Q-SPARSE：用于近场角度-距离谱估计的量子子空间投影
Q-SPARSE: Quantum Subspace Projection for Near-Field Angle-Range Spectrum Estimation
- KTH Royal Institute of Technology（皇家理工学院）
- Ericsson（爱立信）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
针对近场联合角度-距离定位，提出量子子空间投影算法Q-SPARSE，利用量子相位估计避免经典特征态制备瓶颈，在理想条件下与经典MUSIC等价，并在QISKIT上验证了有效性。
中文摘要 AI 辅助
近场波前曲率能够实现联合角度-距离定位，但利用这一特性需要在二维球面流形上进行重复的协方差特征空间测试。我们提出了一种量子子空间投影算法（Q-SPARSE），用于近场参数的超分辨率估计，其采用与MUSIC类似的谱特征。Q-SPARSE将每个球面导向假设制备为量子态，对协方差生成的演化应用量子相位估计（QPE），并将解析出的谱质量转换为定位谱。所提方法无需经典地完整制备特征态，而这正是QPE算法（MUSIC算法量子变体的主要子程序）的主要瓶颈。在理想的信号-噪声划分下，其得分与经典信号子空间重叠完全一致，从而保留了归一化近场MUSIC的最大化器。对于有限数量的量子比特相位寄存器q，我们从完整的QPE核推导出得分，并提出一种基于Marchenko-Pastur校准的逻辑加权决策准则的最近邻选择方案，并采用软阈值处理。在IBM的QISKIT软件平台上展示了近场阵列处理的数值结果。
英文摘要
Near-field wavefront curvature enables joint angle-range localization, but exploiting it entails repeated covariance-eigenspace tests over a two-dimensional spherical manifold. We propose a quantum subspace-projection algorithm (Q-SPARSE) for super-resolution estimation of parameters in the near field, employing spectral signature similar to MUSIC. Q-SPARSE prepares each spherical steering hypothesis as a quantum state, applies quantum phase estimation (QPE) to covariance-generated evolution, and converts the resolved spectral mass into a localization spectrum. The proposed method does not need the full classical preparation of the eigenstates, which is a major bottleneck of the QPE algorithm, the main subroutine in quantum variants of MUSIC algorithms. Under an ideal signal-noise partition, its score equals the classical signal-subspace overlap exactly and thus preserves the maximizer of normalized near-field MUSIC. For a finite q number of qubit phase registers, we derive the score from the complete QPE kernel, and propose a nearest-bin selection scheme with soft-thresholding based on Marchenko-Pastur-calibrated logistic weighting decision criteria. Numerical results on IBM's QISKIT software platform are demonstrated for near-field array processing.
