Holes confined in quantum dots have gained considerable interest in the past few years due to their potential as spin qubits. Here we demonstrate two-axis control of a spin 3/2 qubit in natural Ge. The qubit is formed in a hut wire double quantum dot device. The Pauli spin blockade principle allowed us to demonstrate electric dipole spin resonance by applying a radio frequency electric field to one of the electrodes defining the double quantum dot. Coherent hole spin oscillations with Rabi frequencies reaching 140 MHz are demonstrated and dephasing times of 130 ns are measured. The reported results emphasize the potential of Ge as a platform for fast and electrically tunable hole spin qubit devices.

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A germanium hole spin qubit.

In the effort to develop disruptive quantum technologies, germanium is emerging as a versatile material to realize devices capable of encoding, processing and transmitting quantum information. These devices leverage the special properties of holes in germanium, such as their inherently strong spin–orbit coupling and their ability to host superconducting pairing correlations. In this Review, we start by introducing the physics of holes in low-dimensional germanium structures, providing key insights from a theoretical perspective. We then examine the materials-science progress underpinning germanium-based planar heterostructures and nanowires. We go on to review the most significant experimental results demonstrating key building blocks for quantum technology, such as an electrically driven universal quantum gate set with spin qubits in quantum dots and superconductor–semiconductor devices for hybrid quantum systems. We conclude by identifying the most promising avenues towards scalable quantum information processing in germanium-based systems. Germanium is a promising material to build quantum components for scalable quantum information processing. This Review examines progress in materials science and devices that has enabled key building blocks for germanium quantum technology, such as hole-spin qubits and superconductor–semiconductor hybrids.

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The germanium quantum information route

In the worldwide endeavor for disruptive quantum technologies, germanium is emerging as a versatile material to realize devices capable of encoding, processing, or transmitting quantum information. These devices leverage special properties of the germanium valence-band states, commonly known as holes, such as their inherently strong spin-orbit coupling and the ability to host superconducting pairing correlations. In this Review, we initially introduce the physics of holes in low-dimensional germanium structures with key insights from a theoretical perspective. We then examine the material science progress underpinning germanium-based planar heterostructures and nanowires. We review the most significant experimental results demonstrating key building blocks for quantum technology, such as an electrically driven universal quantum gate set with spin qubits in quantum dots and superconductor-semiconductor devices for hybrid quantum systems. We conclude by identifying the most promising prospects toward scalable quantum information processing.

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Semiconductors, a significant type of material in the information era, are becoming more and more powerful in the field of quantum information. In recent decades, semiconductor quantum computation was investigated thoroughly across the world and developed with a dramatically fast speed. The research varied from initialization, control and readout of qubits, to the architecture of fault-tolerant quantum computing. Here, we first introduce the basic ideas for quantum computing, and then discuss the developments of single- and two-qubit gate control in semiconductors. Up to now, the qubit initialization, control and readout can be realized with relatively high fidelity and a programmable two-qubit quantum processor has even been demonstrated. However, to further improve the qubit quality and scale it up, there are still some challenges to resolve such as the improvement of the readout method, material development and scalable designs. We discuss these issues and introduce the forefronts of progress. Finally, considering the positive trend of the research on semiconductor quantum devices and recent theoretical work on the applications of quantum computation, we anticipate that semiconductor quantum computation may develop fast and will have a huge impact on our lives in the near future.

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Semiconductor quantum computation

The strong coupling limit of cavity quantum electrodynamics (QED) implies the capability of a matter-like quantum system to coherently transform an individual excitation into a single photon within a resonant structure. This not only enables essential processes required for quantum information processing but also allows for fundamental studies of matter-light interaction. In this work we demonstrate strong coupling between the charge degree of freedom in a gate-detuned GaAs double quantum dot (DQD) and a frequency-tunable high impedance resonator realized using an array of superconducting quantum interference devices (SQUIDs). In the resonant regime, we resolve the vacuum Rabi mode splitting of size $2g/2\pi = 238$ MHz at a resonator linewidth $\kappa/2\pi = 12$ MHz and a DQD charge qubit dephasing rate of $\gamma_2/2\pi = 80$ MHz extracted independently from microwave spectroscopy in the dispersive regime. Our measurements indicate a viable path towards using circuit based cavity QED for quantum information processing in semiconductor nano-structures.

Strong Coupling Cavity QED with Gate-Defined Double Quantum Dots Enabled by a High Impedance Resonator

Abstract Operation speed and coherence time are two core measures for the viability of a qubit. Strong spin-orbit interaction (SOI) and relatively weak hyperfine interaction make holes in germanium (Ge) intriguing candidates for spin qubits with rapid, all-electrical coherent control. Here we report ultrafast single-spin manipulation in a hole-based double quantum dot in a germanium hut wire (GHW). Mediated by the strong SOI, a Rabi frequency exceeding 540 MHz is observed at a magnetic field of 100 mT, setting a record for ultrafast spin qubit control in semiconductor systems. We demonstrate that the strong SOI of heavy holes (HHs) in our GHW, characterized by a very short spin-orbit length of 1.5 nm, enables the rapid gate operations we accomplish. Our results demonstrate the potential of ultrafast coherent control of hole spin qubits to meet the requirement of DiVincenzo’s criteria for a scalable quantum information processor. 

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Ultrafast coherent control of a hole spin qubit in a germanium quantum dot

Realizing a strong coupling between spin and resonator is an important issue for scalable quantum computation in semiconductor systems. Benefiting from the advantages of a strong spin–orbit coupling strength and long coherence time, the Ge hut wire, which is proposed to be site-controlled grown for scalability, is considered to be a promising candidate to achieve this goal. Here we present a hybrid architecture in which an on-chip superconducting microwave resonator is coupled to the holes in a Ge quantum dot. The charge stability diagram can be obtained from the amplitude and phase responses of the resonator independently from the DC transport measurement. Furthermore, we estimate the hole-resonator coupling rate of gc/2π = 148 MHz in the single quantum dot-resonator system and estimate the spin–resonator coupling rate gs/2π to be in the range 2–4 MHz. We anticipate that strong coupling between hole spins and microwave photons in a Ge hut wire is feasible with optimized schemes in the future.

Coupling a Germanium Hut Wire Hole Quantum Dot to a Superconducting Microwave Resonator.

As a group IV material with confined holes, the germanium hut wire is considered a promising candidate for achieving fast electrically controlled spin qubits. Here we fabricated a single quantum dot device on a germanium hut wire and a standard charge stability diagram with excited states was observed by DC transport measurements. By analyzing the Zeeman splitting behaviors of each state, we chose a window for distinguishing different hole parities and spin states, launching the first step towards a useful spin qubit. Effective g-factors around 4.3 for both even and odd hole number states were also extracted.

Measuring hole spin states of single quantum dot in germanium hut wire

The germanium (Ge) hut wire system has strong spin-orbit coupling, a long coherence time due to a very large heavy-light hole splitting, and the advantage of site-controlled large-scale hut wire positioning. These properties make the Ge hut wire a promising candidate for the realization of strong coupling of spin to superconducting resonators and scalability for multiple qubit coupling. We have coupled a reflection line resonator to a hole double quantum dot (DQD) formed in Ge hut wire. The amplitude and phase responses of the microwave resonator revealed that the charge stability diagrams of the DQD are in good agreement with those obtained from transport measurements. The DQD interdot tunneling rate is shown to be tunable from 6.2 GHz to 8.5 GHz, which demonstrates the ability to adjust the frequency detuning between the qubit and the resonator. Furthermore, we achieved a hole-resonator coupling strength of up to 15 MHz, with a charge qubit decoherence rate of 0.28 GHz. Meanwhile the hole spin-resonator coupling rate was estimated to be 3 MHz. These results suggest that holes of a DQD in a Ge hut wire are dipole coupled to microwave photons, potentially enabling tunable hole spin-photon interactions in Ge with an inherent spin-orbit coupling.

Gang Xu

Papers

Ultrafast coherent control of a hole spin qubit in a germanium quantum dot

Coupling a Germanium Hut Wire Hole Quantum Dot to a Superconducting Microwave Resonator.

Measuring hole spin states of single quantum dot in germanium hut wire

Dipole coupling of a tunable hole double quantum dot in germanium hut wire to a microwave resonator

Dipole coupling of a hole double quantum dot in germanium hut wire to a microwave resonator