具有性能保证提升的量子近似优化算法递归贪心初始化
Recursive greedy initialization of the quantum approximate optimization algorithm with guaranteed improvement
AI总结：
针对QAOA随机初始化易陷入劣质局部极小值的问题，提出递归贪心初始化及过渡态解析构造，保证增加层数时最小能量下降，且性能媲美现有策略。
摘要：
量子近似优化算法（QAOA）是一种变分量子算法，其中量子计算机实现由p层交替酉算子组成的变分拟设，而经典计算机用于优化变分参数。在随机初始化下，优化通常会陷入性能较差的局部极小值，这促使人们寻找QAOA变分参数的初始化策略。尽管已有大量启发式初始化方法，但对于较大p的解析理解和性能保证仍然难以获得。我们引入了一种QAOA的贪心初始化，该方法保证随着层数增加性能得到提升。我们的主要结果是为具有p+1层的QAOA解析构造2p+1个过渡态——即具有唯一负曲率方向的鞍点，这些过渡态利用了p层QAOA的局部极小值。过渡态连接到新的局部极小值，并且保证这些新局部极小值与p层所找到的极小值相比能够降低能量。我们使用GREEDY过程来穿越因递归应用我们的解析构造而产生的、数量随p指数增长的局部极小值。GREEDY过程的性能与现有初始化策略相当，同时为最小能量随层数p增加而降低提供了保证。
英文摘要：
The quantum approximate optimization algorithm (QAOA) is a variational quantum algorithm, where a quantum computer implements a variational ansatz consisting of $p$ layers of alternating unitary operators and a classical computer is used to optimize the variational parameters. For a random initialization, the optimization typically leads to local minima with poor performance, motivating the search for initialization strategies of QAOA variational parameters. Although numerous heuristic initializations exist, an analytical understanding and performance guarantees for large $p$ remain evasive. We introduce a greedy initialization of QAOA which guarantees improving performance with an increasing number of layers. Our main result is an analytic construction of $2p+1$ transition states - saddle points with a unique negative curvature direction - for QAOA with $p+1$ layers that use the local minimum of QAOA with $p$ layers. Transition states connect to new local minima, which are guaranteed to lower the energy compared to the minimum found for $p$ layers. We use the GREEDY procedure to navigate the exponentially increasing with $p$ number of local minima resulting from the recursive application of our analytic construction. The performance of the GREEDY procedure matches available initialization strategies while providing a guarantee for the minimal energy to decrease with an increasing number of layers $p$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
