Predicting electric-field noise in ion traps using fluctuation electrodynamics

arXiv:2610.01693 · quant-ph · Submitted 2026-10-01 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: I'm Kai, and with me are Mira and Lev, guest researcher.

Mira: Today's paper: "Predicting electric-field noise in ion traps using fluctuation electrodynamics".

Kai: The gist: This method presents a time-dependent approach to predict electric-field noise arising from fluctuations in dielectric and metallic materials within arbitrary ion trap geometries,

Mira: First, who's behind it and why it matters.

Paper summary: Kai: We've gone through how this paper, "Predicting electric-field noise in ion traps using fluctuation electrodynamics," sets up a way to predict electric-field noise by looking at dissipation in materials like dielectrics and metals. We saw that the authors used the fluctuation-dissipation theorem to link that dissipation to the noise power spectral density.

Mira: And we noted how they found different scaling behaviors for those noises, showing that metal noise is frequency independent while dielectric noise has a dependence on omega times xi. They also pointed out an experimental discrepancy and explained it in terms of the loss tangent of the substrate.

Lev: From a practical standpoint, this method gives researchers a way to estimate heating rates based on material loss properties alone, which is a big help when you're trying to design systems for real hardware. It allows you to see what kind of noise you can expect under different conditions and how geometry affects it.

Kai: So, the main point here is that this paper gives us a quantitative method to predict electric-field noise arising from material fluctuations in ion traps, which is a necessary step for predicting gate errors in quantum computers. It helps us identify weaknesses in materials and fabrication approaches.

Mira: It provides a lower bound on what you can expect with any given trap geometry, giving engineers something concrete to work toward when tailoring those geometries to minimize bulk material heating contributions.

Lev: Ultimately, this paper suggests that incorporating a systematic study where the loss tangent of the ion-trap substrate is measured before fabricating traps should be part of the design process for better noise prediction.

Conclusion: Kai: So, we’ve been looking at how this paper uses fluctuation electrodynamics to predict noise in ion traps—this is all about linking dissipation to noise through material properties like metals and dielectrics.

Mira: Right, and it takes those material losses—the loss tangent for dielectrics or the conductivity for metals—and turns them into a prediction for the actual electric-field noise you’ll see on your ion.

Kai: The authors, they’re using finite element analysis to model this whole process, treating the trap geometry itself and how it interacts with these fluctuating fields.

Lev: From my side, I'm thinking about how accurate these predictions are; if we want to run actual quantum experiments, we need to know if this noise floor is actually low enough for error correction.

Kai: The main thing here is that they give us a way to get a lower bound on the noise you’re going to experience just by knowing what materials you’re using and how big your trap setup is.

Mira: They show that the scaling of this noise depends entirely on whether you're dealing with a metal or a dielectric, because the physics governing those two things is fundamentally different.

Lev: It sounds like it helps us decide which components we need to worry about first in terms of noise reduction efforts for a real machine.

Kai: They also point out that the way heating behaves changes depending on the gap size and how you cut the trap structure, suggesting specific designs to keep things quiet.

Mira: They’re suggesting that for smaller gaps, metal noise takes over, but you can shield those dielectric effects by controlling the width of certain features in your design.

Lev: So it moves us toward designing traps where we can actually control which material's noise is dominating the heating rate.

Kai: It gives us a starting point for iterative design—you test a geometry, you use this method to predict the noise, and then you change something to see if the prediction gets better.

Mira: And they suggest that before you even start building these traps, measuring the loss tangent of your substrate could be a really useful first step.

Lev: If we can accurately predict this noise using material parameters instead of just guessing, it makes building reliable quantum hardware much more predictable for error correction schemes.

Markus Teller, Da An, Alberto M. Alonso, Philip C. Holz, Philipp Schindler, Hartmut H¨affner, Tracy E. Northup

Institut f¨ur Experimentalphysik, Universit¨at Innsbruck · Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology Department of Physics, University of California, Berkeley Department of Physics, Lawrence Berkeley National Laboratory · Alpine Quantum Technologies GmbH

quant-ph

Submitted: 2026-10-01

Updated: 2026-10-01

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 82/100

The gist: The gist: This method presents a time-dependent approach to predict electric-field noise arising from fluctuations in dielectric and metallic materials within arbitrary ion trap geometries, extending

Key concepts

Fluctuation-Dissipation Theorem: This fundamental theorem links the random fluctuations (noise) present in a system to the energy dissipation occurring within it. In this context, it connects the mean dissipated power of an electric field inside a material to the power spectral density of the resulting electric-field noise experienced by a test charge.
Complex Permittivity ($\epsilon_k$): This describes how a material responds to an electric field, accounting for both its ability to store energy (relative permittivity, $\epsilon_r$) and its ability to lose energy (loss tangent, $\tan \delta$). Dielectrics are defined by their complex permittivity ($\epsilon_d$), which includes the loss tangent term.
Heating Rate ($ bar{\dot{\xi}}$): This represents how quickly the motion of a trapped ion is randomized or heated due to electric field noise. The paper relates this heating rate to the noise spectral density, showing it depends on whether the noise source is from a metal (proportional to $1/\omega\xi$) or a dielectric (proportional to $1/\omega^2\xi$).
Loss Tangent ($ an \delta$): The loss tangent quantifies how much energy a material absorbs when subjected to an alternating electric field. It is a key material property used in the model, as it determines the dissipation power ($P_k$) within dielectrics and is used to fit experimental data to validate the simulation.

Terminology

Core — 1× in this paper · explained in 2 episodes
Fidelity — 1× in this paper · explained in 2 episodes
Grounding — 1× in this paper · explained in 3 episodes

Summary

The gist: This method presents a time-dependent approach to predict electric-field noise arising from fluctuations in dielectric and metallic materials within arbitrary ion trap geometries, extending previous static methods to include metals and dielectrics

Methodology for Noise Prediction

The key concept of the method is that the fluctuationdissipation theorem allows us to link noise to dissipation. The calculation involves determining the dissipation of dynamic electric fields inside both dielectrics and metals due to a moving test charge. From this dissipation, the noise experienced by the test charge is found, which is then converted into a lower bound on the electric-field noise.

The elements of the method are illustrated in Fig. 1a. A particle with mass m and charge q is trapped at a distance d above a surface ion trap. The electric field inside each material is damped, corresponding to the mean dissipated power P¯k. The fluctuation-dissipation theorem links P¯k to the power spectral density of the electric-field noise SE,k(ωξ) = 8kBTP¯k (qαξωξ)2, at the particle’s position r = (x, y, z), as can be seen by combining Eq. 3 and Eq. 11 of Ref. [9]. The total electric-field noise is then the sum of SE,m and SE,d based on the assumption that the noise terms are uncorrelated.

Noise Characteristics in Different Materials

The paper highlights distinct behaviors for noise originating from metals versus dielectrics based on their material properties. For a metal, the dissipated power P¯m is expected to be proportional to ω2/ξ (see Eq. 11 of Ref. [9]), implying that the electric-field noise from a metal SE,m is independent of frequency and that the heating rate is proportional to 1/ωξ. In contrast, for a dielectric, P¯d ∝ ωξ (Eq. 20, Ref. [9]), implying that SE,d ∝ 1/ωξ and that the heating rate is proportional to 1/ω2ξ.

Experimental Validation and Material Properties

The model was applied to a surface ion trap with an electrically floating electrode, where the contribution from dielectrics was found to be dominant. The experimental heating rates were compared to simulations, and the discrepancy between experiment and simulation was attributed to a difference between the loss tangent of the trap substrate used in the experiments and tan δref. By fitting the model using this free parameter, a fit yielded tan δfit = 4.0(1)·10−3, demonstrating agreement with observed distance scaling. Furthermore, when comparing results with an alternate version where the floating electrode is set to have infinite conductance, the contribution of less than 2.2 quanta/s was found, six orders of magnitude smaller than n¯˙z, confirming that n¯˙z is dominated by noise from the dielectric.

Design Implications for Trap Geometry

The study applied the noise-simulation method to ion-trap design to minimize total electric-field noise and examine the relative importance of metal versus dielectric noise. The analysis showed that for small gaps a ≤ 15 µm, heating due to the metal dominates. Conversely, the important contribution of dielectric noise is shielded by an undercut width b, with b = 10 µm being the threshold below which the heating rate is dominated by dielectrics. The trench depth c should be greater than or equal to a (c ≥ a) to minimize the heating rate. The simulations also showed that dielectric noise dominates along the x and y axes for narrower trench widths, pointing to the importance of simulating heating rates along all three axes.

Conclusion and Future Work

The method successfully introduces a FEA approach that accounts for both dielectrics and conducting materials, allowing quantitative predictions of electric-field noise and ion heating rate in a given trap. The results allow researchers to identify strengths and weaknesses in existing ion traps, including materials choice, fabrication approaches, floating electrodes, and cleaning methods. The simulated values for electric-field noise provide a lower bound on what is achievable with a given ion-trap geometry. This method can be applied as part of an iterative design process to tailor ion-trap geometries such that the bulk materials contribution to particle heating is below a target value. The authors propose a systematic study where the loss tangent of an ion-trap substrate should be measured prior to trap fabrication.

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The paper is titled Predicting electric-field noise in ion traps using fluctuation electrodynamics and it matters because it provides a method to predict the electric-field noise arising from fluctuations in the bulk of dielectric and metallic materials, which is crucial for predicting gate errors in trapped-ion quantum computers.

How it works

The core mechanism links noise to dissipation through the fluctuationdissipation theorem. The calculation involves determining the dissipation of dynamic electric fields inside both dielectrics and metals due to a moving test charge.

The process involves several steps:

**- Define materials by their complex permittivity εk, where m refers to the metal and d to the dielectric. The complex permittivity of the dielectric is defined as εd = ε0εr(1 + itan δ), where ε0 is the vacuum permittivity, εr the relative permittivity, and tan δ the loss tangent. The metal layer has conductivity σ, and its complex permittivity can be approximated as εm = iσ/ωξ [9]. The electric field inside each material is damped, corresponding to the mean dissipated power P¯k [9]. The fluctuation-dissipation theorem links P¯k to the power spectral density of the electric-field noise SE,k(ωξ) = 8kBTP¯k (qαξωξ)2, at the particle’s position r = (x, y, z), as can be seen by combining Eq. 3 and Eq. 11 of Ref. [9]. The electric-field noise can thus be determined from the dissipated power in the materials, which we calculate using finite-element analysis (FEA) software [16]. The particle’s motional amplitude is much smaller than d, so it is modeled as an electric point dipole with dipole moment vector pc,ξ = qωξαξuˆξ (2) pointing in the direction of the unit vector uˆξ ∈ xˆ, yˆ, zˆ. The total electric-field noise is then the sum of SE,m and SE,d based on the assumption that the noise terms are uncorrelated. The heating rate n¯˙ξ is related to the noise spectral density by n¯˙ξ(ωξ) = q2/4mħωξ SE(ωξ), (3). The metal contribution SE,m is expected to be independent of frequency, implying that the heating rate is proportional to 1/ωξ. For a dielectric, P¯d ∝ ωξ (Eq. 20, Ref. [9]), implying that SE,d ∝ 1/ωξ and that the heating rate is proportional to 1/ω2ξ. The total electric-field noise is then the sum of SE,m and SE,d based on the assumption that the noise terms are uncorrelated.

Improvements for AI systems

The improved system can perform quantitative prediction of electric-field noise in ion traps using a method that takes into account not only dielectrics but also conducting materials. This allows for quantitative predictions of the electric-field noise and ion heating rate in a given trap, enabling researchers to identify strengths and weaknesses in existing ion traps, including materials choice, fabrication approaches, floating electrodes, and cleaning methods.
The system can be used for active trap design optimization by parameterizing geometry (trench width a, undercut b, depth c) and predicting the heating rate. This enables researchers to determine parameter regimes in which the trap design fails to shield the ion sufficiently from dielectric components, specifically identifying when the noise is metal-dominated and when it is dielectric-dominated.
The improved system can provide actionable design guidance by quantifying shielding effectiveness. For instance, it can determine that for a given geometry, b = 10 µm is the threshold below which the heating rate is dominated by dielectrics, suggesting that trench depths c ≥ a are required to minimize the heating rate.

Abstract

Electric-field noise in microfabricated surface ion traps contributes to gate errors in trapped-ion quantum computers, but this noise has been challenging to predict. Here, we present a method to predict the electric-field noise arising from fluctuations in the bulk of dielectric and metallic materials. The method is valid for arbitrary trap geometries, and the only relevant material property is energy loss. We apply it to an ion trap with an electrically floating electrode and find the contribution from dielectrics to be dominant. Our model predicts the observed noise for this trap within a factor of four. In addition, we apply our model to typical surface trap designs and analyze how the electrode structures shield the noise.