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arXiv:2204.08212 · Physical Review Applied

Hole Spin Qubits in Thin Curved Quantum Wells

Stefano Bosco, Daniel Loss

Published Oct 14, 2022• 25 citations
arXivHTMLPDF

Abstract

Hole spin qubits are frontrunner platforms for scalable quantum computers because of their large spin-orbit interaction that enables ultrafast all-electric qubit control at low power. The fastest spin qubits to date are defined in long quantum dots with two tight confinement directions, when the driving field is aligned to the smooth direction. However, in these systems the lifetime of the qubit is strongly limited by charge noise, a major issue in hole qubits. We propose here a different, scalable qubit design, compatible with planar CMOS technology, where the hole is confined in a curved germanium quantum well surrounded by silicon. This design takes full advantage of the strong spin-orbit interaction of holes, and at the same time suppresses charge noise in a wide range of configurations, enabling highly coherent, ultrafast qubit gates. While here we focus on a $\mathrm{Si}$/$\mathrm{Ge}$/$\mathrm{Si}$ curved quantum well, our design is also applicable to different semiconductors. These devices allow for ultrafast operations even in short quantum dots by a transversal electric field. This additional driving mechanism relaxes the demanding design constraints, and offers a way to reliably interface spin qubits in a single quantum dot to microwave photons. By considering state-of-the-art high-impedance resonators and realistic qubit designs, we estimate interaction strengths of a few hundreds of megahertz, largely exceeding the decay rate of spins and photons. Reaching such a strong coupling regime in hole spin qubits will be a significant step towards high-fidelity entangling operations between distant qubits, as well as fast single-shot readout, and could pave the way towards the implementation of a large-scale semiconducting quantum processor.

DOI
10.1103/physrevapplied.18.044038

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Hole spin qubits are frontrunner platforms for scalable quantum computers because of their large spin-orbit interaction that enables ultrafast all-electric qubit control at low power. The fastest spin qubits to date are defined in long quantum dots with two tight confinement directions, when the driving field is aligned to the smooth direction. However, in these systems the lifetime of the qubit is strongly limited by charge noise, a major issue in hole qubits. We propose here a different, scalable qubit design, compatible with planar CMOS technology, where the hole is confined in a curved germanium quantum well surrounded by silicon. This design takes full advantage of the strong spin-orbit interaction of holes, and at the same time suppresses charge noise in a wide range of configurations, enabling highly coherent, ultrafast qubit gates. While here we focus on a Si\mathrm{Si}Si/Ge\mathrm{Ge}Ge/Si\mathrm{Si}Si curved quantum well, our design is also applicable to different semiconductors. These devices allow for ultrafast operations even in short quantum dots by a transversal electric field. This additional driving mechanism relaxes the demanding design constraints, and offers a way to reliably interface spin qubits in a single quantum dot to microwave photons. By considering state-of-the-art high-impedance resonators and realistic qubit designs, we estimate interaction strengths of a few hundreds of megahertz, largely exceeding the decay rate of spins and photons. Reaching such a strong coupling regime in hole spin qubits will be a significant step towards high-fidelity entangling operations between distant qubits, as well as fast single-shot readout, and could pave the way towards the implementation of a large-scale semiconducting quantum processor.
Spin qubits in semiconductor quantum dots constitute one of the leading platforms for quantum information processing, combining long coherence times, high-fidelity gate operations, and compatibility with semiconductor industry technologies. In particular, holes confined in planar Ge/SiGe heterostructures have recently emerged as promising qubit candidates owing to their low effective mass, high mobility, low percolation density, absence of valley states, and strong spin-orbit interaction, which enables fast all-electrical spin control. At the same time, spin-orbit interaction also gives rise to a highly anisotropic and electrically tunable gyromagnetic response. Understanding and controlling this response is therefore essential for high-fidelity single- and multi-qubit operations. The realization of scalable quantum processors also requires efficient qubit readout and long-range connectivity. Circuit quantum electrodynamics (cQED), based on the coupling between artificial atoms and microwave photons confined in superconducting resonators, provides a natural framework to address these challenges. However, the implementation of hybrid semiconductor-superconductor devices in planar Ge has so far been hindered by large microwave losses originating from the heterostructure. In this thesis, we demonstrate, for the first time in planar Ge, strong coupling between a hole charge qubit in a double quantum dot and a high-impedance microwave resonator, reaching a cooperativity of C â 100. In addition, we leverage the frequency tunability of the resonator to perform detailed spectroscopy of a multi-level energy spectrum of low-lying states arising from strong Coulomb-correlation effects. To further improve the quality of the hole-photon interface, we investigate the source of microwave losses in different Ge/SiGe heterostructures, identifying defects at the lattice-mismatched Si/Ge interface as the dominant source of resonator losses in reverse-graded heterostructures. To mitigate this limitation, a deep tapered-etching approach is introduced, enabling the fabrication of superconducting resonators directly on etched heterostructures. This method yields internal quality factors exceeding Qint > 10 000 for high-impedance Josephson junction array resonators and Qint > 100 000 for 50 â Nb resonators. Finally, this thesis explores the spin properties of multi-hole quantum dots beyond the conventional single-orbital picture. By reconstructing and electrically tuning the g tensors of holes confined in different orbital states, we show that confinement can substantially modify both their magnitude and orientation. These results open new opportunities for engineering qubit properties through orbital occupation. Furthermore, highly coherent singlet-triplet oscillations are demonstrated in the seven-hole regime, yielding a quality factor of approximately 330 at in-plane magnetic fields as low as 2.5 mT. Together, these results establish a foundation for high-fidelity hole-spin-qubit operation based on g-tensor engineering and for the integration of planar Ge quantum dots with superconducting quantum circuits.
Coherent and strong coupling between photons and solid-state qubits, in the form of circuit quantum electrodynamics (QED), has been harnessed for two-qubit gates mediated by photons and high-fidelity quantum non-demolition readout, which are the building blocks of large-scale quantum computation. Recently, circuit QED has been extended to gate-defined semiconductor quantum dots. In this thesis, we develop a novel hybrid circuit QED architecture composed of a high-impedance superconducting microwave resonator and spins localized in silicon-MOS quantum dots. To control and measure the spin degrees of freedom, this hybrid system needs to operate at finite magnetic field. Consequently, we develop and characterize microwave resonators based on thin niobium nitride (NbN) films featuring a high kinetic inductance. We demonstrate high-impedance resonators with magnetic field resilience and low photon loss rates. We then co-integrate the NbN resonators on silicon spin qubit chips. With a hole confined in a double quantum dot (DQD), we report the first realization of a strong hole charge-photon interaction bordering the ultra-strong coupling regime. At finite magnetic field, putting the spin transition energy in resonance with the microwave cavity, we observe large vacuum Rabi mode splittings, signature of a strong spin-photon coupling. Our findings are well captured by the modelling of a hole DQD with different anisotropic Zeeman response in each dot and spin-orbit coupling dependent tunnel rates. We also find a sizeable spin-photon coupling when the hole is localized in the single quantum dot, in line with recent theoretical predictions. The different works presented in this manuscript pave the way for circuit QED with hole spins in gate-defined semiconductor quantum dots.
The selective confinement of light holes (LHs) is demonstrated by introducing a low-dimensional system consisting of a highly tensile-strained Ge quantum well enabling the design of an ultrafast gate-defined spin qubit under the electric dipole spin resonance. The qubit size-dependent ggg factor and dipole moment are mapped, and the parameters inducing their modulation are discussed. It is found that the LH qubit dipole moment is two to three orders of magnitude higher than that of the canonical heavy-hole qubit. This behavior originates from the significant spin splitting resulting from the combined action of large cubic and linear Rashba spin-orbit interactions that are peculiar to LHs. The qubit relaxation rate is also affected by the strong spin-orbit interaction and follows typically a B7{B}^{7}B7 behavior. The proposed all-group IV, direct band-gap LH qubit provides an effective platform for a scalable qubit-optical photon interface sought after for long-range entanglement distribution and quantum networks.
Hole spin qubits hosted in Germanium quantum dots are promising candidates for scalable quantum computing. The strong spin-orbit interaction can enable fast and all-electrical quantum control. Furthermore, the platform can implement universal quantum control using only baseband signals, which may mitigate the impact of crosstalk and microwave-induced heating. At the same time, spin-orbit interaction gives rise to an anisotropic exchange interaction, whose potential for implementing two-qubit gates has remained largely unexplored. However, the current performance of operating a hole-based quantum computer is mostly limited by dephasing due to low-frequency charge noise. In this work, we propose a novel two-qubit gate protocol for Germanium hole spin qubits operated in the gapless regime. This gate protocol exploits the anisotropic exchange interaction between neighboring spins and utilizes a composite pulse scheme implemented solely through electrical baseband signals. Using this approach, we predict high-fidelity two-qubit controlled-Z operations that can suppress exchange-energy fluctuations, offering a pathway toward fault-tolerant semiconductor quantum processors.
Hole spin qubits hosted in Germanium quantum dots are promising candidates for scalable quantum computing. The strong spin-orbit interaction can enable fast and all-electrical quantum control. Furthermore, the platform can implement universal quantum control using only baseband signals, which may mitigate the impact of crosstalk and microwave-induced heating. At the same time, spin-orbit interaction gives rise to an anisotropic exchange interaction, whose potential for implementing two-qubit gates has remained largely unexplored. However, the current performance of operating a hole-based quantum computer is mostly limited by dephasing due to low-frequency charge noise. In this work, we propose a novel two-qubit gate protocol for Germanium hole spin qubits operated in the gapless regime. This gate protocol exploits the anisotropic exchange interaction between neighboring spins and utilizes a composite pulse scheme implemented solely through electrical baseband signals. Using this approach, we predict high-fidelity two-qubit controlled-Z operations that can suppress exchange-energy fluctuations, offering a pathway toward fault-tolerant semiconductor quantum processors.
Hole spin qubits in semiconductor quantum dots (QDs) enable high-fidelity all-electric control, but conventional electric dipole spin resonance (EDSR) can require substantial rf drive power at the low magnetic fields that are favorable for qubit coherence and readout. In planar Ge hole spin qubits, this can reach -27 dBm at the device, posing challenges for scalable architectures due to heating and crosstalk. Here, we demonstrate a flopping-mode (FM) qubit in Ge, where a single spin is delocalized in a double QD, combining first-order protection against charge noise with exceptionally efficient electric driving. By mapping out coherence sweet-spots as a function of magnetic field orientation we achieve T2∗=1.4μsT_2^*= 1.4μ\mathrm{s}T2∗​=1.4μs, T2Hahn=11.5μsT_2^{\mathrm{Hahn}}= 11.5 μ\mathrm{s}T2Hahn​=11.5μs, T2φ,CPMG32=130μsT^{φ, \mathrm{CPMG32}}_2= 130 μ\mathrm{s}T2φ,CPMG32​=130μs, and T1=226μsT_1= 226 μ\mathrm{s}T1​=226μs, and a single-qubit gate fidelity of up to 99.76%\%% for a gate time tXπ=88t_{Xπ} = 88tXπ​=88 ns. Importantly, these results are obtained at a nearly in-plane magnetic field of 5 mT using only -52 dBm drive power at the device. We further find that qubit relaxation in this regime is consistent with a two-photon Orbach process, providing a route for further optimization. Our results demonstrate that FM-EDSR supports ultra-low-power, high-fidelity single-qubit operations, improvements that could benefit scalable hole-spin-based architectures and hybrid spin-photon interfaces.