基于绝热捷径技术的量子近似优化算法及其应用研究

量子近似优化算法作为当前数字量子计算框架与实验技术水平下可能展现量子优越性且具有实际意义的量子算法，在图论与组合优化问题等方面具有潜在研究价值。申请人近年来提出了量子绝热捷径技术，加快量子绝热“慢”过程，用于实现快速、高保真的量子态制备与操控等，部分理论并得到了国内、外同行的实验验证。最近，申请人认识到量子绝热捷径技术有望结合量子优化算法，提高量子-经典混合算法的效率，进一步实现量子优越性。通过四年的工作，拟取得以下三个方面的成果：（1）结合变分拟设等方法发展新的量子绝热捷径技术，为后续研究提供方法；（2）为模拟量子计算框架下的量子退火，运用量子绝热捷径技术寻找不依赖于能隙的退火路径；（3）针对图论、组合优化的一些经典问题，运用量子绝热捷径技术增强算法表现，探索针对实际问题的量子优越性。

Quantum approximate optimization algorithm (QAOA), as a promising quantum algorithm for achieving quantum advantage in realistic problems under the structure of digital quantum computing and state-of-the-art experimental technologies, is worthwhile to be studied for graph theory and combinational optimization problem. In recent years, the applicant has proposed the techniques of shortcuts to adiabaticity (STA), to accelerate the quantum "slow" adiabatic process for the realization of fast and high-fidelity quantum state preparation and manipulation. In recent research, we notice that the application of STA can be extended to the field of quantum optimization algorithms, enhancing the performance of this quantum-classical algorithm, as well as exploring the possibility of achieving quantum advantage. During four years, we expect to realize the following three results: (1) improving new techniques in the field of STA by variational approximation method, providing tools for further study; (2) designing annealing schedule for quantum annealing, as analog quantum computing, without knowledge of energy gap; (3) improving the performance of QAOA in graph theory and combinational optimization problem by STA, exploring quantum advantage for realistic problems.