通过近最优本征概率滤波实现本征态制备
Eigenstate Preparation Through Near-Optimal Eigenprobability Filtering
浏览论文内容
中文总结 AI 辅助
针对未知本征值或初始态重叠不足时的本征态制备难题，提出DEFEAT算法，通过概率二次放大与阈值化实现近最优主导本征态滤波，提升重叠度依赖并减少辅助量子比特，经模拟验证有效。
中文摘要 AI 辅助
量子模拟有望成为量子计算机在量子化学、材料科学等领域具备实用价值的主要应用方向。然而，制备激发态或一般本征态是一项核心挑战，尤其是在预先未知目标本征值，或与初始态的重叠度不足时。我们提出了通过本征概率放大与阈值化实现主导本征态滤波（DEFEAT）算法，该算法可识别并滤波与给定初始态重叠度最大的本征态。我们的关键发现是无需预先知晓目标本征值，因为我们构建了高效的旋转超算符，可将初始态映射为对角化在哈密顿量本征基上的本征概率密度算子ρ，该算子编码了其谱权重及其块编码实现。我们的关键创新在于通过分解ρ=ρ_sqrt†ρ_sqrt实现概率的二次放大，这与近期提出的平方和谱放大（SOSSA）类似，我们在此用其放大主导分量与次主导分量之间的差距。随后的阈值化可得到主导本征态投影算子。与传统相位估计相比，DEFEAT在对初始态重叠度的依赖上有所改善，同时需要的辅助量子比特显著更少。我们证明了滤波步骤的查询复杂度在对数因子内最优，并针对在纯化查询访问ρ下的本征态制备建立了互补下界。我们在数值模拟中验证了DEFEAT的收敛速率与理论结果匹配。我们的结果为主导本征态滤波与制备以及主导本征态性质估计提供了一种与本征值无关的通用基元。
英文摘要
Quantum simulation is expected to be a main application of quantum computers with realistic utility in quantum chemistry, materials science and beyond. However, preparing excited or general eigenstates is a central challenge, particularly when the desired eigenvalue is not known in advance, or when the overlap with the initial state is insufficient. We introduce the Dominant Eigenstate Filtering via Eigenprobability Amplification and Thresholding (DEFEAT) algorithm that identifies and filters the eigenstate with the largest overlap with the supplied initial state. Our key observation is that we do not need prior knowledge of the target eigenvalue, as we construct efficient twirling superoperators that map initial states to eigenprobability density operators $ρ$, diagonal in the Hamiltonian eigenbasis and encoding its spectral weights, alongside its block-encoding implementation. Our crucial innovation is the quadratic amplification of probabilities via the factorisation $ρ=ρ_{\rm sqrt}^\daggerρ_{\rm sqrt}$, analogous to the recently introduced sum-of-squares spectral amplification (SOSSA), which we use here to amplify the separation between dominant and subdominant components. Thresholding then yields the dominant-eigenstate projector. Compared with conventional phase estimation, DEFEAT improves the dependence on the overlap with the initial state while requiring substantially fewer ancillary qubits. We prove that the query complexity of the filtering step is optimal up to logarithmic factors and establish a complementary lower bound for eigenstate preparation under purified query access to $ρ$. We validate in numerical simulations that the convergence rate of DEFEAT matches our theoretical results. Our results provide a general eigenvalue-agnostic primitive for dominant eigenstate filtering and preparation, and for estimating properties of dominant eigenstates.
