变分优化虚时多项式滤波器用于基态投影
Variationally Optimized Imaginary-time Polynomial Filters for Ground State Projection
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中文总结 AI 辅助
该研究开发了基于多项式滤波的变分虚时演化框架，推导了严格误差界，经横场伊辛模型基准测试，可提升基态投影的精度、稳定性与收敛速度，为近期量子设备的基态制备提供了实用方案。
中文摘要 AI 辅助
在本研究中，我们基于算子层面的作用原理开发了一种基于多项式滤波的变分虚时演化（ITE）框架，该框架生成以哈密顿量多项式形式表示的优化非幺正投影器。从由泰勒展开和Trotter-Suzuki（TS）分解定义的单辅助量子比特一阶虚时更新出发，我们证明用替代变分公式取代这些近似可大幅提升较大时间步长下的精度与稳定性，最终成功概率可提升一个数量级。我们进一步推导了仅依赖哈密顿量静态性质的严格误差界，为模拟时间步长的选择提供了实用指导。对横场伊辛模型的基准测试表明，与标准TS-Taylor ITE相比，该方法收敛到基态能量的速度更快、鲁棒性更强，凸显了变分多项式滤波器是近期量子设备上实现更高保真度基态制备的实用途径。
英文摘要
In this work, we develop a variational imaginary-time evolution (ITE) framework based on polynomial filtering, derived from an operator-level action principle, which yields an optimized non-unitary projector expressed as a polynomial in the Hamiltonian. Starting from a single-ancilla, first-order imaginary-time update defined by a Taylor expansion and Trotter-Suzuki (TS) decompositions, we show that replacing these approximations with alternative variational formulas substantially improves both accuracy and stability at larger time steps, leading to up to an order-of-magnitude enhancement in the final success probability. We further derive rigorous error bounds that depend only on static properties of the Hamiltonian, providing practical guidance for selecting the simulation time step. Benchmarks on the transverse-field Ising model demonstrate faster convergence to the ground-state energy and improved robustness compared to standard TS--Taylor ITE, highlighting variational polynomial filtering as a practical route to higher-fidelity ground-state preparation on near-term quantum devices.
