发表机构
The Institute of Mathematical Sciences; Homi Bhabha National Institute（数学科学研究所; 霍米·巴巴国家研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对受阻自旋-1/2 $J_1$-$J_2$ 模型中 VQE 的态序反转问题，提出双自旋扇区框架，通过优化 $S_z=1$ 三重态并映射到 $S_z=0$，精确分离激发单重态，捕捉关键物理特征并具资源效率。
AI 中文摘要
使用变分量子本征求解器（VQE）寻找受阻自旋系统中的激发态和激发隙，因态序反转而变得复杂。在受阻自旋-1/2 $J_1$-$J_2$ 海森堡模型中，当 $J_2/J_1 < 0.25$ 时，标准单扇区算法（如 $S_z=0$ 扇区中的变分量子缩减（VQD））会失效。在该区域，$S_z=0$ 中最低激发是三重态（$S=1$），其能量低于激发单重态（$S=0$）。标准缩减方法投影掉基态单重态后，会收敛到三重态，从而将其误认为激发单重态。本文提出一种双自旋扇区 VQE 框架，可解决一维自旋链和二维矩形晶格中的这些态序反转问题。通过先在 $S_z=1$ 扇区（其中单重态不存在）优化基态三重态，利用总自旋降低算符 $S^- = \sum_i S_i^-$ 将其映射到 $S_z=0$，并评估双扇区惩罚代价函数，我们得以无变分歧义地分离出激发单重态（$E_S$）。数值态矢量模拟证实了以单位重叠保真度精确收敛到机器精度。该方法捕捉了关键物理特征，包括无能隙相、$J_2/J_1 \approx 0.2411$ 处的 BKT 临界点、Majumdar-Ghosh 二聚体点（$J_2/J_1 = 0.50$），以及二维非磁性受阻区域（$J_2/J_1 \approx 0.40 - 0.60$）。有限采样模拟和最高 $N=100$ 量子比特的门扩展分析表明，该算法在近期量子执行中具有资源效率和采样鲁棒性。
英文摘要
Finding excited states and excitation gaps in frustrated spin systems using Variational Quantum Eigensolvers (VQE) is complicated by state-ordering inversions. In the frustrated spin-1/2 $J_1$-$J_2$ Heisenberg model, standard single-sector algorithms like Variational Quantum Deflation (VQD) in $S_z=0$ fail when $J_2/J_1 < 0.25$. In this regime, the lowest-lying excitation in $S_z=0$ is a Triplet ($S=1$), which lies below the Excited Singlet ($S=0$). Standard deflation projects out the ground singlet and converges onto the Triplet state, misidentifying it as the Excited Singlet. Here, we present a Dual Spin-Sector VQE framework that resolves these state-ordering inversions across 1D spin chains and 2D rectangular lattices. By first optimizing the ground Triplet state in the $S_z=1$ sector (where singlet states cannot exist), mapping it into $S_z=0$ via the total spin-lowering operator $S^- = \sum_i S_i^-$, and evaluating a dual-sector penalty cost function, we isolate the Excited Singlet ($E_S$) without variational ambiguity. Numerical state-vector simulations confirm exact convergence to machine precision with unit overlap fidelity. The method captures key physical features, including the gapless phase, the BKT critical point at $J_2/J_1 \approx 0.2411$, the Majumdar-Ghosh dimer point ($J_2/J_1 = 0.50$), and the 2D non-magnetic frustrated regime ($J_2/J_1 \approx 0.40 - 0.60$). Finite-shot sampling simulations and gate-scaling analytics up to $N=100$ qubits demonstrate the resource efficiency and shot resilience of the algorithm for near-term quantum execution.
Comments9 pages
