SesQ: A Surface Electrostatic Simulator for Precise Energy Participation Ratio Simulation in Superconducting Qubits

TL;DR

SesQ is a surface integral equation simulator that accurately and efficiently computes energy participation ratios in superconducting qubits, overcoming FEM limitations and enabling rapid design optimization.

Contribution

We introduce SesQ, a surface-based electromagnetic simulator that significantly improves the speed and accuracy of EPR calculations in superconducting qubits compared to traditional FEM methods.

Findings

SesQ accelerates capacitance extraction by about 100 times.

SesQ provides more precise EPR calculations than FEM.

FEM underestimates EPR in practical transmon qubit simulations.

Abstract

An accurate and efficient numerical electromagnetic model for superconducting qubits is essential for characterizing and minimizing design-dependent dielectric losses. The energy participation ratio (EPR) is the commonly adopted metric used to evaluate these losses, but its calculation presents a severe multiscale computational challenge. Conventional finite element method (FEM) requires 3D volumetric meshing, leading to prohibitive computational costs and memory requirements when attempting to capture singular electric fields at nanometer-thin material interfaces. To address this bottleneck, we propose SesQ, a surface integral equation simulator tailored for the precise simulation of the EPR. By applying discretization on 2D surfaces, deriving a semi-analytical multilayer Green's function, and employing a dedicated non-conformal boundary mesh refinement scheme, SesQ accurately resolves singular edge fields without an explosive growth in the number of unknowns. Validations with analytically solvable models demonstrate that SesQ accelerates capacitance extraction by roughly two orders of magnitude compared to commercial FEM tools. While achieving comparable accuracy for capacitance extraction, SesQ delivers superior precision for EPR calculation. Simulations of practical transmon qubits further reveal that FEM approaches tend to significantly underestimate the EPR. Finally, the high efficiency of SesQ enables rapid iteration in the layout optimization, as demonstrated by minimizing the EPR of the qubit pattern, establishing the simulator as a powerful tool for the automated design of low-loss superconducting quantum circuits.