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Electrons and holes confined in quantum dots define an excellent building block for quantum emergence, simulation, and computation. In order for quantum electronics to become practical, large numbers of quantum dots will be required, necessitating the fabrication of scaled structures such as linear and 2D arrays. Group IV semiconductors contain stable isotopes with zero nuclear spin and can thereby serve as excellent host for spins with long quantum coherence. Here we demonstrate group IV quantum dot arrays in silicon metal-oxide-semiconductor (SiMOS), strained silicon (Si/SiGe) and strained germanium (Ge/SiGe). We fabricate using a multi-layer technique to achieve tightly confined quantum dots and compare integration processes. While SiMOS can benefit from a larger temperature budget and Ge/SiGe can make ohmic contact to metals, the overlapping gate structure to define the quantum dots can be based on a nearly identical integration. We realize charge sensing in each platform, for the first time in Ge/SiGe, and demonstrate fully functional linear and two-dimensional arrays where all quantum dots can be depleted to the last charge state. In Si/SiGe, we tune a quintuple quantum dot using the N+1 method to simultaneously reach the few electron regime for each quantum dot. We compare capacitive cross talk and find it to be the smallest in SiMOS, relevant for the tuning of quantum dot arrays. These results constitute an excellent base for quantum computation with quantum dots and provide opportunities for each platform to be integrated with standard semiconductor manufacturing. * Corresponding Author: m.veldhorst@tudelft.nl arXiv:1909.06575v1 [cond-mat.mes-hall]

We study lasing in distributed feedback lasers made from square lattices of silver particles in a dye-doped waveguide. We present a systematic analysis and experimental study of the band structure underlying the lasing process as a function of the detuning between the particle plasmon resonance and the lattice Bragg diffraction condition. To this end, as gain medium we use either a polymer doped with Rh6G only, or polymer doped with a pair of dyes (Rh6G and Rh700) that act as Förster energy transfer (FRET)-pair. This allows for gain respectively at 590 nm or 700 nm when pumped at 532 nm, compatible with the achievable size-tunability of silver particles embedded in the polymer. By polarization-resolved spectroscopic Fourier microscopy, we are able to observe the plasmonic/photonic band structure of the array, unravelling both the stop gap width, as well as the loss properties of the four involved bands at fixed lattice Bragg diffraction condition and as function of detuning of the plasmon resonance. To explain the measurements we derive an analytical model that sheds insights on the lasing process in plasmonic lattices, highlighting the interaction between two competing resonant processes, one localized at the particle level around the plasmon resonance, and one distributed across the lattice. Both are shown to contribute to the lasing threshold and the overall emission properties of the array.

We investigate hole spin relaxation in the single- and multihole regime in a 2 × 2 germanium quantum dot array. We find spin relaxation times T 1 as high as 32 and 1.2 ms for quantum dots with single- and five-hole occupations, respectively, setting benchmarks for spin relaxation times for hole quantum dots. Furthermore, we investigate qubit addressability and electric field sensitivity by measuring resonance frequency dependence of each qubit on gate voltages. We can tune the resonance frequency over a large range for both single and multihole qubits, while simultaneously finding that the resonance frequencies are only weakly dependent on neighboring gates. In particular, the five-hole qubit resonance frequency is more than 20 times as sensitive to its corresponding plunger gate. Excellent individual qubit tunability and long spin relaxation times make holes in germanium promising for addressable and high-fidelity spin qubits in dense two-dimensional quantum dot arrays for large-scale quantum information.

The fault-tolerant operation of logical qubits is an important requirement for realizing a universal quantum computer. Spin qubits based on quantum dots have great potential to be scaled to large numbers because of their compatibility with standard semiconductor manufacturing. Here, we show that a quantum error correction code can be implemented using a four-qubit array in germanium. We demonstrate a resonant SWAP gate and by combining controlled-Z and controlled-S−1 gates we construct a Toffoli-like three-qubit gate. We execute a two-qubit phase flip code and find that we can preserve the state of the data qubit by applying a refocusing pulse to the ancilla qubit. In addition, we implement a phase flip code on three qubits, making use of a Toffoli-like gate for the final correction step. Both the quality and quantity of the qubits will require significant improvement to achieve fault-tolerance. However, the capability to implement quantum error correction codes enables co-design development of quantum hardware and software, where codes tailored to the properties of spin qubits and advances in fabrication and operation can now come together to advance semiconductor quantum technology.

Quantum dots fabricated using methods compatible with semiconductor manufacturing are promising for quantum information processing. In order to fully utilize the potential of this platform, scaling quantum dot arrays along two dimensions is a key step. Here, we demonstrate a two-dimensional quantum dot array where each quantum dot is tuned to single-charge occupancy, verified by simultaneous measurements using two integrated radio frequency charge sensors. We achieve this by using planar germanium quantum dots with low disorder and a small effective mass, allowing the incorporation of dedicated barrier gates to control the coupling of the quantum dots. We measure the hole charge filling spectrum and show that we can tune single-hole quantum dots from isolated quantum dots to strongly exchange coupled quantum dots. These results motivate the use of planar germanium quantum dots as building blocks for quantum simulation and computation.

Practical Quantum computing hinges on the ability to control large numbers of qubits with high fidelity. Quantum dots define a promising platform due to their compatibility with semiconductor manufacturing. Moreover, high-fidelity operations above 99.9% have been realized with individual qubits, though their performance has been limited to 98.67% when driving two qubits simultaneously. Here we present single-qubit randomized benchmarking in a two-dimensional array of spin qubits, finding native gate fidelities as high as 99.992(1)%. Furthermore, we benchmark single qubit gate performance while simultaneously driving two and four qubits, utilizing a novel benchmarking technique called N-copy randomized benchmarking, designed for simple experimental implementation and accurate simultaneous gate fidelity estimation. We find two- and four-copy randomized benchmarking fidelities of 99.905(8)% and 99.34(4)% respectively, and that next-nearest neighbor pairs are highly robust to cross-talk errors. These characterizations of single-qubit gate quality are crucial for scaling up quantum information technology.

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