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arxiv: 2604.24716 · v2 · submitted 2026-04-27 · ❄️ cond-mat.mes-hall · quant-ph

Gate-dependent offset charge shifts and anharmonicity in gatemon qubits in the weak tunneling regime

Utkan G\"ung\"ord\"u , Rusko Ruskov , Silas Hoffman , Kyle Serniak , Andrew J. Kerman , Charles Tahan This is my paper

Pith reviewed 2026-05-08 01:56 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall quant-ph
keywords gatemon qubitsAndreev bound statescharge offsetsanharmonicityweak tunneling regimequantum dot junctionsuperconducting qubits
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The pith

An effective Hamiltonian for gatemon qubits predicts gate-dependent charge offsets and capacitance renormalization that shift the energy spectrum and anharmonicity.

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

This paper applies a many-body treatment to the superconductor-quantum dot-superconductor junction in gatemon qubits under weak tunneling conditions. The resulting gate-voltage-dependent Hamiltonian incorporates phase quantization self-consistently and reveals two main effects: renormalization of the junction's effective capacitance and the emergence of charge offsets that depend on both gate voltage and electron occupation when tunneling is asymmetric. These features alter the qubit's transition frequencies and its anharmonicity through the interplay of the two Andreev bound states. The work connects the predictions to simpler models of gatemons and proposes a measurement protocol to detect the charge offsets experimentally.

Core claim

The gate voltage-dependent Hamiltonian derived from the many-body treatment of the S-QD-S junction predicts renormalization of the effective capacitance and the presence of gate-voltage and occupation-dependent charge offsets in junctions with tunneling asymmetry. These effects produce observable modifications to the qubit energy spectrum and anharmonicity as functions of dot-gate voltages and junction transparencies.

What carries the argument

The effective gate voltage-dependent Hamiltonian that self-consistently incorporates phase quantization and describes the dynamics of the two Andreev bound states.

If this is right

  • The qubit transition frequencies shift with gate voltage due to the occupation-dependent charge offsets.
  • Anharmonicity varies with changes in dot-gate voltages and junction transparencies through the interplay of Andreev branches.
  • Simplified models of gatemons can be related to the full treatment to identify when approximations hold.
  • The proposed protocol provides a concrete way to measure the predicted charge offsets in experiment.

Where Pith is reading between the lines

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

  • These offsets might serve as an extra tuning parameter for calibrating gatemon qubits in larger circuits.
  • The same Hamiltonian approach could be tested in related hybrid devices that combine superconductors with quantum dots.
  • Extending the analysis beyond weak tunneling would check whether the charge-offset effects persist or change character.

Load-bearing premise

The many-body-derived effective Hamiltonian from the prior analysis remains accurate and applicable in the weak tunneling regime studied here.

What would settle it

A measurement of the gatemon qubit spectrum across a range of dot-gate voltages that finds no occupation-dependent charge offsets or no capacitance renormalization would contradict the predictions.

Figures

Figures reproduced from arXiv: 2604.24716 by Andrew J. Kerman, Charles Tahan, Kyle Serniak, Rusko Ruskov, Silas Hoffman, Utkan G\"ung\"ord\"u.

Figure 1
Figure 1. Figure 1: FIG. 1. Effective Josephson energy view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Qubit energy oscillations, view at source ↗
Figure 3
Figure 3. Figure 3: (c)): |ψ˜ n(ϕ)⟩ ≈ |ψ˜ n,lower(ϕ)⟩ ≡  0 ψ˜lower n (ϕ)  . (34) This approximation is equivalent to replacing σz → −1, σx,y → 0 in the rotated Hamiltonian, which reduces the full Hamiltonian, Eq. (1) into a scalar Hamiltonian (equivalent to a Cooper pair box) with a charging energy HˆC,eff, Eq. (31), and a potential term ≈ −EJ,eff cos ϕ, Eq. (10). The additional effective charge offset can be obtained from … view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The effective charge offset shift, view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a),(b) Relative anharmonicity changes view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Anharmonicity view at source ↗
Figure 7
Figure 7. Figure 7: In this limit, the result of Eq. (40) is exponentially suppressed (green solid line). On the contrary, the exact numerics and the extended WKB result, α (2) < 0, practi￾cally coincide, while not crossing zero (in agreement with Eq. (10) of Ref. [8]), and reproduce the limiting intercept of α T =1 transmon(ϵg = 0)/EC = −1/4 (41) expected in a short-junction limit [1, 8]. Indeed, in the deep transmon regime … view at source ↗
read the original abstract

Gatemon qubits are based on a superconductor-quantum dot-superconductor (S-QD-S) junction which enables in situ electrostatic tuning via a gate electrode. For a single-channel QD this structure gives rise to two subgap Andreev bound states (ABSs), and generally leads to a richer quantum phase dynamics as compared to conventional transmons. In a recent work [Phys. Rev. B 111, 214503 (2025)] we derived the quantum phase dynamics from a many-body treatment which leads to an effective gate voltage-dependent Hamiltonian that self-consistently incorporates the phase quantization. It predicts (i) a renormalization of the junction's effective capacitance and (ii) the presence of gate voltage and occupation-dependent charge offsets in junctions with tunneling asymmetry. Here, we quantify the observable impact of these effects on the qubit's energy spectrum and anharmonicity, by studying the interplay of the two Andreev branches as a function of dot-gate voltages and junction transparencies. We show the relation of these predictions to simplified gatemon models and propose a protocol to experimentally detect the predicted charge offsets.

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 applies an effective gate-voltage-dependent Hamiltonian, derived via many-body treatment in the authors' prior work, to gatemon qubits formed by S-QD-S junctions in the weak tunneling regime. It claims that phase quantization leads to renormalization of the junction's effective capacitance and to gate-voltage and occupation-dependent charge offsets (especially for tunneling asymmetry), which in turn modify the qubit energy spectrum and anharmonicity through the interplay of the two Andreev bound states. The authors map these effects versus dot-gate voltages and junction transparencies, relate them to simplified gatemon models, and propose an experimental protocol to detect the predicted charge offsets.

Significance. If the effective Hamiltonian remains valid in the weak-tunneling limit, the work supplies concrete, quantitative predictions for how many-body effects alter gatemon anharmonicity and spectrum—quantities directly relevant to qubit design and control. The explicit mapping to experimental observables and the proposed detection protocol are strengths that could enable falsification or confirmation in the lab.

major comments (2)
  1. [Introduction and § on effective Hamiltonian] The load-bearing effective Hamiltonian (including its predictions of capacitance renormalization and occupation-dependent charge offsets) is imported without re-derivation or numerical validation from Phys. Rev. B 111, 214503 (2025). The manuscript studies the weak-tunneling regime (small transparencies, large charging energy relative to gap) but provides no checks on whether higher-order virtual processes or phase-quantization self-consistency hold under these conditions; this directly affects the claimed observable impacts on anharmonicity.
  2. [Results on spectrum and anharmonicity] The quantification of anharmonicity shifts (abstract and results section) is presented as direct consequences of the prior Hamiltonian, yet no sensitivity analysis or comparison against independent numerical diagonalization of the full many-body problem is given for the parameter range of interest. This leaves the magnitude of the predicted effects without an internal consistency test.
minor comments (2)
  1. Notation for the two Andreev branches and the effective capacitance renormalization could be introduced more explicitly with a table of symbols to aid readability.
  2. [Discussion] The proposed experimental protocol would benefit from a brief discussion of required gate-voltage resolution or coherence times to make the charge-offset signature distinguishable from other noise sources.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback on our manuscript. We address each major comment point by point below, providing clarifications and outlining the revisions we will make to strengthen the paper.

read point-by-point responses

  1. Referee: [Introduction and § on effective Hamiltonian] The load-bearing effective Hamiltonian (including its predictions of capacitance renormalization and occupation-dependent charge offsets) is imported without re-derivation or numerical validation from Phys. Rev. B 111, 214503 (2025). The manuscript studies the weak-tunneling regime (small transparencies, large charging energy relative to gap) but provides no checks on whether higher-order virtual processes or phase-quantization self-consistency hold under these conditions; this directly affects the claimed observable impacts on anharmonicity.

    Authors: We thank the referee for highlighting this important point. The effective Hamiltonian was derived in our prior work [Phys. Rev. B 111, 214503 (2025)] using a many-body approach that accounts for the relevant virtual processes in the tunneling regime. In the weak-tunneling limit, which is the focus of this manuscript, the small transparencies ensure that higher-order processes are negligible, and the phase quantization is self-consistently included via the renormalized capacitance. To address the referee's concern, we will add a dedicated paragraph in the introduction that explicitly discusses the validity of the effective model in the weak-tunneling regime, referencing the assumptions from the prior derivation and explaining why higher-order terms are suppressed. revision: partial

  2. Referee: [Results on spectrum and anharmonicity] The quantification of anharmonicity shifts (abstract and results section) is presented as direct consequences of the prior Hamiltonian, yet no sensitivity analysis or comparison against independent numerical diagonalization of the full many-body problem is given for the parameter range of interest. This leaves the magnitude of the predicted effects without an internal consistency test.

    Authors: The predicted shifts in the energy spectrum and anharmonicity arise directly from the gate- and occupation-dependent terms in the effective Hamiltonian, as quantified through the interplay of the Andreev bound states. While we relate these to simplified models in the manuscript, we acknowledge that an explicit sensitivity analysis and comparison to full many-body diagonalization would strengthen the claims. Performing a full numerical diagonalization of the microscopic many-body problem for the qubit is computationally demanding and outside the primary scope of this application-focused work. However, we will revise the results section to include a sensitivity analysis by exploring variations in parameters such as the charging energy, gap, and transparencies within the effective model. This will demonstrate the robustness of the anharmonicity modifications and provide an internal consistency check. revision: partial

Circularity Check

1 steps flagged

Central predictions of capacitance renormalization and charge offsets imported directly from authors' prior self-cited Hamiltonian without re-derivation or benchmarking

specific steps
  1. self citation load bearing [Abstract]
    "In a recent work [Phys. Rev. B 111, 214503 (2025)] we derived the quantum phase dynamics from a many-body treatment which leads to an effective gate voltage-dependent Hamiltonian that self-consistently incorporates the phase quantization. It predicts (i) a renormalization of the junction's effective capacitance and (ii) the presence of gate voltage and occupation-dependent charge offsets in junctions with tunneling asymmetry. Here, we quantify the observable impact of these effects on the qubit's energy spectrum and anharmonicity, by studying the interplay of the two Andreev branches as a f"

    The entire quantification of observable impacts (spectrum, anharmonicity, charge offsets) is performed by applying the effective Hamiltonian and its listed predictions, which the paper explicitly attributes to the authors' prior self-cited publication. No re-derivation of the many-body treatment or verification of its applicability in the weak-tunneling limit appears in the present work, so the central claims reduce directly to the content of the cited prior paper.

full rationale

The paper's derivation chain begins with the effective gate-dependent Hamiltonian and its two key predictions, which are stated to come from the authors' own recent prior work. The present manuscript then quantifies observable impacts on the qubit spectrum and anharmonicity by applying that Hamiltonian to the two-ABS gatemon model. No independent derivation, numerical check of phase quantization self-consistency, or external benchmark for the weak-tunneling regime is supplied here, so the claimed results reduce to the inputs of the self-citation. This matches the self-citation-load-bearing pattern at the core of the analysis.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on the effective Hamiltonian derived in the authors' prior work; no new free parameters or invented entities are introduced in the abstract itself.

free parameters (2)
  • junction transparencies
    The abstract states the study is performed as a function of junction transparencies, implying these are input parameters in the model.
  • dot-gate voltages
    Gate voltages are varied to map the dependence of charge offsets and anharmonicity.
axioms (1)
  • domain assumption The many-body treatment yields an effective gate voltage-dependent Hamiltonian that self-consistently incorporates phase quantization.
    Invoked from the cited prior work to generate the predictions quantified here.

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Reference graph

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