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arxiv: 2603.16025 · v2 · submitted 2026-03-17 · ❄️ cond-mat.mes-hall · cs.CV· quant-ph

3D tomography of exchange phase in a Si/SiGe quantum dot device

Dylan Albrecht , Sarah Thompson , N. Tobias Jacobson , Ryan Jock This is my paper

Pith reviewed 2026-05-15 10:44 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cs.CVquant-ph
keywords exchange interactionSi/SiGe quantum dotsspin qubitsphase unwrapping3D tomographyvoltage spacePUMA algorithm
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The pith

A 3D phase-unwrapping technique recovers the continuous exchange phase volume across gate-voltage space in silicon quantum dot devices.

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

Exchange interaction sets the speed of two-qubit gates in spin processors, yet standard oscillation data hide the underlying phase behind a cosine and are easily scrambled by noise. The paper shows that a phase-shifting measurement sequence followed by three-dimensional max-flow/min-cut unwrapping produces a clean phase volume from ordinary two-dimensional scans. With the volume in hand, a smooth model can be fitted and searched for gate-voltage points that deliver a clean pi rotation with minimal gradient. This removes two long-standing obstacles to extracting the voltage dependence of exchange and opens the way to device-specific calibration.

Core claim

By acquiring wrapped phase maps with a phase-shifting protocol and unwrapping them with the PUMA max-flow/min-cut algorithm in three-dimensional voltage space, the accumulated exchange phase phi(V) is recovered as a continuous function of gate voltages despite the cosine ambiguity and modest device drift.

What carries the argument

The PUMA max-flow/min-cut phase-unwrapping algorithm applied directly to the three-dimensional gate-voltage volume after phase-shifting measurements.

If this is right

  • A smooth model of the phase volume can be optimized to locate gate-voltage points that realize a minimal-gradient pi exchange pulse.
  • The extracted volume supplies quantitative information on spatial disorder that limits device yield.
  • Device models can be calibrated to the measured phase of an individual chip for more accurate error budgeting.
  • Systematic search over the phase volume enables improved voltage schedules for high-fidelity qubit control.

Where Pith is reading between the lines

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

  • The same unwrapping pipeline could be applied to other voltage-tunable interactions in superconducting or trapped-ion qubits.
  • Repeated scans at higher resolution could be used to track slow drift and correct the phase volume in real time.
  • Combining the phase map with fast feedback electronics might allow pulse amplitudes to be adjusted on the fly to stay at low-gradient points.

Load-bearing premise

The measured phase field stays continuous enough across the scanned voltage range that noise does not create residues the unwrapping algorithm cannot resolve.

What would settle it

Direct time-domain exchange oscillations taken at several fixed voltage points inside the scanned volume should integrate to the same phase values given by the unwrapped map; a systematic mismatch would show the unwrapping introduced errors.

Figures

Figures reproduced from arXiv: 2603.16025 by Dylan Albrecht, N. Tobias Jacobson, Ryan Jock, Sarah Thompson.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
read the original abstract

The exchange interaction is a foundational building block for the operation of spin-based quantum processors. Extracting the exchange interaction coefficient $J(\mathbf{V})$, as a function of gate electrode voltages, is important for understanding disorder, faithfully simulating device performance, and operating spin qubits with high fidelity. Typical coherent measurements of exchange in spin qubit devices yield a modulated cosine of an accumulated phase, which in turn is the time integral of exchange. As such, extracting $J(\mathbf{V})$ from experimental data is difficult due to the ambiguity of inverting a cosine, the sensitivity to noise when unwrapping phase, as well as the problem of inverting the integral. As a step toward obtaining $J(\mathbf{V})$, we tackle the first two challenges to reveal the accumulated phase, $\phi(\mathbf{V})$. We incorporate techniques from a wide range of fields to robustly extract and model a 3D phase volume for spin qubit devices from a sequence of 2D measurements. In particular, we present a measurement technique to obtain the wrapped phase, as done in phase-shifting digital holography, and utilize the max-flow/min-cut phase unwrapping method (PUMA) to unwrap the phase in 3D voltage space. We show this method is robust to the minimal observed drift in the device, which we confirm by increasing scan resolution. Upon building a model of the extracted phase, we optimize over the model to locate a minimal-gradient $\pi$ exchange pulse point in voltage space. Our measurement protocol may provide detailed information useful for understanding the origins of device variability governing device yield, enable calibrating device models to specific devices during operation for more sophisticated error attribution, and enable a systematic optimization of qubit control. We anticipate that the methods presented here may be applicable to other qubit platforms.

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 / 1 minor

Summary. The paper claims that a sequence of 2D wrapped-phase measurements in a Si/SiGe quantum dot device can be combined into a reliable 3D unwrapped phase volume φ(V) via a phase-shifting holography-style protocol and the PUMA max-flow/min-cut unwrapping algorithm. This volume is then modeled to locate a minimal-gradient π exchange pulse point in voltage space, with robustness demonstrated by increased scan resolution to confirm minimal drift.

Significance. If the unwrapped volume is accurate, the approach supplies a concrete, drift-robust protocol for mapping exchange phase in voltage space, which could aid device variability studies, model calibration, and systematic pulse optimization for spin qubits. The integration of established phase-unwrapping tools from other fields is a practical strength, though the absence of quantitative validation metrics limits immediate impact.

major comments (2)
  1. [phase unwrapping procedure and results] The central extraction of the 3D phase volume rests on the assumption that the underlying phase field is continuous and free of noise-induced 2π residues across the full voltage grid. The manuscript reports only “minimal observed drift” confirmed by higher-resolution scans but supplies no residue count, re-wrapping error statistic, or consistency metric between forward and inverse operations. This quantitative gap directly affects the reliability of the extracted volume and the subsequent optimization step.
  2. [validation and modeling sections] No comparison is presented against independent measurements of J (e.g., via Ramsey or echo sequences) or against simulated data with known discontinuities. Without such cross-validation, it remains unclear whether the PUMA output recovers the physically correct unwrapped phase or merely a plausible continuous field.
minor comments (1)
  1. [abstract] The abstract states that the method is “robust to the minimal observed drift” but does not define the quantitative threshold used to classify drift as minimal.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback on our manuscript. We appreciate the recognition of the potential impact of our 3D phase tomography method for spin qubit devices. Below, we address each major comment point by point, and we have prepared revisions to incorporate additional quantitative validations as suggested.

read point-by-point responses

  1. Referee: The central extraction of the 3D phase volume rests on the assumption that the underlying phase field is continuous and free of noise-induced 2π residues across the full voltage grid. The manuscript reports only “minimal observed drift” confirmed by higher-resolution scans but supplies no residue count, re-wrapping error statistic, or consistency metric between forward and inverse operations. This quantitative gap directly affects the reliability of the extracted volume and the subsequent optimization step.

    Authors: We agree that providing quantitative metrics for the phase unwrapping quality is important for demonstrating the reliability of the extracted 3D phase volume. In the revised manuscript, we will add the following: (1) the number of 2π residues identified and handled by the PUMA algorithm across the voltage grid, (2) the re-wrapping error statistic, computed as the root-mean-square difference between the original wrapped phase measurements and the phase obtained by wrapping the unwrapped volume, and (3) a consistency metric between forward and inverse operations, such as the maximum deviation in the unwrapped phase after re-wrapping. These will be included in the results section discussing the unwrapping procedure, along with an expanded discussion of the higher-resolution scans to quantify the minimal drift with explicit statistics. We believe these additions will address the concern and strengthen the evidence for the continuity assumption. revision: yes

  2. Referee: No comparison is presented against independent measurements of J (e.g., via Ramsey or echo sequences) or against simulated data with known discontinuities. Without such cross-validation, it remains unclear whether the PUMA output recovers the physically correct unwrapped phase or merely a plausible continuous field.

    Authors: We acknowledge that cross-validation would further support the accuracy of the unwrapped phase. Independent measurements of J via Ramsey or echo sequences were outside the scope of this work, which focuses on developing the phase extraction protocol itself. However, to address the validation concern, we will include in the revised manuscript a comparison against simulated data with known phase discontinuities. Specifically, we will generate synthetic wrapped phase data from a model with known jumps and apply the same holography-style measurement and PUMA unwrapping procedure, then compare the recovered phase to the ground truth. This will be presented in a new validation subsection, demonstrating that the method correctly recovers the phase without introducing artifacts. We argue that this simulation-based validation, combined with the experimental robustness to drift, supports the physical correctness of the results. revision: partial

Circularity Check

0 steps flagged

No circularity: phase volume obtained from direct 2D measurements via standard PUMA unwrapping

full rationale

The derivation chain begins with experimental acquisition of wrapped phase from a sequence of 2D voltage scans using a phase-shifting digital holography-inspired protocol, followed by application of the established external PUMA max-flow/min-cut algorithm to produce the 3D unwrapped phase volume. Subsequent modeling and optimization locate the minimal-gradient π point on this extracted volume. No equations reduce the reported phase to a fitted parameter by construction, no self-citations are load-bearing for the core extraction step, and the unwrapping relies on a pre-existing algorithm whose correctness assumptions (continuity, residue-free field) are external to the paper rather than self-defined. The result is therefore self-contained against the input data.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The method assumes the measured phase is a conservative field that can be unwrapped without topological defects and that device drift is negligible on the timescale of a full 3D scan.

axioms (1)
  • domain assumption The accumulated exchange phase forms a continuous scalar field in 3D voltage space that is suitable for min-cut unwrapping
    Invoked when applying PUMA to the wrapped-phase data cube

pith-pipeline@v0.9.0 · 5638 in / 1213 out tokens · 33601 ms · 2026-05-15T10:44:45.592526+00:00 · methodology

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