非正交量子特征求解器中测量成本缩放的改进
Improved Measurement Cost Scaling in the Nonorthogonal Quantum Eigensolver
AI总结：
针对非正交量子特征求解器（NOQE）的测量成本瓶颈，通过阈值处理将采样次数缩放从 O(M³) 改进为 O(M)，数值实验显示其实际测量成本增长更慢，为量子化学量子计算提供了更优方案。
AI中文摘要：
量子子空间对角化方法是适用于近期量子计算机的有前景的量子化学算法，这类方法可利用浅层量子电路估计分子体系的低能态能量，但需大量电路重复以估计投影矩阵元，而这些矩阵元的误差会因病态重叠矩阵转化为大得多的本征值误差。本文研究非正交量子特征求解器（NOQE）的这一瓶颈，NOQE 从修饰的无限制哈特利-福克态构建紧凑的多参考子空间。我们证明了有限次采样的扰动界，表明经过重叠阈值处理后，本征值敏感性由保留的重叠矩阵的条件数控制，而非最坏情况的维度因子。采用可扩展的阈值方案，达到目标精度所需的每矩阵元采样次数的上界缩放为 O(M)，优于此前已知的 O(M³) 界，其中 M 为参考态数量。对氢链和氢环的数值实验表明，实际中结构化 NOQE 实例的测量成本增长甚至比该线性界更慢。
英文摘要：
Quantum subspace diagonalization methods are promising algorithms for quantum chemistry on near-term quantum computers. These methods can estimate low-lying energies of molecular systems using shallow quantum circuits, at the cost of many circuit repetitions to estimate the projected matrix elements. Errors in these matrix elements can be converted into much larger eigenvalue errors by an ill-conditioned overlap matrix. We study this bottleneck for the nonorthogonal quantum eigensolver (NOQE), which constructs a compact multireference subspace from dressed unrestricted Hartree-Fock states. We prove a finite-shot perturbation bound showing that, after overlap thresholding, the eigenvalue sensitivity is controlled by the condition number of the retained overlap matrix rather than by a worst-case dimension factor. With a scalable thresholding scheme, the upper bound on the per-matrix-element shot count required to reach a target accuracy scales as $\mathcal{O}(M)$, improving on the previously known $\mathcal{O}(M^3)$ bound, where $M$ is the number of reference states. Numerical experiments on hydrogen chains and rings suggest that, in practice, the measurement cost of structured NOQE instances can grow even more slowly than this linear bound.
