AI 中文总结
研究量子电路与系统的诺顿定理，通过高斯消元法等将有限维薛定谔动力学划分，给出约化方程，其在电路表示中对应诺顿导纳和电流源，该定理适用于多种量子系统并可进行多端口约化等。
AI 中文摘要
众所周知，经典模拟电路和系统受益于强大的戴维南定理和诺顿定理。这些定理能对系统其余部分对我们关注部分的影响进行严格且精确的数学简化和表示。我们表明存在“量子诺顿定理”的相应版本，可对量子电路和系统进行精确简化和约化，不仅适用于单端口，也适用于多端口甚至开放量子系统。我们在二能级系统、链、系统 - 环境划分、林德布拉德示例和格罗弗搜索中演示了该方法。格罗弗示例展示了约化网络如何隔离主导理想搜索的亮极点，并揭示对角无序如何将谱权重转移到降低性能的暗极点。通过将有限维薛定谔动力学划分为保留和消除的扇区，我们表明高斯消元法给出了一个精确的约化方程，其中消除的子系统表现为动态自能和源项。在电路表示中，这些项成为保留量子端口看到的诺顿导纳和诺顿电流源。相同的舒尔补构造扩展到多端口约化、复合系统 - 环境划分、密度矩阵动力学以及刘维尔空间中的林德布拉德演化。
英文摘要
It is well known that classical analog circuits and systems benefit from the powerful Thevenin and Norton theorems. These theorems enable rigorous and exact mathematical simplification and representation of the effect of the rest of a system on the part we want to focus on. We show that there are corresponding versions of a "Quantum Norton Theorem" that enable exact simplification and reduction for quantum circuits and systems, not just for one port, but also for multiport and even open quantum systems. We demonstrate the method on two level systems, chains, system environment partitions, Lindblad examples, and Grover search. The Grover examples show how the reduced network isolates the bright pole governing ideal search and exposes how diagonal disorder transfers spectral weight into dark poles that degrade performance. By partitioning finite dimensional Schrodinger dynamics into retained and eliminated sectors, we show that Gaussian elimination gives an exact reduced equation in which the eliminated subsystem appears as a dynamical self energy and a source term. In the circuit representation, these terms become the Norton admittance and Norton current source seen by the retained quantum port. The same Schur complement construction extends to multiport reductions, composite system environment partitions, density matrix dynamics, and Lindblad evolution in Liouville space.
