Hybrid superconductor-semiconductor structures attract increasing attention owing to a variety of potential applications in quantum computing devices. They can serve to the realization of topological superconducting systems, as well as gate-tunable superconducting quantum bits. Here we combine a SiGe/Ge/SiGe quantum-well heterostructure hosting high-mobility two-dimensional holes and aluminum superconducting leads to realize prototypical hybrid devices, such as Josephson field-effect transistors (JoFETs) and superconducting quantum interference devices (SQUIDs). We observe gate-controlled supercurrent transport with Ge channels as long as one micrometer and 1 arXiv:1810.05012v2 [cond-mat.mes-hall] 23 Oct 2018 estimate the induced superconducting gap from tunnel spectroscopy measurements in superconducting point-contact devices. Transmission electron microscopy reveals the diffusion of Ge into the aluminum contacts, whereas no aluminum is detected in the Ge channel.Modern quantum nanoelectronics takes increasing advantage of newly synthesized hybrid superconductor-semiconductor (S-Sm) interfaces. 1 One of the main motivations is the search for Majorana zero modes that are predicted to appear in a topological superconductor. 2-4 A Josephson field effect transistor (JoFET) is one of the basic devices. It consists of a gatetunable semiconductor channel allowing Cooper-pair exchange between two superconducting contacts mediated by the superconducting proximity effect. 5 Gate control on the Josephson coupling has eventually led to the realization of electrically tunable transmon quantum bits, now often referred to as gatemons. 6-8 Many of the reported experimental realizations of hybrid S-Sm devices rely on bottomup fabrication starting from semiconductor nanowires or carbon nanotubes. 9-16 Recently, new hybrid S-Sm devices were demonstrated using top-down fabrication processes based on two-dimensional systems made of graphene, 17 InAs, 18,19 GaAs, 20 InGaAs 21 or Ge/SiGe. 22,23Top-down nanoscale devices offer significant advantages in terms of complexity and scalability. Those based on p-type SiGe heterostructures are readily compatible with silicon technology, 24 and, thanks to their intrinsically strong spin-orbit coupling, they are an attractive candidate for the development of topological superconducting systems. 22,[25][26][27][28][29][30][31][32] In this work, we present proof-of-concept S-Sm devices in which the semiconducting element consists of an undoped SiGe heterostucture embedding a strained Ge quantum-well (QW). A high-mobility two-dimensional hole gas (2DHG) is electrostatically accumulated in the QW by means of a surface gate electrode. (Hole mobilities as high as 5×10 5 cm 2 /Vs were reported for similar heterostructures. 12,22,33,34 ) The superconducting proximity effect induces gate-tunable superconductivity in the 2DHG enabling JoFET operation. This functionality is exploited for the realization of gate-controlled superconducting quantum interference

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Quantum computing crucially relies on the ability to efficiently characterize the quantum states output by quantum hardware. Conventional methods which probe these states through direct measurements and classically computed correlations become computationally expensive when increasing the system size. Quantum neural networks tailored to recognize specific features of quantum states by combining unitary operations, measurements and feedforward promise to require fewer measurements and to tolerate errors. Here, we realize a quantum convolutional neural network (QCNN) on a 7-qubit superconducting quantum processor to identify symmetry-protected topological (SPT) phases of a spin model characterized by a non-zero string order parameter. We benchmark the performance of the QCNN based on approximate ground states of a family of cluster-Ising Hamiltonians which we prepare using a hardware-efficient, low-depth state preparation circuit. We find that, despite being composed of finite-fidelity gates itself, the QCNN recognizes the topological phase with higher fidelity than direct measurements of the string order parameter for the prepared states.

The ability to execute high-fidelity operations is crucial to scaling up quantum devices to large numbers of qubits. However, signal distortions originating from nonlinear components in the control lines can limit the performance of single-qubit gates. In this work, we use a measurement based on error amplification to characterize and correct the small single-qubit rotation errors originating from the nonlinear scaling of the qubit drive rate with the amplitude of the programmed pulse. With our hardware, and for a 15-ns pulse, the rotation angles deviate by up to several degrees from a linear model. Using purity benchmarking, we find that control errors reach 2 × 10 −4 , which accounts for half of the total gate error. Using crossentropy benchmarking, we demonstrate arbitrary-angle single-qubit gates with coherence-limited errors of 2 × 10 −4 and leakage below 6 × 10 −5 . While the exact magnitude of these errors is specific to our setup, the presented method is applicable to most sources of nonlinearity. Our work shows that the nonlinearity of qubit drive line components imposes a limit on the fidelity of single-qubit gates, independent of improvements in coherence times, circuit design, or leakage mitigation when not corrected for.

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High-fidelity control of superconducting qubits requires the generation of microwave-frequency pulses precisely tailored on nanosecond timescales. These pulses are most commonly synthesized by up-converting and superimposing two narrow-band intermediate-frequency signals referred to as the in-phase (I) and quadrature (Q) components. While the calibration of their DC-offsets, relative amplitude and phase allows one to cancel unwanted sideband and carrier leakage, this IQ mixing approach suffers from the presence of additional spurious frequency components. Here, we experimentally study an alternative approach based on double frequency conversion, which overcomes this challenge and circumvents the need for IQ-calibration. We find a spurious-free dynamic range of more than 70 dB and compare the quality of pulse generation against a state-of-the-art IQ mixing scheme by performing repeated single-qubit randomized benchmarking on a superconducting qubit.