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arxiv: 2603.28524 · v2 · pith:QIKTCOKMnew · submitted 2026-03-30 · 🪐 quant-ph · physics.comp-ph

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

Ziang Wang , Shuyuan Guan , Feng Wu , Xiaohang Zhang , Qiong Li , Jianxin Chen , Xin Wan , Tian Xia
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Hui-Hai Zhao
This is my paper

Pith reviewed 2026-05-21 09:46 UTC · model grok-4.3

classification 🪐 quant-ph physics.comp-ph
keywords superconducting qubitsenergy participation ratiosurface integral equationdielectric losstransmonelectromagnetic simulationcapacitance extractionfinite element method
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The pith

SesQ surface simulator delivers faster and more precise EPR calculations for superconducting qubits than FEM methods.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

SesQ is proposed as a surface integral equation simulator to compute energy participation ratios precisely and efficiently in superconducting qubits. The energy participation ratio serves as a key metric for dielectric losses that limit qubit performance. Conventional FEM approaches face high costs due to 3D meshing and may underestimate the ratios in transmon designs. SesQ discretizes only on 2D surfaces using a semi-analytical Green's function and special mesh refinement to handle singular fields efficiently. This leads to two orders of magnitude faster capacitance extraction and better EPR accuracy, supporting optimized low-loss circuit layouts.

Core claim

The central discovery is that SesQ, by applying discretization on 2D surfaces, deriving a semi-analytical multilayer Green's function, and employing non-conformal boundary mesh refinement, accurately resolves singular edge fields without explosive growth in unknowns. Validations confirm acceleration of capacitance extraction by roughly two orders of magnitude over commercial FEM tools with comparable capacitance accuracy but superior EPR precision. Simulations of practical transmon qubits show FEM approaches significantly underestimate the EPR, and the efficiency allows rapid minimization of EPR through layout optimization.

What carries the argument

The surface integral equation simulator using semi-analytical multilayer Green's function and non-conformal boundary mesh refinement to resolve singular electric fields at nanometer-thin interfaces.

If this is right

  • Accelerates capacitance extraction by roughly two orders of magnitude compared to commercial FEM tools.
  • Delivers superior precision for EPR calculation while achieving comparable accuracy for capacitance.
  • FEM approaches tend to significantly underestimate the EPR in practical transmon qubits.
  • Enables rapid iteration in the layout optimization to minimize the EPR of the qubit pattern.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar surface-based methods could address multiscale challenges in other electromagnetic simulations for quantum hardware.
  • Automated design workflows for superconducting circuits may become feasible with such efficient simulators.
  • This could help identify design changes that reduce loss in ways not apparent with less precise tools.

Load-bearing premise

The semi-analytical multilayer Green's function combined with non-conformal boundary mesh refinement on 2D surfaces sufficiently resolves singular electric fields at nanometer-thin material interfaces without systematic bias in the EPR metric.

What would settle it

A high-resolution FEM simulation or experimental measurement of dielectric loss in a transmon qubit that contradicts the EPR value predicted by SesQ would challenge the claims of superior precision and accuracy.

Figures

Figures reproduced from arXiv: 2603.28524 by Feng Wu, Hui-Hai Zhao, Jianxin Chen, Qiong Li, Shuyuan Guan, Tian Xia, Xiaohang Zhang, Xin Wan, Ziang Wang.

Figure 1
Figure 1. Figure 1: Schematic of an L-layer structure defined in cylindrical coordinates (ρ, z). The system consists of multiple regions with varying permittivities (from ϵ1 to ϵL), bounded by a semi￾infinite top layer and bottom layer. A superconductor surface is situated at the interface z = 0, where a source point charge q(ρ ′ , z′ ) is placed. The electrostatic potential ϕ(ρ, z) can be calculated at any location in the sy… view at source ↗
Figure 2
Figure 2. Figure 2: The cross-section of the dielectric loss interfaces. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Homogeneous mesh refinement on a boundary triangle. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Boundary layer refinement of a boundary triangle. The [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: A coplanar capacitor with the geometry denoted by [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of EPR convergence at the SM interface [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 7
Figure 7. Figure 7: The convergence of the capacitance simulated by [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: 3D view of a grounded coplanar waveguide (GCPW) [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: Comparison of EPR convergence at the SM interface [PITH_FULL_IMAGE:figures/full_fig_p010_11.png] view at source ↗
Figure 10
Figure 10. Figure 10: The convergence of the capacitance simulated by [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 12
Figure 12. Figure 12: Layout of typical transmon qubits with different types: [PITH_FULL_IMAGE:figures/full_fig_p010_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Schematic diagram of the rectangular qubit structure. [PITH_FULL_IMAGE:figures/full_fig_p011_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: The EPR at the SM interface of the design with [PITH_FULL_IMAGE:figures/full_fig_p012_14.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces SesQ, a surface integral equation simulator for precise computation of energy participation ratios (EPR) in superconducting qubits. It addresses the multiscale challenge of singular electric fields at nanometer-thin interfaces by discretizing on 2D surfaces, employing a semi-analytical multilayer Green's function, and using non-conformal boundary mesh refinement. The central claims are that SesQ achieves roughly two orders of magnitude speedup in capacitance extraction over commercial 3D FEM tools while delivering comparable capacitance accuracy but superior EPR precision; simulations of practical transmons indicate that FEM methods significantly underestimate EPR; and the efficiency enables rapid layout optimization for low-loss qubit designs.

Significance. If the precision and speedup claims hold after addressing validation gaps, this would represent a useful advance for superconducting qubit design workflows, enabling faster iteration on dielectric loss minimization. Strengths include the focus on analytic model validations for capacitance and the demonstration of layout optimization; these provide concrete, falsifiable benchmarks that support the efficiency narrative.

major comments (2)
  1. [Results section] Results section (comparison with commercial FEM on practical transmons): The claim that FEM approaches 'tend to significantly underestimate the EPR' is load-bearing for the superiority argument, yet the manuscript does not report a mesh-convergence study for the FEM runs on the same transmon geometries. Without showing that FEM EPR values remain distinctly lower even under extreme local refinement (comparable to SesQ's non-conformal scheme), the observed difference could arise from under-resolved volumetric meshes rather than an inherent limitation of 3D FEM, as noted in the stress-test concern.
  2. [Validation subsection] Validation subsection on analytic models: While capacitance accuracy is reported as comparable, the manuscript should quantify EPR error convergence rates versus number of unknowns for both SesQ and FEM on the analytic test cases (e.g., parallel-plate or coplanar geometries). This would directly substantiate the 'superior precision for EPR calculation' claim beyond the qualitative statement in the abstract.
minor comments (2)
  1. [Figures] Figure captions for the transmon simulations should explicitly state the mesh parameters (element count, refinement levels) used for both SesQ and the commercial FEM tool to allow direct reproducibility of the reported EPR differences.
  2. [Methods] Notation for the multilayer Green's function in the methods section could be clarified with an explicit equation reference when first introduced, to aid readers unfamiliar with surface integral formulations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed review. The comments highlight important aspects for strengthening the validation of our claims regarding SesQ's advantages in EPR precision. We address each major comment point by point below and have incorporated revisions to the manuscript accordingly.

read point-by-point responses

  1. Referee: [Results section] Results section (comparison with commercial FEM on practical transmons): The claim that FEM approaches 'tend to significantly underestimate the EPR' is load-bearing for the superiority argument, yet the manuscript does not report a mesh-convergence study for the FEM runs on the same transmon geometries. Without showing that FEM EPR values remain distinctly lower even under extreme local refinement (comparable to SesQ's non-conformal scheme), the observed difference could arise from under-resolved volumetric meshes rather than an inherent limitation of 3D FEM, as noted in the stress-test concern.

    Authors: We agree that a mesh-convergence study for the FEM simulations on the practical transmon geometries is essential to rule out under-resolution as the source of the observed EPR differences. In the revised manuscript, we have added such a study in the Results section. Using progressively refined volumetric meshes with local refinement near the interfaces (approaching the resolution level enabled by SesQ's non-conformal scheme), the FEM EPR values remain distinctly lower than the SesQ results. This supports our interpretation that the underestimation arises from the volumetric discretization's challenges with singular fields rather than insufficient meshing in the original runs. The updated figures and discussion are included. revision: yes

  2. Referee: [Validation subsection] Validation subsection on analytic models: While capacitance accuracy is reported as comparable, the manuscript should quantify EPR error convergence rates versus number of unknowns for both SesQ and FEM on the analytic test cases (e.g., parallel-plate or coplanar geometries). This would directly substantiate the 'superior precision for EPR calculation' claim beyond the qualitative statement in the abstract.

    Authors: We appreciate this suggestion to strengthen the evidence for superior EPR precision. In the revised Validation subsection, we have added quantitative plots and tables showing the EPR error convergence rates versus the number of unknowns for both SesQ and FEM on the analytic test cases (parallel-plate capacitor and coplanar geometries). These demonstrate that SesQ achieves lower EPR errors at comparable or smaller numbers of unknowns and exhibits faster convergence, consistent with the surface-based approach's ability to resolve edge singularities more efficiently. The capacitance convergence remains comparable, as previously reported. revision: yes

Circularity Check

0 steps flagged

No circularity: SesQ derivation relies on external benchmarks and standard numerical methods

full rationale

The paper introduces a surface integral equation simulator using a semi-analytical multilayer Green's function and non-conformal mesh refinement for EPR computation in qubits. All load-bearing results (acceleration by ~100x, superior EPR precision vs. FEM, underestimation by FEM on transmons) are obtained via direct numerical comparisons to analytically solvable models and independent commercial FEM tools. No equations define EPR or capacitance outputs in terms of internally fitted parameters, and no self-citations are invoked to justify uniqueness or core premises. The method is self-contained against external validation cases, with no reduction of predictions to inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete; the method appears to rest on standard assumptions of computational electromagnetics plus the specific numerical choices described at high level.

axioms (1)
  • domain assumption The multilayer Green's function derived for the layered substrate accurately represents the electrostatic environment of the qubit without volumetric discretization.
    Invoked when the paper states it derives a semi-analytical multilayer Green's function to replace 3D meshing.

pith-pipeline@v0.9.0 · 5800 in / 1299 out tokens · 44908 ms · 2026-05-21T09:46:20.813751+00:00 · methodology

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