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arxiv: 2606.28695 · v1 · pith:OJ7B4CXJnew · submitted 2026-06-27 · 🪐 quant-ph · cond-mat.mtrl-sci

High-Fidelity Hole Spin Qubits Reveal Quadrupolar Nuclear-Bath Dynamics in Isotopically Purified Planar Germanium

Jian Zeng , Xiangjun Tan , Hongzhang Wang , Yulei Zhang , Wendong Bian , Lingting Wu , Chenggang Yang , Zhengshan Guo
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Jiankun Li Yongfeng Wang Jun Lu Jun-Wei Luo Tian Pei
This is my paper

Pith reviewed 2026-06-30 09:57 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.mtrl-sci
keywords hole spin qubitsisotopic purificationplanar germaniumnuclear spin bathquadrupolar dynamicsT2* coherencequantum gate fidelityhyperfine interaction
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The pith

Isotopically purified planar germanium enables hole spin qubits with T2* above 3 microseconds off the sweet spot and single-qubit gate fidelity exceeding 99.9 percent in both regimes.

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

The paper shows that growing a two-dimensional hole gas from enriched 70Ge precursor suppresses the dominant source of nuclear spin noise that previously limited germanium hole qubits. This yields coherence times T2* longer than 20 microseconds at the optimal operating point and, crucially, longer than 3 microseconds when the qubit is detuned from that point. The off-point improvement removes the need for precise per-qubit voltage tuning and directly produces gate fidelities above 99.9 percent. Hahn-echo measurements additionally detect a previously unseen finite-frequency noise component whose magnetic-field and angle dependence match the signature of residual 73Ge nuclei whose quadrupolar moments couple to local electric-field gradients at the Ge/SiGe interface and are read out through the holes' anisotropic hyperfine interaction.

Core claim

Synthesis of high-mobility 2DHG in isotopically purified planar germanium extends qubit T2* beyond 20 microseconds on the sweet spot and above 3 microseconds off it, enabling gate fidelities above 99.9 percent in both regimes; the same devices reveal a distinct finite-frequency nuclear-noise channel whose scaling is consistent with quadrupole-modified dynamics of residual 73Ge nuclei transduced by the anisotropic hyperfine interaction of Ge holes.

What carries the argument

Anisotropic hyperfine interaction of holes in germanium that converts interfacial quadrupolar fluctuations of residual 73Ge nuclei into a qubit-visible finite-frequency noise channel.

If this is right

  • Single-qubit gates can be performed at high fidelity without calibrating every qubit exactly to its individual sweet spot, relaxing fabrication uniformity requirements across a wafer.
  • The platform becomes viable for multi-qubit circuits where voltage offsets between neighboring devices would otherwise detune some qubits from their optimal points.
  • Residual 73Ge nuclei now act as a spectroscopic reporter of interfacial electric-field gradients rather than the dominant decoherence source.
  • Isotopic purification removes the main obstacle that had kept germanium hole qubits behind their silicon counterparts in off-sweet-spot performance.

Where Pith is reading between the lines

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

  • The same purification strategy may allow germanium hole qubits to reach the coherence levels needed for surface-code error correction without additional dynamical decoupling overhead.
  • Electric-field gradients engineered at the interface could be used as a controllable knob to study or suppress the quadrupolar noise channel in other hole-based systems.
  • Because the noise is transduced through the anisotropic hyperfine interaction, similar quadrupolar signatures may appear in any hole qubit platform where the valence-band mixing produces strong anisotropy.

Load-bearing premise

The finite-frequency nuclear noise detected in Hahn-echo spectra is produced by quadrupole-modified precession of the remaining 73Ge nuclei under local electric-field gradients at the interface.

What would settle it

A measurement showing that the finite-frequency noise peak either disappears when the interface electric-field gradient is deliberately flattened or fails to exhibit the reported magnetic-field scaling and angle-dependent visibility.

Figures

Figures reproduced from arXiv: 2606.28695 by Chenggang Yang, Hongzhang Wang, Jiankun Li, Jian Zeng, Jun Lu, Jun-Wei Luo, Lingting Wu, Tian Pei, Wendong Bian, Xiangjun Tan, Yongfeng Wang, Yulei Zhang, Zhengshan Guo.

Figure 4
Figure 4. Figure 4: FIG 4 [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
read the original abstract

Planar Germanium has emerged as a promising platform to build spin-based large scale quantum computers. By exploiting the anisotropic hyperfine interaction of holes in Ge, qubits with long T2* have been recently realized. While the performance of single qubits is still more or less limited by 73Ge nuclear spin fluctuations, the site-to-site variation of qubit sweet spot becomes obstacles to maintaining high fidelity of each qubit across the whole wafer. To achieve high performance Ge-based quantum circuit, it is therefore essential to eliminate the origin source of hyperfine noise. In its Silicon counterparts, reduction of 29Si abundance enables exceptional high-fidelity operation. In contrast, hole qubits based on isotopically purified Ge have not been demonstrated. Here, we report the synthesis of high quality 2-dimensional hole gas (2DHG) with enriched 70GeH4 precursor. Due to the suppression of nonzero spin nucleus, the qubits' T2* on the sweet spot is moderately extended beyond 20 us, surpassing the previous best reported Ge hole qubits. More importantly, the qubits' T2* off the sweet spot is enhanced to above 3 us, enabling single qubit gate fidelity exceeding 99.9% in both operating regimes. Hahn-echo spectroscopy further resolves a finite-frequency nuclear-noise channel that is distinct from the conventional Larmor-linked hyperfine response. We associate this channel with quadrupole-modified dynamics of residual 73Ge nuclei sampling local electric-field gradients near the Ge/SiGe interface. Its field scaling and angle-dependent visibility are consistent with a qubit-visible quadrupolar nuclear-noise component transduced through the anisotropic hyperfine interaction of Ge holes. These results establish isotopically purified planar Ge as a high-coherence scalable platform for hole spin qubits and provide a spectroscopic probe of interfacial quadrupolar nuclear dynamics.

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 manuscript reports the growth of high-quality 2DHG in planar Ge using isotopically enriched 70GeH4 precursor and the resulting hole spin qubits. It claims T2* >20 μs on the sweet spot (surpassing prior Ge reports) and T2* >3 μs off the sweet spot, enabling single-qubit gate fidelities >99.9% in both regimes due to suppression of 73Ge nuclear spins. Hahn-echo spectroscopy reveals an additional finite-frequency nuclear noise channel, interpreted as arising from quadrupole-modified dynamics of residual 73Ge nuclei sampling interfacial electric-field gradients and transduced via anisotropic hyperfine coupling.

Significance. If the isotopic composition is verified and the noise-channel assignment holds, the work would establish isotopically purified planar Ge as a high-coherence platform for hole qubits, with the off-sweet-spot performance gain addressing a key scalability obstacle. The experimental demonstration of extended T2* and the spectroscopic identification of a quadrupolar nuclear-bath component would provide both a practical advance and a new probe of interface physics, analogous to isotopic engineering successes in Si.

major comments (2)
  1. [Abstract] Abstract: The central performance claims are explicitly attributed to 'suppression of nonzero spin nucleus' via the enriched 70GeH4 precursor, yet the manuscript contains no direct verification of the residual 73Ge fraction in the 2DHG (no SIMS, atom probe, or NMR data referenced). This leaves open alternative explanations such as improved interface quality and undercuts the causal link required for the headline attribution.
  2. [Hahn-echo spectroscopy] Hahn-echo spectroscopy section: The assignment of the finite-frequency channel to quadrupole-modified 73Ge dynamics is supported only by qualitative consistency with field scaling and angle dependence; without a quantitative model or simulation linking the anisotropic hyperfine interaction to the observed spectrum, the interpretation remains post-hoc and does not yet bear the weight placed on it for the 'reveal' claim.
minor comments (1)
  1. [Results] Ensure that all reported T2* values and fidelities include explicit error bars, fit details, and raw data traces or supplementary files so that the statistical support for the >20 μs and >3 μs thresholds can be assessed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We address the two major comments point-by-point below, clarifying the evidential basis for our claims while acknowledging where additional discussion or qualification is warranted.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central performance claims are explicitly attributed to 'suppression of nonzero spin nucleus' via the enriched 70GeH4 precursor, yet the manuscript contains no direct verification of the residual 73Ge fraction in the 2DHG (no SIMS, atom probe, or NMR data referenced). This leaves open alternative explanations such as improved interface quality and undercuts the causal link required for the headline attribution.

    Authors: We agree that direct post-growth verification of the 73Ge fraction (via SIMS, atom probe, or NMR) is absent from the manuscript. The attribution rests on the use of a commercially enriched 70GeH4 precursor whose specified isotopic purity is stated in the methods, combined with the observed coherence improvements relative to prior natural-abundance Ge devices fabricated in the same growth system. While these performance gains are consistent with nuclear-spin suppression, we acknowledge that interface-quality variations cannot be entirely ruled out without isotopic quantification. In revision we will add a brief methods paragraph citing the precursor specification and a short discussion noting the lack of direct 73Ge assay as a limitation, together with a statement that future devices will include such measurements. revision: partial

  2. Referee: [Hahn-echo spectroscopy] Hahn-echo spectroscopy section: The assignment of the finite-frequency channel to quadrupole-modified 73Ge dynamics is supported only by qualitative consistency with field scaling and angle dependence; without a quantitative model or simulation linking the anisotropic hyperfine interaction to the observed spectrum, the interpretation remains post-hoc and does not yet bear the weight placed on it for the 'reveal' claim.

    Authors: The finite-frequency feature is identified through its distinct dependence on magnetic-field magnitude and orientation, which deviates from the conventional Larmor-frequency hyperfine response. These trends match the expected signatures of quadrupolar splitting of residual 73Ge nuclei under interfacial electric-field gradients, transduced by the anisotropic hyperfine interaction of holes. A full microscopic simulation of the nuclear bath would require detailed knowledge of the interface gradient distribution and nuclear quadrupolar parameters, which lies outside the scope of the present experimental study. We will revise the text to make explicit that the assignment is based on qualitative consistency rather than quantitative modeling, while retaining the interpretation as the most parsimonious explanation of the observed spectroscopy. revision: partial

Circularity Check

0 steps flagged

No circularity: experimental report with direct measurements

full rationale

This is an experimental paper reporting measured T2* values and Hahn-echo spectra in isotopically purified Ge hole qubits. No mathematical derivation, model, or prediction is presented whose output reduces by construction to a fitted parameter, self-citation, or input ansatz. Performance claims are tied to direct observations and external literature comparisons without any load-bearing self-referential step that would require a circularity flag.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No mathematical model, free parameters, or invented entities appear in the abstract; the work is a materials-synthesis and spectroscopy experiment whose claims rest on measured coherence times and spectral features.

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