# Qubit arrays in germanium

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## Abstract

Spin quantum bits (qubits) defined in semiconductor quantum dots have emerged as a promising platform for quantum information processing. Various semiconductor materials have been studied as a host for the spin qubit. Over the last decade, research focussed on the group‐IV semiconductor silicon, owing to its compatibility with semiconductor manufacturing technology and the ability to eliminate magnetic noise through isotope purification. However, to this end, hole states in germanium can be considered as well. Furthermore, their low effective mass and high carrier mobility allow for well‐controlled devices, the lack of valley states ensures a well‐defined qubit manifold and the intrinsic spin‐orbit coupling enables all‐electric control. In this thesis, we study strained planer germanium quantum wells, with a focus on applications for quantum information processing.In Chapter 5, we discuss the material platform growth and properties. We show that starting from a silicon wafer, using a reverse grading process, defect‐free, undoped, strained, and shallow germanium quantum wells can be grown, as confirmed by transmission electron microscopy, secondary ion mass spectrometry, and x‐ray measurements. Using heterostructure field‐effect transistors, we characterise the transport properties of the material and find a carrier mobility of μ > 500,000 cm2/Vs. Furthermore, we study the effect of the quantum well depth on the quantum mobility and charge noise sensitivity (Chapter 6) and observe an improvement in both parameters when the quantum well depth is increased from 20 nm to 60 nm.The spin qubit is defined by a hole spin confined in a gate‐defined quantum dot. In Chapter 7 we study the properties of a quantum dot in planar germanium. We describe the nanofabrication process we use to define gate‐controllable quantum dots, contacted by metallic ohmic leads. A nearby quantum dot is used as a charge sensor, which can be read out using high‐bandwidth reflectometry measurements. This allows us to deplete a two‐by‐two quantum dot array to the single‐hole charge occupation, as a host for the spin qubits.Having established a fabrication integration scheme to define quantum dots and ohmic regions, we move to qubit operation in Chapter 8. We measure a double quantum dot in transport and observe a blockade of the transport current for certain hole occupation numbers. This is found to be caused by Pauli spin blockade and can be used to perform the spin‐to‐charge conversion. When a microwave tone resonant with the magnetic field induced Zeeman splitting is applied, the blockaded transport current recovers. This is the result of an induced spin flip, mediated by electric dipole spin resonance (EDSR). Using a tailored measurement technique to increase the signal‐to‐noise ratio of the transport measurements, we demonstrate coherent rotations of the spins in both quantum dots at a Rabi frequency of up to 100 MHz. By operating at the point of the lowest charge noise sensitivity, we find qubit dephasing times beyond 800 ns and a single qubit control fidelity above 99 %. To form a universal quantum gate set, an entangling operation is needed as well. We implement a two‐qubit conditional rotation gate, mediated by the exchange interaction between the qubits. Using the dedicated tunnel barrier gate, we can set the exchange interaction as high as 60 MHz, enabling fast and coherent two‐qubit rotations.Transport measurements only allow for sampling of the average measurement outcome over an ensemble of individual shots. In Chapter 9 we establish single‐shot measurements of a single‐hole spin qubit by making use of a separate radio‐frequency charge sensor. This allows us to isolate the qubits from their hole reservoirs, and we find increased spin relaxation times of over 1 ms. Furthermore, we observe a strong electric modulation of the hole g‐factor that can be attributed to the spin‐orbit coupling and ensures individual qubit addressability.Practical quantum computing applications require large numbers of qubits and many proposals rely on two‐dimensional (2D) layouts to achieve this. As a first step towards 2D grids of spin qubits, we operate a two‐by‐two qubit array in Chapter 10. A latched readout process is implemented to increase the readout visibility and overcome spin relaxation during spin‐to‐charge conversion. Fast single‐qubit gates are achieved using EDSR, with control fidelities of over 99 % for all four qubits. By implementing dynamical decoupling sequences, low‐frequency noise can be mitigated and the phase coherence of the qubit can be increased by several orders of magnitude, up to 100 μs.Harnessing the electric control over the quantum dot coupling, we show the gate‐controlled isolation and coupling of all four qubits, enabling one‐, two‐, and threefold conditional qubit rotations. The large range of control over the exchange interaction also allows performing a controlled phase (CZ) two‐qubit gate in only 10 ns. Implementing a quantum circuit based on CZ gates between all qubits, we coherently entangle and disentangle the four qubits in a Greenberger‐Horne‐Zeilinger (GHZ) state.Finally, in Chapter 11 we study the integration of superconductors into the platform and define gate‐controlled Josephson junctions. We observe a supercurrent through the quantum well over a length up to 6 μm. The critical current of the junction can be modulated using the top gate, up to a maximum IcRN of 17 μV. We demonstrate the Josephson nature of the supercurrent by showing the presence of both the dc and ac Josephson effect. From multiple Andreev reflection and excess current measurements, we extract a characteristic superconducting gap size of 0.2 meV and a junction transparency of 0.6. Finally, we define a superconducting quantum point contact and observe discretisation of the supercurrent, showing superconducting transport restricted to individual channels.