The multiple signal classification (MUSIC) algorithm is a well-established method to evaluate the direction of arrival (DOA) of signals. However, the construction and eigen-decomposition of the sample covariance matrix (SCM) are computationally costly for MUSIC in hybrid multiple input multiple output (MIMO) systems, which limits the application and advancement of the algorithm. In this paper, we present a novel quantum method for MUSIC in hybrid MIMO systems. Our scheme makes the following three contributions. First, the quantum subroutine for constructing the approximate SCM is designed, along with the quantum circuit for the steering vector and a proposal for quantum singular vector transformation. Second, the variational density matrix eigensolver is proposed to determine the signal and noise subspaces utilizing the destructive swap test. As a proof of principle, we conduct two numerical experiments using a quantum simulator. Finally, the quantum labelling procedure is explored to determine the DOA. The proposed quantum method can potentially achieve exponential speedup on certain parameters and polynomial speedup on others under specific moderate circumstances, compared with their classical counterparts.

多信号分类 (MUSIC) 算法是一种行之有效的评估信号到达方向 (DOA) 的方法。然而，对于混合多输入多输出（MIMO）系统中的MUSIC，样本协方差矩阵（SCM）的构建和特征分解的计算成本很高，这限制了该算法的应用和进步。在本文中，我们提出了一种用于混合 MIMO 系统中 MUSIC 的新型量子方法。我们的方案做出以下三个贡献。首先，设计了构造近似单片机的量子子程序，设计了转向向量的量子电路，提出了量子奇异向量变换的方案。其次，提出了变分密度矩阵特征求解器来利用破坏性交换测试确定信号和噪声子空间。作为原理证明，我们使用量子模拟器进行了两次数值实验。最后，探索量子标记程序以确定 DOA。与经典对应物相比，所提出的量子方法可以潜在地在某些参数上实现指数加速，在特定温和情况下在其他参数上实现多项式加速。