发表机构
Qclairvoyance Quantum Labs; Dayananda Sagar University; The University of Arizona; Ahmedabad University（Qclairvoyance量子实验室; 达亚南达·萨加尔大学; 亚利桑那大学; 艾哈迈达巴德大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究针对 NISQ 硬件上量子相位估计难的问题，提出解析训练变分代理框架，用浅 VQC 重现 QPE 测量分布，经经典计算训练目标消除模拟瓶颈，应用于氢分子实验，实现可扩展、硬件高效的 QPE 分子能量估计范式。
AI 中文摘要
量子相位估计（QPE）是分子基态能量估计的基础算法，但由于其对深度电路的要求，在有噪声的中等规模量子（NISQ）设备上直接硬件执行不切实际。我们提出了一个基于解析的变分代理框架，其中一个浅变分量子电路（VQC）被训练来重现 QPE 测量分布，而无需任何量子电路模拟。训练目标完全通过狄利克雷核经典计算，直接从全配置相互作用（FCI）基态能量、辅助量子比特数和时间演化参数进行评估，消除了先前代理方法的指数级缩放模拟瓶颈。我们将此框架应用于具有对称锥形哈密顿量的氢分子（H₂），在 IBM 量子硬件上进行了四阶段实验研究。第一阶段比较了 R_Y - R_Z - CZ 近似的线性和全纠缠器拓扑，有无 XpXm 动态解耦（DD），跨越四个分布度量（赫林格距离、保真度误差、总变差距离、詹森 - 香农散度），确定线性纠缠器为最优。第二阶段改变线性纠缠器近似的 VQC 层数（p = 1 到 5），确定在硬件噪声下单层深度为最优。第三阶段将此配置应用于简化的 R_Y - CZ 近似，比较理想和有噪声模拟器训练的参数。在 p ∈ {8,64} 处的补充噪声分析表征了电路深度和 DD 有效性之间的深度依赖相互作用。该框架使用线性缩放的 VQC 实现了忠实的 QPE 模拟，在化学精度阈值（1 kcal/mol）内恢复基态能量，构成了一种用于 NISQ 设备上基于 QPE 的分子能量估计的可扩展、硬件高效范式。
英文摘要
Quantum Phase Estimation (QPE) is a foundational algorithm for molecular ground-state energy estimation, but its deep circuit requirements make direct hardware execution impractical on Noisy Intermediate-Scale Quantum (NISQ) devices. We present an analytically grounded variational surrogate framework in which a shallow Variational Quantum Circuit (VQC) is trained to reproduce the QPE measurement distribution without any quantum circuit simulation. The training target is computed entirely classically via the Dirichlet kernel, evaluated directly from the Full Configuration Interaction (FCI) ground-state energy, the ancilla qubit count, and the time evolution parameter, eliminating the exponentially scaling simulation bottleneck of prior surrogate approaches. We apply this framework to the hydrogen molecule (H$_2$) with a symmetry-tapered Hamiltonian, conducting a four-stage experimental investigation on IBM Quantum hardware. Stage 1 compares linear and full entangler topologies for the $R_Y$-$R_Z$-$CZ$ ansatz, with and without XpXm Dynamical Decoupling (DD), across four distributional metrics (Hellinger distance, fidelity error, total variation distance, Jensen-Shannon divergence), identifying the linear entangler as optimal. Stage 2 varies VQC layers ($p=1$ to $5$) for the linear-entangler ansatz, identifying single-layer depth as optimal under hardware noise. Stage 3 applies this configuration to the reduced $R_Y$-$CZ$ ansatz, comparing ideal and noisy simulator-trained parameters. A supplementary noise analysis at $p \in \{8,64\}$ characterizes the depth-dependent interplay between circuit depth and DD effectiveness. The framework enables faithful QPE mimicry using a linearly scaling VQC, recovering the ground-state energy within the chemical accuracy threshold (1 kcal/mol), constituting a scalable, hardware-efficient paradigm for QPE-based molecular energy estimation on NISQ devices.
Comments30 pages, 12 figures
