III-V semiconductor nanowires have shown great potential in various quantum transport experiments. However, realizing a scalable high-quality nanowire-based platform that could lead to quantum information applications has been challenging. Here, we study the potential of selective area growth by molecular beam epitaxy of InAs nanowire networks grown on GaAs-based buffer layers. The buffered geometry allows for substantial elastic strain relaxation and a strong enhancement of field effect mobility. We show that the networks possess strong spin-orbit interaction and long phase coherence lengths with a temperature dependence indicating ballistic transport. With these findings, and the compatibility of the growth method with hybrid epitaxy, we conclude that the material platform fulfills the requirements for a wide range of quantum experiments and applications.Material science plays a key role in quantum computing research. Long quantum state lifetimes -the fundamental prerequisite for realizing quantum computers -rely on the ability to produce materials with high purity and structural quality. Together with the requirements of scalability and reproducibility, these properties are what mainly defines the challenges of material science in quantum computing today. Proposals for topological quantum computing, 1-3 which are based on hybrid semiconductor-superconductor nanowire (NW) networks, are being pursued by numerous research groups and have ignited intense research efforts on hybrid epitaxy. 4-8 NW scalability is tightly related to the semiconductor growth approach. Top-down lithography has been used to define NWs in two-dimensional layers 5,9 and a variety of methods have been pursued for alignment and positioning of bottom-up vapor-liquid-solid (VLS) grown NWs, such as dielectrophoresis techniques, 10 nanoscale combing 11 and magnetic aligning of NWs. 12 Despite of these developments, large-scale synthesis of bottom-up grown high-mobility NW networks that are compatible with epitaxial interwire connections and semiconductor/superconductor epitaxy has still not been realized. To realize the epitaxial connections, a lot of effort has been put into the growth of branched NWs via the VLS method. 8,13-15 A scalable approach has been developed in Ref. [16,17] using template assisted growth of inplane NW networks. 18 Nonetheless, this approach is not yet compatible with superconductor epitaxy. An alternative scalable approach is to use lithographically defined openings in a mask on a crystalline substrate. This method is referred to as selective area growth (SAG) and until recently has mainly been used in conjunction with metal organic chemical vapour deposition 19,20 , metal organic vapour phase epitaxy 21,22 , chemical beam epitaxy and metal organic molecular beam epitaxy (chemical beam epitaxy). [23][24][25][26] In contrast to molecular beam epitaxy (MBE), the dissociation kinetics of the chemical precursors in these methods enhance the growth selectivity on masked substrates by expanding the growth parameter window, ...

The coherent tunnelling of Cooper pairs across Josephson junctions (JJs) generates a nonlinear inductance that is used extensively in quantum information processors based on superconducting circuits, from setting qubit transition frequencies and interqubit coupling strengths to the gain of parametric amplifiers for quantum-limited readout. The inductance is either set by tailoring the metal oxide dimensions of single JJs, or magnetically tuned by parallelizing multiple JJs in superconducting quantum interference devices with local current-biased flux lines. JJs based on superconductor-semiconductor hybrids represent a tantalizing all-electric alternative. The gatemon is a recently developed transmon variant that employs locally gated nanowire superconductor-semiconductor JJs for qubit control. Here we go beyond proof-of-concept and demonstrate that semiconducting channels etched from a wafer-scale two-dimensional electron gas (2DEG) are a suitable platform for building a scalable gatemon-based quantum computer. We show that 2DEG gatemons meet the requirements by performing voltage-controlled single qubit rotations and two-qubit swap operations. We measure qubit coherence times up to ~2 μs, limited by dielectric loss in the 2DEG substrate.

We introduce selective area grown hybrid InAs/Al nanowires based on molecular beam epitaxy, allowing arbitrary semiconductor-superconductor networks containing loops and branches. Transport reveals a hard induced gap and unpoisoned 2e-periodic Coulomb blockade, with temperature dependent 1e features in agreement with theory. Coulomb peak spacing in parallel magnetic field displays overshoot, indicating an oscillating discrete near-zero subgap state consistent with device length. Finally, we investigate a loop network, finding strong spin-orbit coupling and a coherence length of several microns. These results demonstrate the potential of this platform for scalable topological networks among other applications.Majorana zero modes (MZMs) at the ends of onedimensional topological superconductors are expected to exhibit non-Abelian braiding statistics [1, 2], providing naturally fault-tolerant qubits [3, 4]. Proposed realizations of braiding [5, 6], interference-based topological qubits [7-9] and topological quantum computing architectures [10] require scalable nanowire networks. While relatively simple branched or looped wires can be realized by specialized growth methods [11,12] or by etchand gate-confined two-dimensional hybrid heterostructures [13][14][15][16], selective area growth [17] enables deterministic patterning of arbitrarily complex structures. This allows complex continuous patterns of superconductorsemiconductor hybrids and topological networks.Following initial theoretical proposals [18,19], a number of experiments have reported signatures of Majorana zero modes (MZMs) in hybrid semiconductorsuperconductor nanowires [11], including zero-bias conductance peaks [15,16,[20][21][22][23][24][25][26] and Coulomb blockade peak spacing oscillations [27,28]. To date, experiments have used individual vapor-liquid-solid (VLS) nanowires [20][21][22][23][24][25] or gate-confined two-dimensional heterostructures [15,16]. Within these approaches, constructing complex topological devices and networks containing branches and loops [5-10] is a challenge. Recently, branched and looped VLS growth has been developed toward this goal [12,29].In this Letter, we investigate a novel approach to the growth of semiconductor-superconductor hybrids that allows deterministic on-chip patterning of topological superconducting networks based on SAG. We characterize key physical properties required for building Majorana networks, including a hard superconducting gap, induced in the semiconductor, phase-coherence length of several microns, strong spin-orbit coupling, and Coulomb block-ade peak motion compatible with interacting Majoranas. Overall, these properties show great promise for SAGbased topological networks.Selective area growth was realized on a semi-insulating (001) InP substrate. PECVD grown SiO x was patterned using electron beam lithography and wet etching. InAs wires with triangular cross-sections were grown by molecular beam epitaxy (MBE). The Al was grown in-situ by MBE using angled deposition covering one of the facet...

We present conductance-matrix measurements of a three-terminal superconductor-semiconductor hybrid device consisting of two normal leads and one superconducting lead. Using a symmetry decomposition of the conductance, we find that the antisymmetric components of pairs of local and nonlocal conductances match at energies below the superconducting gap, consistent with expectations based on a non-interacting scattering matrix approach. Further, the local charge character of Andreev bound states is extracted from the symmetry-decomposed conductance data and is found to be similar at both ends of the device and tunable with gate voltage. Finally, we measure the conductance matrix as a function of magnetic field and identify correlated splittings in low-energy features, demonstrating how conductance-matrix measurements can complement traditional tunneling-probe measurements in the search for Majorana zero modes.PACS numbers: 03.67. Lx, 81.07.Gf, 85.25.Cp Symmetry relations for quantum transport are often connected to deep physical principles, and make strong predictions for comparison with experiment. For instance, the Onsager-Casimir relations [1-3] arise from microscopic reversibility, and were central in early studies of quantum-coherent transport [4][5][6]. Later, predicted departures from these relations due to interaction effects [7-9], which include bias-dependence of the effective potentials, were observed in nonlinear transport [10,11]. The introduction of superconducting terminals results in additional symmetries, as conductance occurs via Andreevreflection from electrons to holes, and is invariant under particle-hole conjugation [12]. For a two-terminal normal-superconducting device, the conductance, g(V ), is a symmetric function of bias voltage, V , neglecting interaction effects. As shown in a partner theoretical paper, for multi-terminal superconducting devices g(V ) need not be symmetric, although a curious relation exists between the antisymmetric components of the local and nonlocal conductances [13]. These predictions have, to our knowledge, not been tested.Hybrid superconductor-semiconductor nanowire structures have recently become a topic of intense interest [14][15][16][17][18][19], motivated in part by proposals for achieving topological superconductivity and Majorana zero modes (MZM) [20,21]. In two-terminal superconductor-semiconductor devices, observed asymmetries in the subgap conductance [22] have been suggested to arise from a dissipative fermionic reservoir, effectively acting as a third lead [23], although, as in the normal-conducting case [3], biasdependence of the self-consistent potential can also cause a deviation from symmetry [24]. Multi-terminal super-conducting devices are a topic of particular interest, as they can be used for MZM [25][26][27][28][29][30][31], Cooper-pair splitter [32,33], and multi-terminal Josephson studies [34][35][36][37][38]. In multi-terminal superconducting quantum dot devices, bias asymmetries have been observed [39], and a relationship between nonloca...