FET: Small: Optimizing quantum circuit design

量子近似优化算法(QAOA)是利用量子计算技术解决复杂组合优化(CO)问题的主要候选算法。该算法是在迭代中执行的；虽然它总是被证明能找到CO问题的最优解，但它不一定总是在有限的迭代次数中找到解。因此，需要更好的技术来更快地找到CO问题的最优解。该项目研究了一种名为ma-QAOA的算法的新修改，它扩展了QAOA使用的参数数量，并允许增加自由度。这些变化增加了更快地找到CO问题的最优解的可能性。如果成功，这个项目将开发新的技术来解决包括运筹学和计算机科学在内的各种应用中目前难以解决的问题。该项目也将成为研究生级别的量子算法课程的基础，该课程将扩展基于量子优化和运算研究的能力。量子计算应用的主要限制是门的可靠性。误差随着电路中使用的门的数量呈指数增加，误差越大，获得高保真解所需的样本就越多。收集这些样本所需的时间可能会超过与给定解决方案相关的任何节省的时间。通过依赖经典优化和图论技术，该项目寻求减少解决复杂组合优化问题所需的门的总数。该项目的第一个目标是确定对于特定的问题实例，需要进行多少次QAOA迭代才能获得与ma-QAOA相当的结果。第二个目标是使用机器学习方法来确定如何最优地选择MA-QAOA的参数。第三个目标将使用图论技术来设计能够有效实施MA-QAOA的电路，第四个目标是确定将额外参数纳入算法的物理意义。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The quantum approximate optimization algorithm (QAOA) is a leading candidate for leveraging quantum computing techniques to solve complex combinatorial optimization (CO) problems. The algorithm is performed in iterations; while it has been proven always to find an optimal solution to a CO problem, it may not always find the solution in a finite number of iterations. Thus, better techniques are required to find optimal solutions to CO problems more quickly. This project investigates a new modification to the algorithm called ma-QAOA, which expands the number of parameters that QAOA uses and allows for additional degrees of freedom. These changes increase the likelihood of finding optimal solutions to CO problems more quickly. If successful, this project will develop new techniques for solving currently intractable problems from a diverse range of applications, including operations research and computer science. This project will also become the basis for a graduate-level quantum algorithms class that expands competency in quantum-based optimization and operations research.The main restriction for quantum computing applications is the reliability of gates. Errors increase exponentially with the number of gates used in a circuit, and the larger the error, the more samples are required to obtain high-fidelity solutions. The time required to collect these samples can outweigh any time savings associated with a given solution. By relying on classical optimization and graph theory techniques, this project seeks to reduce the total number of gates needed to solve complex combinatorial optimization problems. The first objective of this project is to determine how many iterations of QAOA are required to achieve results comparable to those of ma-QAOA for specific problem instances. The second objective is to use machine learning methods to determine how to select parameters for ma-QAOA optimally. The third objective will use graph theory techniques to design circuits that can efficiently implement ma-QAOA, and the fourth objective is to determine the physical significance of incorporating additional parameters into the algorithm.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.