标题： 黎曼几何在双括号量子虚时间演化中的作用 显示英文标题

标题： Role of Riemannian geometry in double-bracket quantum imaginary-time evolution

摘要： 双括号量子虚时间演化（DB-QITE）是一种量子算法，它在能量代价函数的方向上一致地实现黎曼最陡下降步骤。 DB-QITE 源自 Brockett 的双括号流，该流在梯度消失的鞍点处表现出特性。 在这项工作中，我们对 DB-QITE 进行了数值模拟，并描述了通过这些鞍点附近区域时的特征。 我们使用在 Qrisp 中编写的量子汇编提供了明确的门计数分析。 显示英文摘要

摘要： Double-bracket quantum imaginary-time evolution (DB-QITE) is a quantum algorithm which coherently implements steps in the Riemannian steepest-descent direction for the energy cost function. DB-QITE is derived from Brockett's double-bracket flow which exhibits saddle points where gradients vanish. In this work, we perform numerical simulations of DB-QITE and describe signatures of transitioning through the vicinity of such saddle points. We provide an explicit gate count analysis using quantum compilation programmed in Qrisp.