Quantum state preparation plays a crucial role in several areas of quantum information science, in applications such as quantum simulation, quantum metrology and quantum computing. However, typically state preparation requires resources that scale exponentially with the problem size, due to their probabilistic nature or otherwise, making studying such models challenging. In this article, we propose a method to prepare the ground state of the Affleck-Lieb-Kennedy-Tasaki (AKLT) model deterministically using a measurement-based imaginary time evolution (MITE) approach. By taking advantage of the special properties of the AKLT state, we show that it can be prepared efficiently using the MITE approach. Estimates based on the convergence of a sequence of local projections, as well as direct evolution of the MITE algorithm suggest a constant scaling with respect to the number of AKLT sites, which is an exponential improvement over the naive estimate for convergence. We show that the procedure is compatible with qubit-based simulators, and show that using a variational quantum algorithm for circuit recompilation, the measurement operator required for MITE can be well approximated by a circuit with a much shallower circuit depth compared with the one obtained using the default Qiskit method.

中文翻译：

---

使用基于测量的虚时间演化高效准备 AKLT 状态


量子态制备在量子信息科学的多个领域中发挥着至关重要的作用，例如量子模拟、量子计量学和量子计算等应用。然而，通常状态准备需要的资源随着问题的大小呈指数级扩展，因为它们的概率性或其他原因，这使得研究此类模型具有挑战性。在本文中，我们提出了一种使用基于测量的虚时间演化 （MITE） 方法确定性地准备 Affleck-Lieb-Kennedy-Tasaki （AKLT） 模型的基态的方法。通过利用 AKLT 状态的特殊性质，我们证明了可以使用 MITE 方法有效地准备它。基于一系列局部投影的收敛以及 MITE 算法的直接演变的估计表明，AKLT 站点的数量是恒定的缩放，这比收敛的朴素估计呈指数级改进。我们表明该程序与基于量子比特的模拟器兼容，并表明使用变分量子算法进行电路重新编译，与使用默认 Qiskit 方法获得的电路相比，MITE 所需的测量运算符可以很好地近似为电路深度要浅得多的电路。