AI 中文总结
本研究提出扭转虚时间演化（TITE），用随机实时间演化替代一半虚时间，二次降低基态制备的成本，在不可积伊辛链的噪声模拟中性能优于标准虚时间演化（ITE）。
AI 中文摘要
虚时间演化（Imaginary-time evolution, ITE）是量子计算机上制备基态的基础方法。然而，由于ITE是非幺正的，现有实现的样本复杂度和/或经典代价随目标虚时间β呈指数级增长。此外，该态本身的收敛速度慢于能量，这使得任意基态可观测量的精确估计成本更高。在本研究中，我们对标准ITE进行改进，引入了扭转虚时间演化（twirled imaginary-time evolution, TITE），该方法将ITE与从精心设计的分布中抽取的随机时长的实时间演化相结合。我们证明，这种随机化可二次抑制与基态的迹距离，进而抑制任意可观测量的误差，这使得在保持相同精度水平的同时，约一半的虚时间可被实时间演化替代（β→β/2）。由于实时间演化是幺正的，且不会产生样本复杂度或经典计算的额外开销，这为包括Trotter化和量子虚时间演化在内的任意黑盒ITE实现的成本提供了二次降低。我们在不可积伊辛链的噪声电路级模拟中验证了该算法的效率，结果显示其性能显著优于标准ITE。
英文摘要
Imaginary-time evolution (ITE) is a foundational method for ground state preparation on quantum computers. However, because ITE is non-unitary, existing implementations incur a sample complexity and/or classical cost that scales exponentially with the target imaginary time $β$. Moreover, the state itself converges slower than the energy, making accurate estimation of arbitrary ground state observables even more expensive. In this work, we improve upon standard ITE by introducing twirled imaginary-time evolution (TITE), which pairs ITE with real-time evolution applied for a random duration drawn from a carefully designed distribution. We prove that this randomization quadratically suppresses the trace distance to the ground state, and thus also the error of arbitrary observables, which allows roughly half of the imaginary time to be replaced with real-time evolution ($β\mapsto β/2$) while maintaining the same level of accuracy. Because real-time evolution is unitary and does not incur an overhead in sample complexity or classical computation, this affords a quadratic reduction in the cost of any black-box ITE implementation, including Trotterization and quantum imaginary-time evolution. We demonstrate the efficiency of our algorithm in noisy circuit-level simulations of a non-integrable Ising chain, showing substantial improvements over standard ITE.
Comments20 pages. V2: updated simulations
