量子多特征值高斯滤波搜索：一种高效且通用的量子相位估计方法
Quantum Multiple Eigenvalue Gaussian filtered Search: an efficient and versatile quantum phase estimation method
AI总结：
本文提出量子多特征值高斯滤波搜索（QMEGS），利用Hadamard测试电路和简单经典后处理，无需谱隙假设即可实现海森堡极限标度，并能以显著降低的电路深度估计主导特征值，适用于有隙和无隙系统。
摘要：
量子相位估计是最强大的量子原语之一。本文针对多特征值估计问题提出了一种新方法：量子多特征值高斯滤波搜索（QMEGS）。QMEGS利用Hadamard测试电路结构，仅需简单的经典后处理。QMEGS是首个同时满足以下两个性质的算法：（1）它能够在不依赖任何谱隙假设的情况下实现海森堡极限标度。（2）在具有正能量隙且对初始态有额外假设的条件下，与标准量子相位估计算法相比，QMEGS能够以显著降低的电路深度将所有主导特征值估计到ε精度。在最有利的情况下，最大运行时间可降低至log(1/ε)。这意味着QMEGS是一种高效且通用的方法，在有隙和无隙系统中均能取得已知最佳结果。数值结果验证了所提算法在各种情形下的效率。
英文摘要：
Quantum phase estimation is one of the most powerful quantum primitives. This work proposes a new approach for the problem of multiple eigenvalue estimation: Quantum Multiple Eigenvalue Gaussian filtered Search (QMEGS). QMEGS leverages the Hadamard test circuit structure and only requires simple classical postprocessing. QMEGS is the first algorithm to simultaneously satisfy the following two properties: (1) It can achieve the Heisenberg-limited scaling without relying on any spectral gap assumption. (2) With a positive energy gap and additional assumptions on the initial state, QMEGS can estimate all dominant eigenvalues to $ε$ accuracy utilizing a significantly reduced circuit depth compared to the standard quantum phase estimation algorithm. In the most favorable scenario, the maximal runtime can be reduced to as low as $\log(1/ε)$. This implies that QMEGS serves as an efficient and versatile approach, achieving the best-known results for both gapped and gapless systems. Numerical results validate the efficiency of our proposed algorithm in various regimes.
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