Holstein极化子的本征向量延拓晶格拼接方法
Lattice stitching by eigenvector continuation for Holstein polaron
AI总结：
本文提出一种基于本征向量延拓的晶格拼接算法，将大晶格Holstein极化子基态问题分解为小型独立片段的本征值问题，实现希尔伯特空间指数级缩减，使100格点、32声子体系仅需11量子比特的变分量子本征求解器即可计算。
摘要：
晶格粒子-声子系统的模拟从根本上受到量子态数量随晶格尺寸指数增长的制约。本文展示了一种算法，该算法从小型独立晶格片段的本征值问题出发，在扩展晶格中构造Holstein模型的最低本征值和本征向量。这导致计算希尔伯特空间的指数级缩减，并允许将变分量子算法应用于大晶格中的粒子-声子相互作用。我们说明，在从弱到强的整个电子-声子耦合范围内，以及迄今为止数值计算所考虑的最低 phonon 频率（$ω/t = 0.1$）下，Holstein极化子的基态可以通过一系列最多四格点问题获得。当与量子算法结合时，本方法导致所需量子资源的急剧减少。我们表明，具有100个格点和32个格点声子的晶格中Holstein极化子的基态可以通过具有11个量子比特的变分量子本征求解器计算。
英文摘要：
Simulations of lattice particle - phonon systems are fundamentally restricted by the exponential growth of the number of quantum states with the lattice size. Here, we demonstrate an algorithm that constructs the lowest eigenvalue and eigenvector for the Holstein model in extended lattices from eigenvalue problems for small, independent lattice segments. This leads to exponential reduction of the computational Hilbert space and allows applications of variational quantum algorithms to particle - phonon interactions in large lattices. We illustrate that the ground state of the Holstein polaron in the entire range of electron - phonon coupling, from weak to strong, and the lowest phonon frequency ($ω/t = 0.1$) considered by numerical calculations to date can be obtained from a sequence of up to four-site problems. When combined with quantum algorithms, the present approach leads to a dramatic reduction of required quantum resources. We show that the ground state of the Holstein polaron in a lattice with 100 sites and 32 site phonons can be computed by a variational quantum eigensolver with 11 qubits.
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