Efficient Quantum State Preparation Algorithms

量子计算有潜力解决量子多体物理中许多尚未解决的问题。但是，必须解决严重的效率低下问题。在这个项目中，探索了几种方法来提高量子态制备的量子计算算法的性能。这些方法包括增加成功概率的预处理方法，能级密度的采样方法，以及由于时间步长而导致的系统误差的减少。作为这项研究计划更广泛影响的一部分，将邀请量子计算和应用领域的鼓舞人心和多样化的公众演讲者在高级研究门户系列中进行公开演讲。rodeo算法是一种高效的量子计算算法，可以制备量子哈密顿量的一般特征态。在这个项目中，二维Heisenberg模型作为基准系统，开发了几种方法来加速和提高rodeo算法的性能。将测试块划分方法和变分牛仔竞技算法这两种不同的初始状态预处理方法。然后将使用有限能量分辨率的随机方法来确定整个能谱。小跑步绝热演化将用于执行外推小跑步长。该奖项由量子信息科学项目颁发，由数学和物理科学理事会物理系理论核物理研究所联合支持。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Quantum computing has the potential to address many of the unsolved problems of quantum many-body physics. However, there are serious inefficiencies that must be addressed. In this project, several methods are explored to improve the performance of quantum computing algorithms for quantum state preparation. These include preconditioning methods that increase the probability of success, sampling methods for the density of energy levels, and the reduction of systematic errors due to time step size. As part of the broader impacts of this research proposal, inspiring and diverse public speakers in the field of quantum computing and applications will be invited to present public talks in the Advanced Studies Gateway series.The rodeo algorithm is an efficient quantum computing algorithm that can prepare general eigenstates of quantum Hamiltonians. In this project, the 2D Heisenberg model is used as a benchmark system to develop several methods to accelerate and improve the performance of the rodeo algorithm. The block partition method and the variational rodeo algorithm, two different methods for preconditioning the initial state, will be tested. Stochastic methods with finite energy resolution will then be used to determine the full energy spectrum. Trotter step adiabatic evolution will be used to perform extrapolations to small Trotter step size.This award by the Quantum Information Science program is jointly supported by the Theoretical Nuclear Physics in the Division of Physics within the Directorate for Mathematical and Physical Sciences.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.