走向关联拓扑物质中的量子效用：分数量子霍尔流形的变分制备
Toward Quantum Utility in Correlated Topological Matter: Variational Preparation of Fractional Quantum Hall Manifolds
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中文总结 AI 辅助
研究利用变分量子算法在近期量子处理器上制备和表征分数量子霍尔态，针对\(\nu = 1/3\) 劳克林相，在霍尔丹球面和环面两种几何结构中进行基准测试，结果显示能近似重建低能结构，为量子模拟提供途径。
中文摘要 AI 辅助
我们研究了使用变分量子算法在近期量子处理器上制备和表征分数量子霍尔态。聚焦于由\(V_1\) 霍尔丹赝势描述的\(\nu = 1/3\) 劳克林相，我们在二次量子化中制定了最低朗道能级问题，并实现了与变分量子本征求解器（VQE）和变分量子消胀（VQD）相结合的粒子数守恒变分电路。我们在两种互补几何结构（霍尔丹球面和环面形状）中对该方法进行了基准测试。在霍尔丹球面上，目标态是唯一的零能量劳克林基态，可对变分工作流程和激发态重建进行可控测试。在环面上，该问题保留了量子霍尔液体真正的二维周期性特征，并展现出\(\nu = 1/3\) 分数填充因子预期的三重拓扑基态简并性。我们使用能量估计、误差缓解可观测量和子空间包含诊断，将硬件优化的变分态与精确对角化进行基准测试。结果表明，混合量子算法可以近似重建小型分数量子霍尔系统的低能结构，包括环面上的拓扑基态流形。这种几何分辨方法不仅为量子硬件提供了基准，还为分数陈绝缘体和现实二维材料中强关联拓扑相的量子模拟提供了途径。
英文摘要
We investigate the use of variational quantum algorithms to prepare and characterize fractional quantum Hall states on near-term quantum processors. Focusing on the $ν=1/3$ Laughlin phase described by the $V_1$ Haldane pseudopotential, we formulate the lowest-Landau-level problem in second quantization, and implement particle-number-preserving variational circuits combined with the variational quantum eigensolver (VQE) and variational quantum deflation (VQD). We benchmark the approach in two complementary geometries: Haldane sphere and torus shape. On the Haldane sphere, the target state is a unique zero-energy Laughlin ground state, providing a controlled test of the variational workflow and of excited-state reconstruction. On the torus, the problem retains the genuinely two-dimensional periodic character of the quantum Hall liquid and exhibits the threefold topological ground-state degeneracy expected for the $ν=1/3$ fractional filling factor. This feature makes the torus a more demanding benchmark than the quasi-one-dimensional cylinder or thin-torus limits commonly exploited in state-preparation quantum protocols. We benchmark the hardware-optimized variational states against exact diagonalization using energy estimates, error-mitigated observables, and subspace-containment diagnostics. Our results show that hybrid quantum algorithms can approximately reconstruct the low-energy structure of small fractional quantum Hall systems, including the topological ground-state manifold on the torus. Beyond serving as a benchmark for quantum hardware, this geometry-resolved approach provides a route toward quantum simulations of fractional Chern insulators and strongly correlated topological phases in realistic two-dimensional materials.
