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Qubits based on ions trapped in linear radio-frequency traps form a successful platform for quantum computing, due to their high fidelity of operations, all-to-all connectivity and degree of local control. In principle there is no fundamental limit to the number of ion-based qubits that can be confined in a single 1D register. However, in practice there are two main issues associated with long trapped-ion crystals, that stem from the 'softening' of their modes of motion, upon scaling up: high heating rates of the ions' motion, and a dense motional spectrum; both impede the performance of high-fidelity qubit operations. Here we propose a holistic, scalable architecture for quantum computing with large ion-crystals that overcomes these issues. Our method relies on dynamically-operated optical potentials, that instantaneously segment the ion-crystal into cells of a manageable size. We show that these cells behave as nearly independent quantum registers, allowing for parallel entangling gates on all cells. The ability to reconfigure the optical potentials guarantees connectivity across the full ion-crystal, and also enables efficient mid-circuit measurements. We study the implementation of large-scale parallel multi-qubit entangling gates that operate simultaneously on all cells, and present a protocol to compensate for crosstalk errors, enabling full-scale usage of an extensively large register. We illustrate that this architecture is advantageous both for fault-tolerant digital quantum computation and for analog quantum simulations.

Thin NbSe$_2$ retains superconductivity at high in-plane magnetic field up to 30 T. In this work we construct an atomically thin, all van der Waals SQUID, in which current flows between NbSe$_2$ contacts through two parallel graphene weak links. This fully planar device remains uniquely stable at high in-plane field. This enables tracing the evolution of the critical current interference patterns as a function of the field up to 4.5 T, allowing nm-scale sensitivity to deviations from a perfect atomic plane. We present numerical methods to retrieve asymmetric current distributions J$_0$ from measured interference maps, and suggest a new application of the dual junction geometry to probe the current density in the absence of phase information. The interference maps exhibit a striking field-driven transition, indicating a redistribution of supercurrents to narrow channels. Our results suggest the existence of a preferred conductance channel with an exceptional stability to in-plane magnetic field.

Thin transition metal dichalcogenides sustain superconductivity at large in-plane magnetic fields due to Ising spin-orbit protection, which locks their spins in an out-of-plane orientation. Here we use thin NbSe$_2$ as superconducting electrodes laterally coupled to graphene, making a planar, all van der Waals two-dimensional Josephson junction (2DJJ). We map out the behavior of these novel devices with respect to temperature, gate voltage, and both out-of-plane and in-plane magnetic fields. Notably, the 2DJJs sustain supercurrent up to $H_\parallel$ as high as 8.5 T, where the Zeeman energy $E_Z$ rivals the Thouless energy $E_{Th}$, a regime hitherto inaccessible in graphene. As the parallel magnetic field $H_\parallel$ increases, the 2DJJ's critical current is suppressed and in a few cases undergoes suppression and recovery. We explore the behavior in $H_\parallel$ by considering theoretically two effects: a 0-$\pi$ transition induced by tuning of the Zeeman energy and the unique effect of ripples in an atomically thin layer which create a small spatially varying perpendicular component of the field. The 2DJJs have potential utility as flexible probes for two-dimensional superconductivity in a variety of materials and introduce high $H_\parallel$ as a newly accessible experimental knob.

Energy spectroscopy of strongly interacting phases requires probes which minimize screening while retaining spectral resolution and local sensitivity. Here we demonstrate that such probes can be realized using atomic sized quantum dots bound to defects in hexagonal Boron Nitride tunnel barriers, placed at nanometric distance from graphene. With dot energies capacitively tuned by a planar graphite electrode, dot-assisted tunneling becomes highly sensitive to the graphene excitation spectrum. The spectra track the onset of degeneracy lifting with magnetic field at the ground state, and at unoccupied exited states, revealing symmetry-broken gaps which develop steeply with magnetic field - corresponding to Land\'e $g$ factors as high as 160. Measured up to $B = 33$ T, spectra exhibit a primary energy split between spin-polarized excited states, and a secondary spin-dependent valley-split. Our results show that defect dots probe the spectra while minimizing local screening, and are thus exceptionally sensitive to interacting states.

The two-dimensional nature of graphene Josephson junctions offers the possibility of creating effective superconductor-ferromagnet-superconductor junctions with tunable Zeeman splitting caused by an in-plane magnetic field. Such junctions would be able to alternate between a conventional superconducting ground state and a ground state with an intrinsic phase difference, making them controllable $0-\pi$ Josephson junctions. However, in addition to the Zeeman splitting, an in-plane magnetic field will in general also produce an orbital effect because of height variations in graphene, colloquially known as ripples. Both the Zeeman and orbital effect will thus affect the critical current, so to be able to identify $0-\pi$ transitions it is necessary to understand their combined effect. From both analytical and numerical solutions of the Usadel equation we find that ripples can in fact produce a current response similar to that which is characteristic of a $0-\pi$ transition. Hence, additional analysis is required in order to reveal the presence of a $0-\pi$ transition caused by spin-splitting in graphene with ripples. We provide a closed form analytical expression for the critical current in the presence of exchange field and ripple effects as well as an expression for the scaling of critical current zeroes with junction parameters., Comment: 10 pages, 7 figures

We report on fabrication of devices integrating FeTe$_{0.55}$Se$_{0.45}$ with other van-der-Waals materials, measuring transport properties as well as tunneling spectra at variable magnetic fields and temperatures down to 35 mK. Transport measurements are reliable and repeatable, revealing temperature and magnetic field dependence in agreement with prior results, confirming that fabrication processing does not alter bulk properties. However, cross-section scanning transmission microscopy reveals oxidation of the surface, which may explain a lower yield of tunneling device fabrication. We nonetheless observe hard-gap planar tunneling into FeTe$_{0.55}$Se$_{0.45}$ through a MoS$_2$ barrier. Notably, a minimal hard gap of 0.5 meV persists up to a magnetic field of 9 T in the $ab$ plane and 3 T out of plane. This may be the result of very small junction dimensions, or a quantum-limit minimal energy spacing between vortex bound states. We also observed defect assisted tunneling, exhibiting bias-symmetric resonant states which may arise due to resonant Andreev processes., Comment: 10 pages, 5 figures

We report on a strongly coupled bilayer graphene (BLG) - \bise\ device with a junction resistance of less than 1.5 k$\Omega\mu$m$^2$. This device exhibits unique behavior at the interface, which cannot be attributed to either material in absence of the other. We observe quantum oscillations in the magnetoresistance of the junction, indicating the presence of well-resolved Landau levels due to hole carriers of unknown origin with a very large Fermi surface. These carriers, found only at the interface, could conceivably arise due to significant hole doping of the bilayer graphene with charge transfer on the order of 2$\times$10$^{13}$ cm$^{-2}$, or due to twist angle dependent mini-band transport.