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arxiv: 2606.25595 · v1 · pith:JTXT2AB6new · submitted 2026-06-24 · 💻 cs.CE · cs.DC

Optimizing Semiconductor Device Simulations through Low-Precision Arithmetic

Alexander Maeder , Denghui Lu , Nicolas Vetsch , Vincent Maillou , Anders Winka , Jiang Cao , Mauro Dossena , Alexandros Nikolaos Ziogas
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Mathieu Luisier
This is my paper

Pith reviewed 2026-06-25 20:22 UTC · model grok-4.3

classification 💻 cs.CE cs.DC
keywords low-precision arithmeticnumerical stabilityquantum transportsemiconductor simulationshigh-performance computingreduced precisiondevice modeling
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The pith

Low-precision arithmetic enables 51% higher throughput in quantum transport simulations using 40% fewer resources.

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

The paper investigates the potential of reduced-precision arithmetic in a quantum transport solver for semiconductor device simulations. Through analysis of numerical stability on three benchmark structures, it identifies conditions under which lower precision formats can be used without significant accuracy loss. These findings are applied to a larger realistic system to demonstrate substantial improvements in computational efficiency.

Core claim

By performing a detailed numerical stability analysis when moving from high- to low-precision formats, the application reveals opportunities for performance gains. Applying these insights to a larger system achieves up to 51% higher throughput while maintaining accurate results on 40% fewer HPC resources than the standard high-precision reference.

What carries the argument

Numerical stability analysis of the solver's computations across different precision formats, identifying safe reductions that preserve result accuracy.

If this is right

  • Quantum transport simulations can achieve higher throughput by using low-precision formats where stability allows.
  • High-performance computing resources can be reduced by 40% for equivalent accurate results.
  • Modern GPU architectures with low-precision units become more accessible for this type of scientific computing.
  • The approach generalizes the benefits of precision reduction to other similar applications after benchmark validation.

Where Pith is reading between the lines

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

  • Other HPC codes with similar computational patterns might benefit from analogous stability checks to adopt low-precision arithmetic.
  • Future hardware could be optimized for mixed-precision workloads based on application-specific insights like these.
  • Testing on additional device structures could help map out the boundaries of safe precision reduction more broadly.

Load-bearing premise

The numerical stability properties observed in the three representative benchmark structures generalize to the larger, more realistic system without introducing unacceptable accuracy degradation.

What would settle it

Executing the larger realistic system simulation with the selected low-precision formats and finding that the results deviate unacceptably from the high-precision reference or produce errors.

Figures

Figures reproduced from arXiv: 2606.25595 by Alexander Maeder, Alexandros Nikolaos Ziogas, Anders Winka, Denghui Lu, Jiang Cao, Mathieu Luisier, Mauro Dossena, Nicolas Vetsch, Vincent Maillou.

Figure 1
Figure 1. Figure 1: To enable execution of the full solver with a relatively [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Range and precision studies of DFT+NEGF+scGW for the (a) CNT, (b) MoS [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Condition numbers of (a) the Green’s function system [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Precision study of the quadratic solve ( [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Relative error in the electronic current flowing through [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Same as Fig. 5, but all variables are stored in FP64, and all ZGEMM operations are performed with the Ozaki scheme II. [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: (a) Convergence of the electronic current with respect to [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
read the original abstract

Architectural changes in GPUs, especially the promotion of low-precision computational units, pose significant challenges to traditional, FP64-based high-performance computing (HPC) applications, while also presenting opportunities. Adopting reduced-precision data formats is a promising avenue to exploit the increased throughput capabilities. However, straightforward data conversions may lead to degraded accuracy or even erroneous results. For a given application, only an in-depth analysis of its numerical stability can reveal the potential of low-precision arithmetic. In this work, we consider the open-source quatrex package, a quantum transport solver capable of breaking the sustained FP64 Eflop/s barrier, to illustrate trade-offs between accuracy losses and computational speed-ups when moving from high- to low-precision formats. We use three representative benchmark structures to explore the application's numerical properties. Applying the gained insights to a larger, more realistic system, we achieve up to 51% higher throughput while maintaining accurate results, on 40% fewer HPC resources than the FP64 reference.

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

1 major / 0 minor

Summary. The manuscript examines the potential of low-precision arithmetic in the open-source quatrex quantum transport solver for semiconductor device simulations. It analyzes numerical stability trade-offs using three representative benchmark structures and applies the resulting insights to a larger, more realistic system, claiming up to 51% higher throughput while maintaining accurate results on 40% fewer HPC resources than the FP64 reference.

Significance. If the generalization of numerical stability holds with quantified error bounds, the work would provide a concrete demonstration of performance gains from reduced-precision formats in a production-grade quantum transport code that already exceeds FP64 Eflop/s. The empirical focus on an open-source package and the move from controlled benchmarks to a realistic device constitute a practical contribution to HPC optimization in computational electronics.

major comments (1)
  1. [Abstract] Abstract: the central claim of 'maintaining accurate results' on the larger system with 51% throughput improvement rests on the unverified transfer of stability properties from the three benchmark structures. No quantitative error metrics (relative error in current, carrier density, or transmission), no tolerance thresholds, and no explicit comparison of larger-system errors against benchmark errors are supplied, preventing assessment of whether accuracy degradation remains acceptable.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address the single major comment below and will revise the manuscript to strengthen the presentation of quantitative accuracy metrics.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim of 'maintaining accurate results' on the larger system with 51% throughput improvement rests on the unverified transfer of stability properties from the three benchmark structures. No quantitative error metrics (relative error in current, carrier density, or transmission), no tolerance thresholds, and no explicit comparison of larger-system errors against benchmark errors are supplied, preventing assessment of whether accuracy degradation remains acceptable.

    Authors: We agree that the abstract would be strengthened by explicit quantitative error metrics and a direct comparison to the benchmark results. The three benchmark structures were selected to capture the dominant numerical sensitivities of the quantum transport solver (potential barriers, scattering rates, and device geometry variations). The realistic system employs identical numerical kernels and material models, providing the basis for transferring stability observations; however, we acknowledge that this transfer should be quantified rather than asserted. In the revised version we will update the abstract to report the relative errors in current, carrier density, and transmission for the larger system, state the tolerance thresholds applied, and include a sentence comparing these error magnitudes to those measured on the benchmarks. These values are already computed in our internal analysis and will be added without altering any results or conclusions. revision: yes

Circularity Check

0 steps flagged

No circularity; empirical benchmarks and application are independent of inputs by construction.

full rationale

The paper reports direct empirical measurements of numerical stability on three benchmark structures, followed by application of those observations to a larger system. No derivation, equation, or claim reduces to its own inputs by construction, no fitted parameter is relabeled as a prediction, and no self-citation chain supplies a load-bearing uniqueness result. The central throughput claim is presented as an observed outcome of the larger-system run rather than a logical consequence of the benchmark data alone.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities are identifiable from the abstract; the contribution rests on empirical numerical stability testing of an existing solver.

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discussion (0)

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