标题： 使用捕获离子量子处理器的定点-QAOA实验分解整数 显示英文标题

标题： Experimental factoring integers using fixed-point-QAOA with a trapped-ion quantum processor

摘要： 整数分解对于经典方法来说被认为是一个计算困难的问题，而存在一种多项式时间的Shor量子算法可以解决这个问题。 然而，对于现实任务运行Shor算法的要求超出了现有和即将出现的量子计算设备的能力，这促使人们寻找替代方法。 在本工作中，我们使用捕获离子量子处理器，通过Schnorr方法和量子近似优化算法（QAOA）的改进版本，实验演示了整数的分解。 与最近提出的基于QAOA的分解方法相比，我们方法的关键区别在于使用了固定点特性，该特性依赖于通用参数的使用。 我们展示了使用6个量子比特分解$1591=37\times43$的实验结果，以及使用10个量子比特分解$74425657=9521\times7817$和使用15个量子比特分解$35183361263263=4194191\times8388593$的模拟结果。 同时，我们提供了重现我们结果的所有必要细节，并对分解方法的性能进行了分析，该方法在经典和量子领域中的可扩展性仍需要进一步研究。 显示英文摘要

摘要： Factoring integers is considered as a computationally-hard problem for classical methods, whereas there exists polynomial-time Shor's quantum algorithm for solving this task. However, requirements for running the Shor's algorithm for realistic tasks, which are beyond the capabilities of existing and upcoming generations of quantum computing devices, motivates to search for alternative approaches. In this work, we experimentally demonstrate factoring of the integer with a trapped ion quantum processor using the Schnorr approach and a modified version of quantum approximate optimization algorithm (QAOA). The key difference of our approach in comparison with the recently proposed QAOA-based factoring method is the use of the fixed-point feature, which relies on the use of universal parameters. We present experimental results on factoring $1591=37\times43$ using 6 qubits as well as simulation results for $74425657=9521\times7817$ with 10 qubits and $35183361263263=4194191\times8388593$ with 15 qubits. Alongside, we present all the necessary details for reproducing our results and analysis of the performance of the factoring method, the scalability of this approach both in classical and quantum domain still requires further studies.