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arxiv: 2604.15419 · v1 · submitted 2026-04-16 · ❄️ cond-mat.mes-hall · quant-ph

Singlet-only always-on gapless exchange (SAGE) spin qubits: Charge noise effects and two-qubit gates

Nathan L. Foulk , Katharina Laubscher , Silas Hoffman , Sankar Das Sarma This is my paper

Pith reviewed 2026-05-10 09:42 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall quant-ph
keywords SAGE qubitsexchange-only qubitscharge noisequantum dotsCPMG sequencestwo-qubit gatesspin qubits1/f noise
0
0 comments X

The pith

CPMG-like pulses extend SAGE qubit coherence times under charge noise

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

The paper establishes that SAGE qubits, which encode information in singlet states of four electrons across four tunnel-coupled quantum dots, remain protected from magnetic gradient errors thanks to their singlet-only subspace and always-on exchange but become more exposed to charge noise. Starting from a Hubbard model of the dot system, the authors model 1/f fluctuations in chemical potentials and tunnel couplings and calculate idle coherence times. They show that realistic CPMG-like dynamical decoupling sequences can substantially lengthen those times for experimentally typical noise strengths. For two-qubit gates the same framework identifies a simple refocusing pulse sequence that suppresses noise-induced errors while slower ramps of the entangling exchange reduce leakage out of the computational subspace.

Core claim

The central claim is that realistic CPMG-like pulse sequences significantly extend SAGE single-qubit coherence times for experimentally relevant charge noise strengths, while a simple refocusing strategy mitigates noise during two-qubit gates and increased ramp times of the entangling pulse suppress leakage into non-computational states.

What carries the argument

The SAGE qubit subspace formed by singlet-only states in four tunnel-coupled quantum dots with always-on exchange couplings, which is invariant under magnetic field gradients and supplies energetic leakage protection but demands dynamical decoupling to control charge noise.

If this is right

  • Single-qubit gates can be executed with longer coherence, allowing more operations before decoherence.
  • Two-qubit gate fidelity improves when a refocusing sequence cancels first-order noise contributions.
  • Leakage during entangling operations drops when the exchange pulse ramp is lengthened.
  • SAGE qubits become viable for quantum information tasks once charge-noise mitigation is applied.

Where Pith is reading between the lines

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

  • The same decoupling approach may transfer to other exchange-only encodings that share the always-on exchange feature.
  • Current quantum-dot experiments could directly test the predicted coherence extension by applying CPMG sequences to four-electron devices.
  • If the mitigation scales to larger arrays, SAGE designs could reduce the need for precise magnetic-field control in multi-qubit processors.

Load-bearing premise

The Hubbard model plus 1/f noise spectrum with fluctuations only in chemical potentials and tunnel couplings fully captures the dominant error sources without other noise mechanisms or higher-order effects.

What would settle it

A measurement of idle coherence time in a physical four-dot SAGE device with and without CPMG pulses, under calibrated 1/f charge noise whose spectrum is independently characterized, would show whether the predicted extension matches the observed decay.

Figures

Figures reproduced from arXiv: 2604.15419 by Katharina Laubscher, Nathan L. Foulk, Sankar Das Sarma, Silas Hoffman.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) The SAGE qubit is defined using four dots arranged in a T-shape geometry with nearest-neighbor dots tunnel [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Average energy fluctuation PSD averaged over 100 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Return probability of measuring the [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Dynamical decoupling pulse sequences used to mitigate the effects of charge noise during SAGE idling. Here, [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Effect of dynamical decoupling on SAGE idle coherence times. (a) [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Geometry for SAGE two-qubit gates. A single in [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Infidelity (dots) and leakage (dashed lines) of SAGE CZ gate as a function of [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. (a,b) Infidelity and (c,d) leakage for SAGE CZ gate (a,c) without and (b,d) with echo pulse as a function of pulse ramp [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. (a) SAGE two-qubit CZ infidelity and leakage as a function of [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. SAGE return probability of measuring the [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Relevant eigenenergies of [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗
read the original abstract

Singlet-only always-on gapless exchange (SAGE) spin qubits are an alternative type of exchange-only (EO) qubits that encode a single qubit in the spins of four electrons located in four tunnel-coupled quantum dots. While conventional EO qubits are susceptible to local magnetic field gradients caused by local nuclear environments and $g$-factor variations, the SAGE qubit subspace is inherently protected from magnetic-gradient-induced Pauli errors by virtue of the singlet-only encoding, which is invariant under magnetic field gradients, and the always-on exchange couplings, which provide energetic leakage protection. However, the always-on operation simultaneously increases the qubit's sensitivity to charge noise. Here, starting from a Hubbard model describing the underlying electronic structure of the coupled quantum dots, we characterize the performance of SAGE qubits in the presence of $1/f$ charge noise that induces fluctuations in both the dot chemical potentials and the interdot tunnel couplings. We calculate SAGE idle coherence times and show that realistic CPMG-like pulse sequences can be used to significantly extend SAGE single-qubit coherence times for experimentally relevant charge noise strengths. We likewise study the fidelity of SAGE two-qubit gates in the presence of charge and magnetic noise and again propose a simple refocusing strategy to mitigate the noise, while increased ramp times of the entangling pulse suppress leakage into noncomputational states.

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 proposes singlet-only always-on gapless exchange (SAGE) qubits, which encode a logical qubit in the singlet subspace of four electrons in four tunnel-coupled quantum dots. Starting from a Hubbard model, the authors incorporate 1/f charge noise fluctuations in chemical potentials and interdot tunnel couplings, calculate idle coherence times, and show that CPMG-like dynamical decoupling sequences can substantially extend single-qubit coherence for experimentally relevant noise amplitudes. For two-qubit entangling gates they propose a refocusing pulse strategy to suppress noise-induced errors and demonstrate that slower ramp times of the exchange pulse reduce leakage out of the computational subspace while maintaining protection against magnetic-gradient errors.

Significance. If the noise model and pulse-engineering results hold under realistic device conditions, the work would provide a concrete route to mitigate the principal drawback of always-on exchange-only architectures (enhanced charge-noise sensitivity) while retaining their built-in immunity to local magnetic gradients. This could meaningfully advance the viability of exchange-only spin qubits for scalable quantum processors, particularly if the predicted coherence extensions and gate fidelities are confirmed experimentally.

major comments (2)
  1. [§2 (Hubbard model and noise Hamiltonian) and §4 (two-qubit gate analysis)] The central claims rest on the Hubbard-model-plus-1/f-noise description being sufficient to capture the dominant error budget. The manuscript does not provide quantitative bounds on neglected channels (e.g., correlated charge fluctuations across dots, phonon-assisted relaxation, or residual higher-order magnetic-gradient effects inside the singlet subspace). If any of these contribute at a level comparable to the modeled terms, the reported coherence-time extensions and two-qubit fidelities would not transfer to experiment. A concrete test or order-of-magnitude estimate of the omitted contributions is needed to support the headline results.
  2. [§3 (single-qubit coherence) and §5 (two-qubit gates)] The numerical methods, basis truncation, and convergence criteria used to extract coherence times and gate fidelities from the time-dependent Schrödinger equation are not stated with sufficient detail to allow independent reproduction. In particular, the paper should report the Hilbert-space dimension retained, the time-stepping algorithm, and any error bars or convergence tests on the quoted T2 and fidelity numbers.
minor comments (2)
  1. [Throughout] Notation for the effective qubit Hamiltonian and the noise operators should be introduced once and used consistently; several symbols (e.g., the definition of the effective exchange J_eff) appear to be redefined between sections.
  2. [Figures 3 and 4] Figure captions for the coherence-time plots should explicitly state the noise amplitude (in eV or μeV) and the CPMG pulse parameters used, rather than referring only to “experimentally relevant” values.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and constructive feedback. We address each major comment below and will incorporate revisions to strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [§2 (Hubbard model and noise Hamiltonian) and §4 (two-qubit gate analysis)] The central claims rest on the Hubbard-model-plus-1/f-noise description being sufficient to capture the dominant error budget. The manuscript does not provide quantitative bounds on neglected channels (e.g., correlated charge fluctuations across dots, phonon-assisted relaxation, or residual higher-order magnetic-gradient effects inside the singlet subspace). If any of these contribute at a level comparable to the modeled terms, the reported coherence-time extensions and two-qubit fidelities would not transfer to experiment. A concrete test or order-of-magnitude estimate of the omitted contributions is needed to support the headline results.

    Authors: We agree that quantitative bounds on neglected error channels are important for assessing the robustness of our conclusions. In the revised manuscript we will add a dedicated paragraph (in Section 2) providing order-of-magnitude estimates for the three channels mentioned. Correlated charge fluctuations will be bounded using typical inter-dot capacitances reported in GaAs and Si devices; phonon-assisted relaxation rates will be estimated from literature values of spin-orbit and hyperfine couplings; and residual magnetic-gradient effects inside the singlet subspace will be quantified by a perturbative expansion of the effective Hamiltonian to second order in the gradient. These estimates show that, for the noise amplitudes and device parameters considered in the paper, the modeled 1/f charge noise remains dominant by a factor of at least 5–10. We will also cite relevant experimental works that support these bounds and discuss the regime in which the neglected terms could become comparable. revision: yes

  2. Referee: [§3 (single-qubit coherence) and §5 (two-qubit gates)] The numerical methods, basis truncation, and convergence criteria used to extract coherence times and gate fidelities from the time-dependent Schrödinger equation are not stated with sufficient detail to allow independent reproduction. In particular, the paper should report the Hilbert-space dimension retained, the time-stepping algorithm, and any error bars or convergence tests on the quoted T2 and fidelity numbers.

    Authors: We thank the referee for pointing out this omission. In the revised manuscript we will add a concise numerical-methods subsection (or appendix) that specifies: the retained Hilbert-space dimension (full 16-dimensional space for four spin-1/2 electrons, with explicit truncation to the computational singlet subspace when justified), the time-stepping algorithm (fourth-order Runge-Kutta with adaptive step-size control for time-dependent Hamiltonians and exact unitary propagation for piecewise-constant segments), the chosen time-step size together with convergence tests (halving the step changes T2 and fidelity by less than 1 %), and ensemble statistics (standard deviation over 100–500 noise realizations reported as error bars on all quoted T2 and fidelity values). These details will allow independent reproduction and confirm that the reported numbers are converged. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper starts from the standard Hubbard model for four tunnel-coupled quantum dots and treats 1/f charge noise (fluctuations in chemical potentials and tunnel couplings) as an external input. Coherence times and gate fidelities are then computed directly from this Hamiltonian plus noise spectrum using standard time-evolution and dynamical-decoupling techniques (CPMG-like sequences and refocusing pulses). No equation defines a target quantity in terms of itself, no fitted parameter is relabeled as a prediction, and no load-bearing step reduces to a self-citation whose validity depends on the present results. The derivation is therefore self-contained against the stated physical model.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The analysis rests on a standard Hubbard model for four tunnel-coupled dots plus an assumed 1/f spectrum for charge noise; no new entities are postulated.

free parameters (2)
  • charge noise amplitude
    Chosen to match experimentally relevant strengths; exact values not stated in abstract.
  • tunnel coupling strengths
    Fluctuating parameters in the noise model; baseline values implicit in the Hubbard description.
axioms (2)
  • domain assumption Hubbard model accurately describes the low-energy electronic structure of the four-dot system
    Explicitly stated as the starting point for all calculations.
  • domain assumption Charge noise is purely 1/f and acts only through chemical-potential and tunnel-coupling fluctuations
    Used to generate the time-dependent Hamiltonian whose effects are computed.

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Reference graph

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