AI 中文总结
研究提出广义非线性虚时演化（NITE）用于量子态制备，给出其硬件高效变分实现及与量子自然梯度下降的联系，应用于多个子例程任务，证明有局部指数收敛率，优于标准梯度下降，可用于基态制备外的变分任务。
AI 中文摘要
虚时演化（ITE）是用于给定哈密顿量基态制备的有力方法。归一化的ITE可视为能量期望值相对于富比尼 - 斯图迪度量的梯度流。本文提出广义非线性虚时演化（NITE）用于更一般的量子态制备任务，给出其硬件高效变分实现并揭示与量子自然梯度下降的联系。NITE应用于多个子例程任务，在合理假设下证明其具有局部指数收敛率，结果表明NITE优于标准梯度下降且可作为基态制备之外变分任务的有效优化方法。
英文摘要
Imaginary-time evolution (ITE) is a powerful method for ground-state preparation of a given Hamiltonian. The normalized ITE can be viewed as a gradient flow of the energy expectation value with respect to the Fubini--Study metric. In this work, we propose a generalized nonlinear imaginary-time evolution (NITE) for more general quantum state-preparation tasks. We further present a hardware-efficient variational implementation of NITE and reveal its connection to quantum natural gradient descent. NITE is applied to several subroutine tasks, including variance minimization in variational eigensolvers, probe-state preparation in variational quantum sensing, and excited-state preparation using penalty terms. We prove that NITE achieves a local exponential convergence rate under reasonable assumptions. Our results show that NITE outperforms standard gradient descent and can serve as an efficient optimization method for variational tasks beyond ground-state preparation.
Comments6 + 7 pages, 2 + 4 figures
