多体纠缠态在量子模拟中的优化制备

Multipartite entangled states are indispensable resources for novel quantum technologies, e.g., quantum computing and quantum simulation. The ability of creating given high-fidelity genuine multipartite entangled states, for instance, many-body Schrodinger-cat states, will remarkably generalize the application of quantum computer and quantum simulator to answering more complex questions and release genuine quantum advantage. In practice, however, limited by the preparation scheme and finite lifetimes of the underlying physical systems, the largest Schrodinger-cat state only contains 18 qubits, which is way less than the requirement of meaningful quantum simulation/ computation. In this project, we plan to coherently combine optimal control strategies and tensor network algorithms to derive more efficient schemes to prepare large-scale multipartite entangled states on ultra-cold Rydberg atoms and superconducting circuits, which are the most appealing physical platforms for quantum simulation/computation. Then we will use the developed scheme to explore the quantum speed limit time for preparing multipartite entangled states on the two platforms studied in this project. The preparation scheme will be optimized such that (1) the main figure of merit, i.e., fidelity or entanglement, is close to maximal, (2) the size of the prepared multipartite entangled state will exceed the largest ever by approximately 10 qubits, (3) the time cost in states preparation is (much) shorter than the lifetimes and the coherence times of the underlying quantum systems, and (4) the obtained control scheme is robust against relevant experimental defects and disorders.

多体量子纠缠态是量子计算和量子模拟等新兴量子技术所必需的宝贵资源。高保真度制备给定的多体量量子纠缠态，例如多体薛定谔猫态，将会使量子计算和量子模拟的应用范围拓展到对更复杂问题的探索，释放出真正的量子优势。然而受限于制备方案的粗简和系统相干时间的制约，目前实验上实际能制备出的最大尺寸的多体纠缠态仅仅包含18个量子比特，远远不能满足量子模拟和量子计算的真正需求。本项目拟以超冷里德堡原子和超导量子线路这两个实现量子模拟和量子计算最有竞争力的实验平台为研究对象，将CRAB优化控制策略和张量网络态算法有机结合，导出制备给定多体量子纠缠态的调控方案，并探索在这两个平台上制备各种多体纠缠态的量子极限时间,使得制备的多体纠缠态的保真度及纠缠接近最大可能值，制备的多体纠缠态的尺寸超过现存记录十个左右量子比特数，制备所需时间远小于系统的寿命和相干时间，并且得到的制备方案有足够的稳定性对抗系统噪声和缺陷。

项目严格按照任务书进行，主要研究了多体量子系统中量子纠缠的数学结构和现有技术条件下量子计算实验可测量的能够代替量子纠缠的物理量（对角熵），及其在判定量子相变、多体局域化-热化动力学相变等方面的应用；改进了量子近似优化算法(QAOA)并用其导出了里德堡原子阵列系统中制备 GHZ 态的一种全新方案；针对全连接型的超导量子芯片系统完成了矩阵乘积态数值计算程序，并以此与dCRAB优化控制方法结合导出了20比特GHZ态制备方案，其保真度达到63.3%，明显高于50%的真多体纠缠态阈值；在4里德堡原子系统中确认并导出了GHZ态制备的量子极限时间，加深了对该系统和动力学过程的理解。