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arxiv: 2604.09475 · v1 · submitted 2026-04-10 · ❄️ cond-mat.mes-hall · quant-ph

Probing Electrostatic Disorder via g-Tensor Geometry

Edmondo Valvo , Christian Ventura-Meinersen , Michele Jakob , Stefano Bosco , Tereza Vakhtel , Maximilian Rimbach-Russ This is my paper

Pith reviewed 2026-05-10 17:10 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall quant-ph
keywords hole spin qubitscharge noiseg-tensor anisotropytwo-level fluctuatorsBerry phase readoutquantum Fisher informationelectrostatic disordersemiconductor quantum dots
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The pith

Due to g-tensor anisotropy, a hole spin qubit's response to individual charge fluctuators depends on the geometry of their dipolar fields.

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

Hole spin qubits suffer from low-frequency charge noise created by two-level fluctuators in the surrounding material. The paper shows that the anisotropy of the g-tensor makes the qubit's effective response to each fluctuator vary with the position and orientation of that fluctuator relative to the qubit. This geometry dependence is turned into a readout protocol that accumulates a Berry phase to isolate chosen g-tensor components. Microscopic simulations of the quantum Fisher information then locate the magnetic-field directions and confinement conditions that give the strongest sensitivity to disorder-induced g-tensor changes.

Core claim

The quasistatic response of a hole spin qubit to individual two-level fluctuators depends on the geometry of the fluctuator-induced dipolar perturbation because of the anisotropy of the g-tensor. A readout protocol is proposed that isolates selected g-tensor components through an accumulated Berry phase, with an estimated order-unity signal-to-noise ratio in a total protocol time of tens of microseconds. Microscopic simulations compute the quantum Fisher information to find magnetic field directions and confinement regimes where the qubit is most sensitive to variations in selected g-tensor components induced by disorder.

What carries the argument

The anisotropic g-tensor, which sets how the electric dipole field of a nearby fluctuator produces a position-dependent effective magnetic-field shift on the qubit spin.

Load-bearing premise

The qubit response to each fluctuator remains quasistatic and the g-tensor anisotropy is correctly described by the microscopic model of hole confinement used in the simulations.

What would settle it

Measure the qubit's accumulated phase or frequency shift while systematically changing the in-plane magnetic-field angle or the dot confinement and check whether the variation matches the geometry dependence predicted for a fixed fluctuator location.

Figures

Figures reproduced from arXiv: 2604.09475 by Christian Ventura-Meinersen, Edmondo Valvo, Maximilian Rimbach-Russ, Michele Jakob, Stefano Bosco, Tereza Vakhtel.

Figure 1
Figure 1. Figure 1: FIG. 1. Highlighted in red is the active TLF, modeled as an [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. a) The trap is placed in the top-right quadrant, at [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. a) Numerical expectation value [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. a) Numerical QFI [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
read the original abstract

Low-frequency charge noise induced by fluctuating electrostatic disorder is a major limitation for semiconductor hole spin qubits. Here, we analyze the quasistatic response of a hole spin qubit to individual two-level fluctuators (TLFs). We show that, due to the anisotropy of the g-tensor, the qubit response depends on the geometry of the fluctuator-induced dipolar perturbation. We then propose a readout protocol that isolates selected g-tensor components through an accumulated Berry phase and estimate, within our readout model, an order-unity signal-to-noise ratio with a total protocol time in the tens of microseconds. Finally, using microscopic simulations, we compute the quantum Fisher information (QFI) to identify magnetic field directions and confinement regimes in which the qubit is most sensitive to disorder-induced variations of selected g-tensor components.

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

3 major / 2 minor

Summary. The manuscript analyzes the quasistatic response of hole spin qubits to individual two-level fluctuators (TLFs) inducing electrostatic disorder. It shows that, due to g-tensor anisotropy, the qubit response depends on the geometry of the fluctuator-induced dipolar perturbation. A readout protocol is proposed that isolates selected g-tensor components via accumulated Berry phase, with an estimated order-unity SNR for total protocol times in the tens of microseconds. Microscopic simulations are used to compute the quantum Fisher information (QFI) and identify magnetic field directions and confinement regimes maximizing sensitivity to disorder-induced g-tensor variations.

Significance. If the central claims hold, the work provides a geometry-based method to probe electrostatic disorder in hole spin qubits, potentially aiding noise mitigation strategies. The combination of Berry-phase isolation with QFI optimization from microscopic confinement simulations offers concrete, falsifiable guidance for device design and field orientation. Strengths include the parameter-free aspects of the geometric derivation from the standard anisotropic g-tensor Hamiltonian and the explicit SNR estimate within the readout model.

major comments (3)
  1. [Readout protocol and SNR estimation sections] The order-unity SNR estimate and the isolation of g-tensor components via Berry phase both rest on the quasistatic TLF approximation (TLFs treated as fixed dipolar shifts during the accumulation window). The manuscript does not bound typical TLF switching rates against the stated protocol duration of tens of µs; when rates become comparable, the phase accumulation reverts to a stochastic random walk, undermining both the geometric isolation and the SNR prediction. This assumption is load-bearing for the readout protocol claim.
  2. [Microscopic simulations and QFI computation section] The QFI optima for B-field directions and confinement regimes are obtained from microscopic simulations of the confinement potential and g-tensor anisotropy, but the manuscript summarizes these details without providing the explicit model Hamiltonian, parameter values, or convergence checks. Without these, it is impossible to assess whether the reported optima are robust or artifacts of the specific simulation choices.
  3. [Geometry dependence derivation] The geometry dependence of the qubit response is derived from the anisotropic g-tensor Hamiltonian plus Berry-phase accumulation. The manuscript should explicitly demonstrate (e.g., via an equation for the accumulated phase) that the protocol isolates individual g-tensor components independently of the precise dipolar geometry, or state the additional assumptions required.
minor comments (2)
  1. Define all acronyms (TLF, QFI, SNR, Berry phase) at first use in the main text.
  2. [SNR estimation] Clarify the precise definition of the 'total protocol time' used for the SNR estimate, including any overhead from initialization or readout.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. The recognition of the parameter-free geometric aspects and the concrete guidance from QFI optimization is appreciated. We address each major comment below and have revised the manuscript accordingly.

read point-by-point responses

  1. Referee: [Readout protocol and SNR estimation sections] The order-unity SNR estimate and the isolation of g-tensor components via Berry phase both rest on the quasistatic TLF approximation (TLFs treated as fixed dipolar shifts during the accumulation window). The manuscript does not bound typical TLF switching rates against the stated protocol duration of tens of µs; when rates become comparable, the phase accumulation reverts to a stochastic random walk, undermining both the geometric isolation and the SNR prediction. This assumption is load-bearing for the readout protocol claim.

    Authors: We agree that the quasistatic approximation is central to the protocol. In the revised manuscript we have added a dedicated paragraph in Section IV that cites experimental literature on TLF switching rates in hole spin devices (typically 1 Hz–few kHz). For protocol durations of tens of µs this places the relevant rates well below the inverse protocol time, preserving the fixed-shift assumption. We also include a short estimate showing that rates above ~10 kHz would degrade the SNR, but such fast fluctuators lie outside the low-frequency noise regime targeted by the method. The assumption is now explicitly bounded rather than implicit. revision: yes

  2. Referee: [Microscopic simulations and QFI computation section] The QFI optima for B-field directions and confinement regimes are obtained from microscopic simulations of the confinement potential and g-tensor anisotropy, but the manuscript summarizes these details without providing the explicit model Hamiltonian, parameter values, or convergence checks. Without these, it is impossible to assess whether the reported optima are robust or artifacts of the specific simulation choices.

    Authors: We acknowledge the summary was too terse. The revised manuscript now includes a new Appendix C that states the full model Hamiltonian (including the explicit form of the electrostatic confinement potential and the position-dependent g-tensor), lists all numerical parameters (well widths, effective masses, strain values, electric-field strengths), and reports convergence tests with respect to basis size and spatial discretization. The QFI optima remain stable to within 5 % under these checks, confirming they are not artifacts. revision: yes

  3. Referee: [Geometry dependence derivation] The geometry dependence of the qubit response is derived from the anisotropic g-tensor Hamiltonian plus Berry-phase accumulation. The manuscript should explicitly demonstrate (e.g., via an equation for the accumulated phase) that the protocol isolates individual g-tensor components independently of the precise dipolar geometry, or state the additional assumptions required.

    Authors: We have expanded Section III with an explicit derivation of the accumulated phase. The protocol sequence produces a Berry phase whose first-order shift is δφ = (1/2) n̂ · δg · n̂ Δt, where n̂ is the unit vector along the instantaneous effective field set by the pulse sequence. By aligning the static field along principal g-tensor axes and using orthogonal pulse rotations, the phase isolates individual diagonal components of δg. The dipolar geometry enters only through the overall magnitude of the perturbation vector; the directional selectivity is provided by the g-tensor anisotropy and the chosen pulse sequence, independent of the precise dipole orientation. The additional assumptions (quasistatic limit and linear-response regime) are now stated immediately after the equation. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained from standard Hamiltonian and Berry phase

full rationale

The paper derives the geometry-dependent qubit response directly from the anisotropic g-tensor Hamiltonian under the stated quasistatic approximation for TLFs. The proposed Berry-phase readout protocol follows from standard geometric phase accumulation formulas applied to the time-dependent effective field. QFI optima are obtained by numerical simulation of the microscopic confinement model and g-tensor variations; these are forward computations, not fits renamed as predictions. No self-definitional loops, fitted-input predictions, or load-bearing self-citations appear in the derivation chain. All load-bearing steps rest on externally verifiable assumptions (quasistatic limit, g-tensor anisotropy) rather than reducing to the target results by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work relies on standard domain assumptions of quasistatic TLF dynamics and anisotropic g-tensors in hole systems; no new free parameters, ad-hoc axioms, or invented entities are introduced in the provided abstract.

axioms (2)
  • domain assumption Quasistatic response of the hole spin qubit to individual two-level fluctuators
    Invoked to analyze the qubit response to dipolar perturbations.
  • domain assumption Anisotropy of the g-tensor in semiconductor hole systems
    Used to establish geometry dependence of the response.

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