[Paper Review] Fully tunable hyperfine interactions of hole spin qubits in Si and Ge quantum dots

Bosco, Stefano, Loss, Daniel|arXiv (Cornell University)|Jun 25, 2021

Quantum and electron transport phenomena61 citations

TL;DR

This paper demonstrates that hyperfine interactions in hole spin qubits within Si and Ge quantum dots can be fully tuned via device design and external electric fields, enabling hyperfine noise suppression by an order of magnitude. By exploiting strong spin-orbit coupling in elongated quantum dots, the authors identify tunable 'sweet spots' where both hyperfine and charge noise are simultaneously minimized, significantly enhancing qubit coherence and gate fidelity without requiring isotopic purification.

ABSTRACT

Hole spin qubits are frontrunner platforms for scalable quantum computers, but state-of-the-art devices suffer from noise originating from the hyperfine interactions with nuclear defects. We show that these interactions have a highly tunable anisotropy that is controlled by device design and external electric fields. This tunability enables sweet spots where the hyperfine noise is suppressed by an order of magnitude and is comparable to isotopically purified materials. We identify surprisingly simple designs where the qubits are highly coherent and are largely unaffected by both charge and hyperfine noise. We find that the large spin-orbit interaction typical of elongated quantum dots not only speeds up qubit operations, but also dramatically renormalizes the hyperfine noise, altering qualitatively the dynamics of driven qubits and enhancing the fidelity of qubit gates. Our findings serve as guidelines to design high performance qubits for scaling up quantum computers.

Motivation & Objective

• To address the major decoherence source in hole spin qubits—hyperfine interactions with nuclear defects in Si and Ge quantum dots.
• To investigate whether these hyperfine interactions can be engineered and tuned via external electric fields and device geometry.
• To identify optimal operating points where both hyperfine and charge noise are minimized, enhancing qubit coherence.
• To explore the interplay between direct Rashba spin-orbit coupling (DRSOI) and hyperfine interactions, and its impact on qubit dynamics and gate fidelity.
• To provide design guidelines for scalable, high-performance hole spin qubits in realistic device architectures such as FinFETs.

Proposed method

• Modeling the hole quantum dot system using a Luttinger-Kohn Hamiltonian with a confining potential and an external electric field Ey perpendicular to the long axis.
• Numerically solving the Schrödinger equation to determine spinor wavefunctions ψH,L(ρ) and the spin-orbit length lSO, which depend on Ey.
• Computing the hyperfine coupling matrix Γ(r) and g-factor tensor gij using spin-resolved wavefunctions and the DRSOI-induced phase rotation.
• Projecting the hyperfine and Zeeman Hamiltonians onto the spin-singlet ground state to derive the Overhauser field h and its covariance matrix Σ.
• Using a Gaussian noise model for nuclear spins to compute the qubit dephasing time T0 and transition probability P(t), incorporating both Gaussian and power-law decay components.
• Applying analytical approximations to the spin dynamics under time-dependent fields, including Rabi oscillations and dephasing, under the assumption ℏω ≫ √Σii.

Experimental results

Research questions

• RQ1 Can hyperfine interactions in hole spin qubits be fully tuned via external electric fields and device geometry in Si and Ge quantum dots?
• RQ2 What are the conditions under which both hyperfine and charge noise are simultaneously suppressed in hole spin qubits?
• RQ3 How does the strong direct Rashba spin-orbit interaction (DRSOI) renormalize hyperfine noise and alter qubit dynamics in driven experiments?
• RQ4 What is the impact of DRSOI on the fidelity of electrically driven single-qubit gates in hole spin qubits?
• RQ5 Can the tunability of hyperfine interactions enable high-coherence qubits without isotopic purification?

Key findings

• Hyperfine noise is suppressed by an order of magnitude in optimized device designs, achieving coherence comparable to isotopically purified materials without requiring isotopic enrichment.
• In Si FinFETs, there exist working points where both hyperfine and charge noise are simultaneously suppressed, leading to significantly enhanced qubit coherence.
• The DRSOI-induced spin-orbit length lSO strongly renormalizes the hyperfine noise, altering the decay dynamics from Gaussian to a combination of Gaussian and power-law components.
• For natural Si and Ge quantum dots with ~10^4 atoms, the characteristic dephasing time T0 is ~0.36 µs (Si) and ~0.11 µs (Ge), which are substantially extended through tuning.
• The interplay between DRSOI and hyperfine interactions leads to a qualitative change in driven qubit dynamics, enhancing gate fidelity and enabling faster, more coherent operations.
• The analytical framework accurately captures long-time spin decay even when hyperfine broadening is comparable to Rabi frequency, validating the use of approximate models in realistic parameter regimes.