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.

Hole spins have gained considerable interest in the past few years due to their potential for fast electrically controlled qubits. Here, we study holes confined in Ge hut wires, a so-far unexplored type of nanostructure. Low-temperature magnetotransport measurements reveal a large anisotropy between the in-plane and out-of-plane g-factors of up to 18. Numerical simulations verify that this large anisotropy originates from a confined wave function of heavy-hole character. A light-hole admixture of less than 1% is estimated for the states of lowest energy, leading to a surprisingly large reduction of the out-of-plane g-factors compared with those for pure heavy holes. Given this tiny light-hole contribution, the spin lifetimes are expected to be very long, even in isotopically nonpurified samples.

Spin qubits are considered to be among the most promising candidates for building a quantum processor 1 . Group IV hole spin qubits have moved into the focus of interest due to the ease of operation and compatibility with Si technology 2;3;4;5;6 . In addition, Ge offers the option for monolithic superconductor-semiconductor integration. Here we demonstrate a hole spin qubit operating at fields below 10 mT, the critical field of Al, by exploiting the large out-ofplane hole g-factors in planar Ge and by encoding the qubit into the singlet-triplet states of a double quantum dot 7;8 . We observe electrically controlled X and Z-rotations with tunable frequencies exceeding 100 MHz and dephasing times of 1 µs which we extend beyond 15 µs with echo techniques. These results show that Ge hole singlet triplet qubits outperform their electronic Si and GaAs based counterparts in speed and dephasing time, respectively. In addition, their rotation frequency and coherence time are on par with Ge single spin qubits, but they can be operated at much lower fields underlining their potential for on chip integration with superconducting technologies.

attention due to its high hole mobility, [10][11][12][13] low effective mass in 2D hole gases, [14,15] good contacts with metals, [16][17][18] strong spin-orbit interactions, [19][20][21][22] capability of isotopic purification, [23] and compatibility with Si. These attractive features make Ge a promising candidate not only as a transistor channel material but also as a host for spin [6,24,25] and even topological qubits. [26,27] Excitingly, the first hole spin qubit [6] and proximity-induced superconductivity with a hard gap [28] have been realized recently in 1D Ge.Despite much progress that has been made so far, it remains a formidable challenge to have individuals as well as arrays of NWs with a high degree of addressability and scalability for the next generation of NW-based quantum devices. For example, in the field of group III-V semiconductors, precisely positioned NW networks have been achieved with predefined metal islands. [29] The out-of-plane grown NW structures, however, need to be transferred from the growth wafer to a second substrate for device fabrication, which limits their scalability. [7,29] Very recently, high-quality inplane NW networks have been successfully demonstrated with Semiconductor nanowires have been playing a crucial role in the development of nanoscale devices for the realization of spin qubits, Majorana fermions, single photon emitters, nanoprocessors, etc. The monolithic growth of site-controlled nanowires is a prerequisite toward the next generation of devices that will require addressability and scalability. Here, combining top-down nanofabrication and bottom-up self-assembly, the growth of Ge wires on prepatterned Si (001) substrates with controllable position, distance, length, and structure is reported. This is achieved by a novel growth process that uses a SiGe strain-relaxation template and can be potentially generalized to other material combinations. Transport measurements show an electrically tunable spin-orbit coupling, with a spin-orbit length similar to that of III-V materials. Also, charge sensing between quantum dots in closely spaced wires is observed, which underlines their potential for the realization of advanced quantum devices. The reported results open a path toward scalable qubit devices using nanowires on silicon.