发表机构
N. L. Dukhov All-Russia Research Institute of Automatics（N.L.杜霍夫全俄自动学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为具有Dzyaloshinskii-Moriya相互作用的Heisenberg三角形构造精确量子电路，通过基变换和局部旋转实现至多14个CNOT门，并应用于kagome晶格模拟。
AI 中文摘要
我们为具有Dzyaloshinskii-Moriya (DM)相互作用的三自旋Heisenberg三角形构造了精确量子电路。基变换将具有任意耦合的纯DM演化简化为两个单量子比特旋转，从而给出至多8个CNOT门的电路。当所有键上的$J$和$D$各自相同时，一个固定基给出对任意实数$J,D,t$至多10个CNOT门的电路。局部自旋旋转将构造推广到具有不等DM耦合和非零交换相互作用的族，所需CNOT门至多14个。所有电路作用于完整Hilbert空间。另一种纯DM实现使用五个两量子比特DM门：通过解析地重新调整一个对称Strang步骤的角度使其精确。一个12自旋kagome示例说明了这些精确局域块在晶格模拟中的应用。
英文摘要
We construct exact quantum circuits for a three-spin Heisenberg triangle with Dzyaloshinskii-Moriya (DM) interaction. A change of basis reduces pure DM evolution with arbitrary couplings to two single-qubit rotations, giving a circuit with at most 8 CNOT gates. When $J$ and $D$ are each the same on all bonds, one fixed basis gives a circuit with at most 10 CNOT gates for any real $J,D,t$. Local spin rotations extend the construction to a family with unequal DM couplings and nonzero exchange, requiring at most 14 CNOT gates. All circuits act on the full Hilbert space. An alternative pure DM implementation uses five two-qubit DM gates: analytically retuning the angles of one symmetric Strang step makes it exact. A 12-spin kagome example illustrates the use of these exact local blocks in lattice simulation.
Comments13 pages, 6 figures. Supplementary material and code are available at https://doi.org/10.5281/zenodo.22747778
