AI 中文总结
本研究提出一种快速边界积分方程求解器，可精确模拟超导量子器件的二维电场密度，速度较传统求解器提升约两个数量级，还应用该求解器研究了共面波导截面的介电参与比特性及刻蚀影响。
AI 中文摘要
二能级系统引起的介电损耗是限制超导量子比特弛豫时间的关键因素，这些损耗主要源于超导器件中纳米级的界面缺陷区域，而器件的平面尺寸通常为微米至毫米级，因此用传统电磁求解器精确模拟这些区域的电场密度会耗费大量资源。本研究展示了一种快速边界积分方程求解器，可实现对这些薄区域电场密度的精确模拟，与传统求解器相比速度提升约两个数量级，在10分钟的求解运行时间内相对误差约为$10^{-7}$。通过利用格林第一恒等式计算参与比而不对电场取平方，该方法受导体拐角处的场奇点影响更小。我们将该求解器应用于基本的无沟槽共面波导截面，结果表明，参与比与介电常数呈线性关系的常见假设在部分界面成立、在另一些界面不成立；具体而言，金属-空气（MA）顶部和拐角强烈遵循该线性关系，但MA侧壁不遵循。随后我们对比了各向同性与各向异性刻蚀的影响，发现MA侧壁和金属-空气-衬底三重结是受影响最显著的区域。目前我们正利用该求解器探索可独特分离不同电介质参与比的几何结构，最终计划将该求解器框架与全三维微波求解器结合，以精确计算超导量子比特中已知损耗源的薄电介质的参与比。
英文摘要
Dielectric loss due to two-level systems is a limiting factor for superconducting qubit relaxation times. These losses arise mostly from nanometer-scale interfacial defect regions in superconducting devices with planar dimensions of microns to millimeters, thus making it resource intensive to accurately simulate the electric field density in these regions with traditional electromagnetic solvers. In this work, we demonstrate a fast boundary integral equation solver that allows precise simulation of electric field density in these thin regions, showing a speedup of around two orders of magnitude over traditional solvers, with relative errors around $10^{-7}$ for a ten-minute solution runtime. By computing participation ratios through Green's first identity without squaring the electric field, our approach is less susceptible to the field singularities near conductor corners. We apply this solver to a basic untrenched coplanar waveguide cross-section, showing that the common assumption of participation ratio linearity with dielectric constant holds well for some interfaces and not others; in particular, while the metal-air (MA) top and corner follow this linear relationship strongly, the MA sidewall does not. We then compare isotropic and anisotropic etching, showing that the MA sidewall and the metal-air-substrate triple junction are the most strongly affected. We are currently leveraging this solver to explore geometries that will uniquely isolate the participation ratios of the different dielectrics. Finally, we are working to combine this solver framework with a full 3D microwave solver to accurately calculate participation ratios for the thin dielectrics that are known sources of loss in superconducting qubits.
