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

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.

• The paper demonstrates a 20-fold reduction in 73Ge abundance, enabling extended coherence times (T*_2 up to 22.5 μs) for hole spin qubits.
• It employs ultra-high vacuum CVD growth and advanced charge sensing techniques to achieve single-shot spin readout with gate fidelities above 99.9%.
• Spectroscopic analysis uncovers quadrupolar nuclear-bath dynamics that both limit decoherence and offer a new avenue for quantum metrology.

High-Fidelity Hole Spin Qubits and Nuclear-Bath Dynamics in Isotopically Purified Planar Ge

Introduction

The performance, scalability, and ultimate feasibility of quantum computing architectures based on semiconductor spin qubits are fundamentally constrained by the interaction of qubits with their nuclear spin environments. Germanium (Ge) planar heterostructures, particularly those hosting two-dimensional hole gases (2DHGs), have drawn considerable attention due to their strong spin-orbit coupling and compatibility with advanced semiconductor fabrication. However, the hyperfine interaction between qubits and residual $^{73}$Ge nuclear spins represents a principal source of dephasing. This work presents the synthesis and characterization of isotopically purified planar Ge quantum wells with substantially reduced $^{73}$Ge abundance, enabling order-of-magnitude improvements in coherence while revealing previously unobserved quadrupolar dynamics in the nuclear bath.

Synthesis of Isotopically Purified Ge Heterostructures

The Ge/SiGe quantum well heterostructures were grown using ultra-high vacuum chemical vapor deposition (UHV-CVD) with isotopically enriched $^{70}$GeH$_4$ as precursor. The resulting quantum wells exhibit a $^{73}$Ge abundance below 0.4%, which is a 20-fold reduction over natural Ge. Secondary ion mass spectrometry (SIMS) and quantum Hall transport measurements confirm high isotopic purity, well-defined QHE plateaus, and high hole mobility up to $9.3 \times 10^5$ cm$^2$/Vs. While not yet at the mobility record for natural Ge, the primary limiting factors are identified as background impurity and interface roughness within the enriched layer, both tractable with further purification and growth optimization.

Device Architecture and Qubit Operation

Electrostatically defined double quantum dots in the isotopically purified 2DHG serve as hosts for hole spin qubits. Charge sensing is implemented via an adjacent single hole transistor (SHT) with high-bandwidth readout circuitry. These devices support initialization, manipulation, and readout protocols using Pauli spin blockade (PSB) latency schemes and electrical dipole spin resonance (EDSR). The measured devices allow for coherent manipulation and high-fidelity single-shot spin state readout.

Coherence Extension and Qubit Fidelity

The hallmark result is the demonstration of significantly extended inhomogeneous dephasing times $T^*_2$, particularly:

• At the hyperfine interaction sweet spot: $T^*_2 = 22.5\,\mu\mathrm{s}$, setting a new benchmark for Ge hole qubits.
• Off the sweet spot: $T^*_2$ exceeds $^{73}$0, a 5-fold improvement over previous devices operating in natural Ge.

The dependence of $^{73}$1 on magnetic field orientation confirms sweet-spot tunability, but highlights site-to-site g-tensor variation—a crucial consideration for large-scale integration. Notably, single-qubit gate fidelities above 99.9% are achieved both on and off the sweet spot, a strong claim that demonstrates the necessity and sufficiency of isotopic purification for robust scaling.

Spectroscopic Exploration of Nuclear-Bath Dynamics

Employing Hahn-echo spectroscopy, the authors not only confirm expected Larmor-linked hyperfine noise from residual $^{73}$2Ge but resolve an additional, field-stationary component attributable to quadrupolar nuclear resonance (NQR) processes. Key observations include:

• Echo collapse-and-revival features that cannot be explained by Larmor precession alone.
• Fit to a noise power spectral density (PSD) comprising charge noise, hyperfine peaks, and ensemble-broadened NQR-like branches.
• Dominant, angular-dependent quadrupolar branch centered at $^{73}$3 (consistent with $^{73}$4 of $^{73}$5Ge nuclei experiencing local EFGs at the Ge/SiGe interface) and another feature near $^{73}$6.

Angular dependence of quadrupolar noise visibility demonstrates sensitivity to local electric field gradients, suggesting the axes of the EFG, quantization, and hyperfine transduction tensors are generally non-collinear. These findings indicate a practical route for using hole spin qubits as local probes of interfacial disorder, strain, and electric field environments, which could inform next-generation device engineering.

Theoretical and Practical Implications

The work advances understanding of hole spin decoherence in Ge qubits by demonstrating that, at reduced $^{73}$7Ge content, quadrupolar channels emerge as an intrinsic limit to further coherence improvement. This mechanism parallels the quadrupole-dominated decoherence already well-studied in GaAs and, to a lesser extent, Si spin qubits, though the geometrical and interfacial dependencies in Ge present novel challenges and opportunities.

Practical consequences of this research include:

• Establishing isotopically purified planar Ge as a platform capable of delivering high-fidelity (>99.9%), scalable hole spin qubits.
• Demonstrating the effectiveness of isotope engineering in the Group-IV family—mirroring and extending the silicon paradigm.
• Revealing a spectroscopically accessible nuclear quadrupolar channel, which can serve both as performance constraint and as a metrological tool for interface and strain mapping.

Speculation on future directions:

• Further precursor purification and interface engineering are anticipated to push $^{73}$8Ge content even lower; recent demonstrations report $^{73}$9 $^{70}$0Ge, which should correspondingly extend $^{70}$1 and further suppress hyperfine/quadruple noise.
• The controllable interaction between hole spins and single $^{70}$2Ge nuclei, now rendered visible by the suppressed nuclear background, could support hybrid electron-nuclear spin quantum registers or high-resolution electrometers.
• These results point toward advanced architectures leveraging tunable strain, EFGs, and electric fields to engineer the eigenmode structure of the nuclear bath for optimal qubit performance or for novel sensor modalities.

Conclusion

This work establishes a robust empirical link between isotopic purification and coherence improvement in planar Ge hole spin qubits, simultaneously providing detailed spectroscopic insight into the quadrupolar dynamics of the nuclear bath proximate to heterostructure interfaces. The strong numerical results, including $^{70}$3 and gate fidelities $^{70}$4 off sweet spots, underscore the feasibility of scalable, high-performance Ge-based qubit architectures. Finally, the demonstrated sensitivity of hole spin qubits to local quadrupolar nuclear environments lays the groundwork for both improved device engineering and new quantum metrology approaches.