论文标题
通过结构化搜索对连续多变量函数进行量子优化
Quantum Optimisation for Continuous Multivariable Functions by a Structured Search
论文作者
论文摘要
解决优化问题是量子计算机的近期应用。量子变异算法利用量子叠加和纠缠使用经典可调的单位交替序列在指数较大的解决方案空间上进行优化。但是，先前的工作主要解决了离散优化问题。另外，这些算法通常是在非结构化解决方案空间的假设下设计的，该算法将其加速限制在非结构化Grover的量子搜索算法的理论限制上。在本文中，我们表明，量子变异算法可以通过利用超过非结构量子搜索限制的离散连续解决方案空间的一般结构特性来有效地优化连续的多变量函数。我们介绍了量子多变量优化算法（QMOA），并证明其优于先前存在的方法，尤其是在优化高维和振荡函数时。
Solving optimisation problems is a promising near-term application of quantum computers. Quantum variational algorithms leverage quantum superposition and entanglement to optimise over exponentially large solution spaces using an alternating sequence of classically tunable unitaries. However, prior work has primarily addressed discrete optimisation problems. In addition, these algorithms have been designed generally under the assumption of an unstructured solution space, which constrains their speedup to the theoretical limits for the unstructured Grover's quantum search algorithm. In this paper, we show that quantum variational algorithms can efficiently optimise continuous multivariable functions by exploiting general structural properties of a discretised continuous solution space with a convergence that exceeds the limits of an unstructured quantum search. We introduce the Quantum Multivariable Optimisation Algorithm (QMOA) and demonstrate its advantage over pre-existing methods, particularly when optimising high-dimensional and oscillatory functions.
