通过量子嵌入方法获得高基态重叠
High ground state overlap via quantum embedding methods
AI总结：
本文研究量子嵌入中引导态制备问题，证明可按基态重叠选择轨道空间，并通过生物化学相关分子的数值实验表明平均场态足以支持量子相位估计。
摘要：
量子计算机可以利用相位估计精确计算基态能量，但这需要一个与真实基态具有显著重叠的引导态。对于大分子和扩展材料，随着分子尺寸增大，很难找到具有良好基态重叠的引导态。此外，所需的量子比特和量子门数量可能会大到令人难以承受。应对这些挑战的一种方法是使用量子嵌入方法，该方法允许将问题归约为嵌入在更大量子区域中的一个或多个更小型量子核心。在这种情况下，尚不清楚嵌入方法如何影响构建良好引导态的难度。因此，在本工作中，我们研究量子嵌入方法背景下的引导态制备。我们扩展了此前关于量子杂质问题的工作，在该框架中可以严格分析轨道子集的嵌入。虽然已有关于以能量最小化为目标的最优活性轨道空间选择结果，但我们严格证明了相同原理如何可用于根据与基态的重叠来定义用于态制备的所选轨道空间。此外，我们对与生物化学相关的分子系统进行了数值研究；由于蛋白质和核酸等生物大分子尺寸庞大，生物化学是一个需要量子嵌入方法的领域。我们研究了两种不同的嵌入策略，它们可以表现出性质上不同的轨道纠缠。在所有情况下，我们都证明了易于获得的平均场态将与目标态具有足够高的重叠，从而可以执行量子相位估计。
英文摘要：
Quantum computers can accurately compute ground state energies using phase estimation, but this requires a guiding state that has significant overlap with the true ground state. For large molecules and extended materials, it becomes difficult to find guiding states with good ground state overlap for growing molecule sizes. Additionally, the required number of qubits and quantum gates may become prohibitively large. One approach for dealing with these challenges is to use a quantum embedding method, which allows a reduction to one or multiple smaller quantum cores embedded in a larger quantum region. In such situations it is unclear how the embedding method affects the hardness of constructing good guiding states. In this work, we therefore investigate the preparation of guiding states in the context of quantum embedding methods. We extend previous work on quantum impurity problems, a framework in which we can rigorously analyze the embedding of a subset of orbitals. While there exist results for optimal active orbital space selection in terms of energy minimization, we rigorously demonstrate how the same principles can be used to define selected orbital spaces for state preparation in terms of the overlap with the ground state. Moreover, we perform numerical studies of molecular systems relevant to biochemistry, one field in which quantum embedding methods are required due to the large size of biomacromolecules such as proteins and nucleic acids. We investigate two different embedding strategies which can exhibit qualitatively different orbital entanglement. In all cases we demonstrate that the easy-to-obtain mean-field state will have a sufficiently high overlap with the target state to perform quantum phase estimation.
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