Zoltán György

Hole spin qubits provide one of the leading platforms for spin-based quantum computing due to their large intrinsic spin-orbit interaction (SOI), which enables fast electrical manipulation. The SOI of planar quantum dots has mostly been investigated in theoretical studies by examining the SOI already present in the two-dimensional hole gas (2DHG). Here, we study the SOI created by the in-plane confinement by deriving non-perturbative effective Hamiltonians numerically for hole spin qubits. We find that the quantum geometry of the 2DHG naturally emerges, leading to a meaningful non-perturbative definition of pseudospin valid far away from the $Γ$-point. The SOI of the 2DHG and of the in-plane confinement have different forms; therefore, they cannot be turned off simultaneously, ruining the perfect spin-orbit switch functionality of spin qubits. We construct effective Hamiltonians using the symmetry approach for various low-dimensional hole systems: (i) a heavy-hole confined in a SiGe/Ge/SiGe heterostructure, (ii) a light-hole confined in SnGe/Ge, (iii) a gate-defined nanowire in SiGe/Ge/SiGe, and (iv) a hole confined in a Ge/Si core/shell nanowire. The non-perturbative effective Hamiltonians provide results with excellent agreement with the full Hamiltonians.

The g-tensor formalism is a powerful method for describing the electrical driving of semiconductor spin qubits. However, up to now, this technique has only been applied to the simplest qubit dynamics, resonant monochromatic driving by a single gate. Here we study the description of (i) monochromatic driving using two driving gates and bichromatic driving via (ii) one or (iii) two gates. Assuming a general Hamiltonian with qubit states well separated from excited orbital states, we find that when (i) two driving gates are used for monochromatic driving or (ii) a single one for bichromatic, the $g$-tensor formalism successfully captures the leading-order dynamics. We express the Rabi frequency and the Bloch-Siegert shift using the $g$-tensor and its first and second derivatives with respect to the gate voltage. However, when (iii) bichromatic driving is realized using two distinct driving gates, we see a breakdown of $g$-tensor formalism: the Rabi frequency cannot be expressed using the $g$-tensor and its derivatives. We find that beyond the $g$-tensor and its derivatives, three additional parameters are needed to capture the dynamics. We demonstrate our general results by assuming an electron (hole) confined in a circular quantum dot, subjected to Rashba spin-orbit interaction.

Electrically driven spin resonance is a powerful technique for controlling semiconductor spin qubits. However, it faces challenges in qubit addressability and off-resonance driving in larger systems. We demonstrate coherent bichromatic Rabi control of quantum dot hole spin qubits, offering a spatially selective approach for large qubit arrays. By applying simultaneous microwave bursts to different gate electrodes, we observe multichromatic resonance lines and resonance anticrossings that are caused by the ac Stark shift. Our theoretical framework aligns with experimental data, highlighting interdot motion as the dominant mechanism for bichromatic driving.

Electrically driven spin resonance (EDSR) is an established tool for controlling semiconductor spin qubits. Here, we theoretically study a frequency-mixing variant of EDSR, where two driving tones with different drive frequencies are applied, and the resonance condition connects the spin Larmor frequency with the sum of the two drive frequencies. Focusing on flopping-mode operation, we calculate the parameter dependence of the Rabi frequency and the Bloch-Siegert shift. A shared-control spin qubit architecture could benefit from this bichromatic EDSR scheme, as it enables simultaneous single-qubit gates.