and its second-order frame potential approaches the theoretical lower bound more rapidly at shallow layer counts than the frame potentials of the three 1D ansatze. We also evaluate the gradient variance of the Pauli-$Z$-string expectation value $\langle Z_0\otimes\cdots\otimes Z_{15}\rangle$ with respect to the first $R_y$ angle. For this Pauli-$Z$ string and fixed parameter, the gradient variance is smaller for the 2D circuit at $L=1$--$4$. The differences narrow at $L=5$, and the four ansatze yield statistically compatible variances at $L=6$.
Comments25 pages, 10 figures
