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One of the main limitations in state-of-the art solid-state quantum processors are qubit decoherence and relaxation due to noise in their local environment. For the field to advance towards full fault-tolerant quantum computing, a better understanding of the underlying microscopic noise sources is therefore needed. Adsorbates on surfaces, impurities at interfaces and material defects have been identified as sources of noise and dissipation in solid-state quantum devices. Here, we use an ultra-high vacuum package to study the impact of vacuum loading, UV-light exposure and ion irradiation treatments on coherence and slow parameter fluctuations of flux tunable superconducting transmon qubits. We analyse the effects of each of these surface treatments by comparing averages over many individual qubits and measurements before and after treatment. The treatments studied do not significantly impact the relaxation rate $\Gamma_1$ and the echo dephasing rate $\Gamma_2^\textrm{e}$, except for Ne ion bombardment which reduces $\Gamma_1$. In contrast, flux noise parameters are improved by removing magnetic adsorbates from the chip surfaces with UV-light and NH$_3$ treatments. Additionally, we demonstrate that SF$_6$ ion bombardment can be used to adjust qubit frequencies in-situ and post fabrication without affecting qubit coherence at the sweet spot.

Call graphs play an important role in different contexts, such as profiling and vulnerability propagation analysis. Generating call graphs in an efficient manner can be a challenging task when it comes to high-level languages that are modular and incorporate dynamic features and higher-order functions. Despite the language's popularity, there have been very few tools aiming to generate call graphs for Python programs. Worse, these tools suffer from several effectiveness issues that limit their practicality in realistic programs. We propose a pragmatic, static approach for call graph generation in Python. We compute all assignment relations between program identifiers of functions, variables, classes, and modules through an inter-procedural analysis. Based on these assignment relations, we produce the resulting call graph by resolving all calls to potentially invoked functions. Notably, the underlying analysis is designed to be efficient and scalable, handling several Python features, such as modules, generators, function closures, and multiple inheritance. We have evaluated our prototype implementation, which we call PyCG, using two benchmarks: a micro-benchmark suite containing small Python programs and a set of macro-benchmarks with several popular real-world Python packages. Our results indicate that PyCG can efficiently handle thousands of lines of code in less than a second (0.38 seconds for 1k LoC on average). Further, it outperforms the state-of-the-art for Python in both precision and recall: PyCG achieves high rates of precision ~99.2%, and adequate recall ~69.9%. Finally, we demonstrate how PyCG can aid dependency impact analysis by showcasing a potential enhancement to GitHub's "security advisory" notification service using a real-world example.

Type I superconductivity has recently been reported for the Dirac semimetal PdTe$_2$ (Tc approximately 1.6K) with, remarkably, multiple critical fields and a complex phase diagram. Here, measurements of the specific heat utilizing a thermal relaxation technique are presented. Conventional weak-coupling BCS superconductivity is confirmed by examining the temperature dependence of the specific heat in zero field. By probing the latent heat accompanying the superconducting transition, thermodynamic evidence for type I superconductivity is attained. The presence of the intermediate state is observed as a significant broadening of the superconducting transition onto lower temperatures at high fields as well as irreversibility in the specific heat in zero field cooled data at 8.5 mT., Comment: 6 pages, 4 figures and Supplemental Material

In circuit-based quantum computing, the available gate set typically consists of single-qubit gates acting on each individual qubit and at least one entangling gate between pairs of qubits. In certain physical architectures, however, some qubits may be 'hidden' and lacking direct addressability through dedicated control and readout lines, for instance because of limited on-chip routing capabilities, or because the number of control lines becomes a limiting factor for many-qubit systems. In this case, no single-qubit operations can be applied to the hidden qubits and their state cannot be measured directly. Instead, they may be controlled and read out only via single-qubit operations on connected 'control' qubits and a suitable set of two-qubit gates. We first discuss the impact of such restricted control capabilities on the quantum volume of specific qubit coupling networks. We then experimentally demonstrate full control and measurement capabilities in a superconducting two-qubit device with local single-qubit control and iSWAP and controlled-phase two-qubit interactions enabled by a tunable coupler. We further introduce an iterative tune-up process required to completely characterize the gate set used for quantum process tomography and evaluate the resulting gate fidelities.

We give a complete list of non-isometric bidimensional rotation invariant K\"ahler-Einstein submanifolds of a finite dimensional complex projective space endowed with the Fubini-Study metric. This solves in the aforementioned case a classical and long-staying problem addressed among others in [5] and [24]., Comment: 13 pages

Spatiotemporal spin dynamics under spin-orbit interaction is investigated in a (001) GaAs two-dimensional electron gas using magneto-optical Kerr rotation microscopy. Spin polarized electrons are diffused away from the excited position, resulting in spin precession because of the diffusion-induced spin-orbit field. Near the cancellation between spin-orbit field and external magnetic field, the induced spin precession frequency depends nonlinearly on the diffusion velocity, which is unexpected from the conventional linear relation between the spin-orbit field and the electron velocity.This behavior originates from an enhancement of the spin relaxation anisotropy by the electron velocity perpendicular to the diffused direction. We demonstrate that the spin relaxation anisotropy, which has been regarded as a material constant, can be controlled via diffusive electron motion., Comment: 5 pages, 5 figures

In this paper we address the problem of studying those complex manifolds $M$ equipped with extremal metrics $g$ induced by finite or infinite dimensional complex space forms. We prove that when $g$ is assumed to be radial and the ambient space is finite dimensional then $(M, g)$ is itself a complex space form. We extend this result to the infinite dimensional setting by imposing the strongest assumption that the metric $g$ has constant scalar curvature and is well-behaved (see Definition 1 in the Introduction). Finally, we analyze the radial Kaehler-Einstein metrics induced by infinite dimensional elliptic complex space forms and we show that if such a metric is assumed to satisfy a stability condition then it is forced to have constant non-positive holomorphic sectional curvature., Comment: 24 pages

The possibility to utilize different types of two-qubit gates on a single quantum computing platform adds flexibility in the decomposition of quantum algorithms. A larger hardware-native gate set may decrease the number of required gates, provided that all gates are realized with high fidelity. Here, we benchmark both controlled-Z (CZ) and exchange-type (iSWAP) gates using a parametrically driven tunable coupler that mediates the interaction between two superconducting qubits. Using randomized benchmarking protocols we estimate an error per gate of $0.9\pm0.03\%$ and $1.3\pm0.4\%$ fidelity for the CZ and the iSWAP gate, respectively. We argue that spurious $ZZ$-type couplings are the dominant error source for the iSWAP gate, and that phase stability of all microwave drives is of utmost importance. Such differences in the achievable fidelities for different two-qubit gates have to be taken into account when mapping quantum algorithms to real hardware., Comment: 24 pages, including supplementary information

Let $\mathrm S^3$ be the unit sphere of $\mathbb C^2$ with its standard Cauchy-Riemann (CR) structure. This paper investigates the CR geometry of curves in $\mathrm S^3$ which are transversal to the contact distribution, using the local CR invariants of $\mathrm S^3$. More specifically, the focus is on the CR geometry of transversal knots. Four global invariants of transversal knots are considered: the phase anomaly, the CR spin, the Maslov index, and the CR self-linking number. The interplay between these invariants and the Bennequin number of a knot are discussed. Next, the simplest CR invariant variational problem for generic transversal curves is considered and its closed critical curves are studied., Comment: 44 pages, 7 figures. This is an extended version of a talk presented at the Conference "Geometry, Differential Equations and Analysis" in memory of A. V. Pogorelov for his 100th birthday anniversary, June 17-21, 2019, Kharkiv, Ukraine

The lower-order cr-invariant variational problem for Legendrian curves in the 3-sphere is studied and its Euler-Lagrange equations are deduced. Closed critical curves are investigated. Closed critical curves with non-constant cr-curvature are characterized. We prove that their cr-equivalence classes are in one-to-one correspondence with the rational points of a connected planar domain. A procedure to explicitly build all such curves is described. In addition, a geometrical interpretation of the rational parameters in terms of three phenomenological invariants is given., Comment: 37 pages, 10 figures, to appear in "Annali di Matematica Pura ed Applicata"

A typical goal of a quantum simulation is to find the energy levels and eigenstates of a given Hamiltonian. This can be realized by adiabatically varying the system control parameters to steer an initial eigenstate into the eigenstate of the target Hamiltonian. Such an adiabatic quantum simulation is demonstrated by directly implementing a controllable and smoothly varying Hamiltonian in the rotating frame of two superconducting qubits, including longitudinal and transverse fields and iSWAP-type two-qubit interactions. The evolution of each eigenstate is tracked using time-resolved state tomography. The energy gaps between instantaneous eigenstates are chosen such that depending on the energy transition rate either diabatic or adiabatic passages are observed in the measured energies and correlators. Errors in the obtained energy values induced by finite $T_1$ and $T_2$ times of the qubits are mitigated by extrapolation to short protocol times., Comment: 5 pages, 4 figures

Inspired by the work of Z. Lu and G. Tian \cite{lutian}, in this paper we address the problem of studying those \K\ manifolds satisfying the $\Delta$-property, i.e. such that on a neighborhood of each of its points the $k$-th power of the \K Laplacian is a polynomial function of the complex Euclidean Laplacian, for all positive integer $k$ (see below for its definition). We prove two results: 1. if a \K\ manifold satisfies the $\Delta$-property then its curvature tensor is parallel; 2. if an Hermitian symmetric space of classical type satisfies the $\Delta$-property then it is a complex space form (namely it has constant holomorphic sectional curvature). In view of these results we believe that if a complete and simply-connected \K\ manifold satisfies the $\Delta$-property then it is a complex space form., Comment: 13 pages

For the variational quantum eigensolver we propose to generate trial wavefunctions from a small amount of selected Pauli terms of the problem Hamiltonian. Two different approaches, one inspired by the quantum approximate optimization algorithm and the other by imaginary-time evolution, are proposed and studied in detail. Using numerical calculations, we study the efficiency of these trial wavefunctions for finding the ground-state energy of three molecules: H2, LiH and H2O. We find that only a small number of Pauli terms are needed to reach chemical accuracy, leading to short-depth quantum circuits with a small number of variational parameters. For the LiH molecule, the quantum circuit consists of 36 two-qubit gates, 45 one-qubit gates, and four variational parameters, with a favorable scaling for larger molecules.