Sweet-spot operation of a germanium hole spin qubit with highly anisotropic noise sensitivity

Quantum Physics Information Science Physics Semiconductors and Information Devices Condensed Matter Physics
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Optimal Working Point of Heavy Hole Spin Qubit in Germanium and Its High Anisotropic Noise Sensitivity

Background and Motivation

Heavy Hole Double Quantum System

The development of quantum computers holds great promise for solving complex problems. However, building a fault-tolerant quantum computer requires the integration of a large number of highly coherent qubits. Spin qubits, especially those based on hole qubits in germanium (Ge) quantum wells, have been increasingly recognized due to their low-noise environment, efficient control, and ease of fabrication. Nevertheless, controlling these qubits often encounters decoherence and control challenges caused by the anisotropy of the g-tensor induced by electric fields.

It is particularly noteworthy that heavy holes play a crucial role in these spin qubits. Heavy hole spin qubits not only allow for fast and high-fidelity operations but also enable rapid scalable qubit control through electric fields. However, the nature of driving mechanisms and decoherence, as well as the anisotropy issues involved, have not been fully understood.

Summary of the Paper

This paper, written by scientists from IBM Research Europe-Zurich and IBM Quantum, T. J. Watson Research Center, includes major authors such as N.W. Hendrickx, L. Massai, M. Mergenthaler, F.J. Schupp, S. Paredes, S.W. Bedell, G. Salis, and A. Fuhrer. It was published in “Nature Materials” in 2024, exploring the driving mechanisms and decoherence mechanisms of heavy hole spin qubits in germanium.

Research Process and Experimental Details

This experiment defined a double-qubit system based on hole spins confined in strained Ge/SiGe heterostructure quantum wells. By measuring the charge stability diagram with a charge sensor, Pauli spin blockade readout in the (1,1) charge state was performed to distinguish |↓↓⟩ and |↓↑⟩ states.

Heavy Hole g-Tensor Measurement

The confinement of holes in a two-dimensional strained germanium quantum well separates heavy hole and light hole bands. The heavy hole component in the hole wave function affects the g-tensor, resulting in high anisotropy. This g-tensor can be described as a rotated diagonal 3×3 matrix, revealing that the substantial anisotropy of the heavy hole g-tensor aligns almost with the growth direction z of the sample, being approximately 30 and 180 times gx’ and gy’, respectively.

This anisotropy causes a misalignment between the quantization axis of the qubit and the applied magnetic field, reflecting the influence of local strain gradients on the g-tensor. Evaluation of the influence of electric fields from different directions on the orientation of the qubit quantization axis revealed that the g-tensor is particularly sensitive to electric fields, significantly modulating the qubit’s Larmor frequency.

Electric Field Sensitivity and Verification of Omnidirectional Electric Field and Noise Interaction

Using the Hahn echo experiment, the sensitivity of q2’s frequency to potential changes on the gate electrode was measured. It was found that decoherence occurs when frequency changes parallel (longitudinal) to electric field fluctuations, while perpendicular changes (transverse) drive qubit operations via g-tensor magnetic resonance. Experimental results showed that coherence time improved by more than an order of magnitude based on electric field sensitivity to various magnetic field directions.

Further Confirmation of Experimental Results

Through g-tensor magnetic resonance, the reconstructed ∂⃖⃗g/∂vi closely estimated and adjusted the omnidirectionality of qubits under high g-tensor anisotropy. Results consistent with expected Rabi frequencies and g-tensor magnetic resonance effects confirmed the strictness of this theoretical prediction. The relationship between qubit frequency sensitivity and noise data further verified the effectiveness of a series of experiments.

Main Research Results and Contributions

  1. Confirmation of Heavy Hole g-Tensor Anisotropy: The experiment fully characterized the heavy hole g-tensor influenced by electric fields, revealing its high anisotropic properties for the first time.
  2. Electric Field-Induced Decoherence and Qubit Driving Mechanism: The study showed that qubit decoherence mainly stems from electric field modulation of the g-tensor and predictive Ising-type hyperfine interaction effects, analyzing the main influence of charge noise on quanta.
  3. Optimal Working Point Selection: Operating qubits at low magnetic fields can significantly enhance coherence time, while maintaining high single-qubit gate fidelity (>99%) even at high temperatures (>1 K).
  4. New Material Usage Recommendations: Despite the anisotropy limitations of germanium quantum wells in some application ideal working points, practical application can further optimize performance through Germanium isotopic purification technology, significantly reducing the nuclear noise interference with qubits.

Conclusion and Outlook

Through systematic experiments and data analysis, this paper identifies various physical properties and the optimal operation point of heavy hole spin qubits in germanium quantum wells. This not only provides important guidance for the design of future large-scale, high-fidelity qubit arrays but also offers a theoretical basis for developing more efficient qubit driving and protection mechanisms. Future optimization of quantum dot materials and isotopic purification techniques is expected to significantly enhance the work efficiency and stability of qubits.