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The low temperature physics of structurally amorphous materials is governed by two-level system defects (TLS), the exact origin and nature of which remain elusive despite decades of study. Recent advances towards realising stable high-coherence platforms for quantum computing has increased the importance of studying TLS in solid-state quantum circuits, as they are a persistent source of decoherence and instability. Here we perform scanning gate microscopy on a live superconducting quantum circuit at millikelvin temperatures to locate individual TLS. Our method directly reveals the microscopic nature of TLS and is also capable of deducing the three dimensional orientation of individual TLS electric dipole moments. Such insights, when combined with structural information of the underlying materials, can help unravel the detailed microscopic nature and chemical origin of TLS, directing strategies for their eventual mitigation.

The theory of nilpotent orbits of simple Lie algebras has seen tremendous developments over the past decades. In this context an important role is played by the component group of the stabilizer of a nilpotent element. In this work, the aim is to show computational methods to obtain explicit generators of the component group of the centralizer of a nilpotent element in a simple Lie algebra over $\mathbb{C}$. In some cases such generators had already been determined by impressive hand calculations but these often use the specific form of the chosen representative and are thus not immediately applicable to different representatives of the same orbit. It is then interesting to show how to overcome this issue constructing specific algorithms: for the classical types there is a straightforward method that directly translates well-known theoretical constructions; for the exceptional types we devise a method using the double centralizer of an $\mathfrak{sl}_2$-triple. In particular, it gives an independent construction of the component group, that does not depend on the prior knowledge of its isomorphism type. For our purposes, we needed to construct many algorithms which have been mainly implemented in the computational algebra system GAP.

Bosonic codes offer a hardware-efficient strategy for quantum error correction by redundantly encoding quantum information in the large Hilbert space of a harmonic oscillator. However, experimental realizations of these codes are often limited by ancilla errors propagating to the encoded logical qubit during syndrome measurements. The Kerr-cat qubit has been proposed as an ancilla for these codes due to its theoretically-exponential noise bias, which would enable fault-tolerant error syndrome measurements, but the coupling required to perform these syndrome measurements has not yet been demonstrated. In this work, we experimentally realize driven parametric coupling of a Kerr-cat qubit to a high-quality-factor microwave cavity and demonstrate a gate set enabling universal quantum control of the cavity. We measure the decoherence of the cavity in the presence of the Kerr-cat and discover excess dephasing due to heating of the Kerr-cat to excited states. By engineering frequency-selective dissipation to counteract this heating, we are able to eliminate this dephasing, thereby demonstrating a high on-off ratio of control. Our results pave the way toward using the Kerr-cat to fault-tolerantly measure error syndromes of bosonic codes.

Purpose: To harmonize the use of color for MR relaxometry maps and therefore recommend the use of specific color-maps for representing T1 and T2 maps. Methods: Perceptually linearized color-maps were chosen to have similar color settings as those proposed by Griswold et al. in 2018. A Delphi process, polling the opinion of a panel of 81 experts, was used to generate consensus on the suitability of these maps. Results: Consensus was reached on the suitability of the logarithm-processed Lipari color-map for T1 and the logarithm-processed Navia color-map for T2. There was consensus on color bars being mandatory and on the use of a specific value indicating invalidity. There was no consensus on whether the ranges should be fixed per anatomy. Conclusion: The authors recommend the use of the logarithm-processed Lipari color map for displaying quantitative T1 maps and R1 maps; likewise, the authors recommend the logarithm-processed Navia color-map for displaying T2, T2*, R2 and R2* maps., Comment: 22 pages; embedded are 5 figures and 5 tables; contact the first author for supplementary material. Submitted to Magnetic Resonance in Medicine

Quantum control of a linear oscillator using a static dispersive coupling to a nonlinear ancilla underpins a wide variety of experiments in circuit QED. Extending this control to more than one oscillator while minimizing the required connectivity to the ancilla would enable hardware-efficient multi-mode entanglement and measurements. We show that the spectrum of an ancilla statically coupled to a single mode can be made to depend on the joint photon number in two modes by applying a strong parametric beamsplitter coupling between them. This `joint-photon number-splitting' regime extends single-oscillator techniques to two-oscillator control, which we use to realize a hardware-efficient erasure check for a dual-rail qubit encoded in two superconducting cavities. By leveraging the beamsplitter coupling already required for single-qubit gates, this scheme permits minimal connectivity between circuit elements. Furthermore, the flexibility to choose the pulse shape allows us to limit the susceptibility to different error channels. We use this scheme to detect leakage errors with a missed erasure fraction of $(9.0 \pm 0.5)\times10^{-4}$, while incurring an erasure rate of $2.92 \pm 0.01\%$ and a Pauli error rate of $0.31 \pm 0.01\%$, both of which are dominated by cavity errors., Comment: Updated references

We propose a class of cellular automata for the Hamiltonian of a free particle. It is based on a two-step unitary evolution operator in discrete time and space. Various experiments with one and two-dimensional cellular automata are used to analyze 1) phase velocities of plane waves, 2) dispersion and group velocities of wavepackets, 3) energy levels of infinite potential wells and harmonic oscillators, and 4) interference from double-slit diffraction. Some of the differences between their known (analytical) results and the cellular-automata approximations are intriguing.

Superconducting travelling wave parametric amplifiers (TWPAs) are broadband near-quantum limited microwave amplifiers commonly used for qubit readout and a wide range of other applications in quantum technologies. The performance of these amplifiers depends on achieving impedance matching to minimise reflected signals. Here we apply a microwave calibration technique to extract the S-parameters of a Josephson junction based TWPA in-operando. This enables reflections occurring at the TWPA and its extended network of components to be quantified, and we find that the in-operation performance can be well described by the off-state measured S-parameters.

Colloidal gels have strong industrial relevance as they can behave liquid- and solid-like. The latter allows them to support the buoyant weight against gravity. However, the system is intrinsically out-of-equilibrium, which means that the colloids must eventually settle out of the suspension. The process of settling has been captured theoretically, but the presence of a delay time during which the gel appears relatively unaffected by gravity has not. Here, we modify existing frameworks to capture this delay, by treating the gel as a continuum with viscoelastic response that is based on the local bond density. We can solve our model numerically to obtain the evolution of the colloid density profile and recover qualitatively the accumulation of a dense layer on top of the settling gel, as is experimentally observed in depletion gels. This numerical study is complemented by a theoretical analysis that allows us to identify an emergent time and length scale that set the dynamics of the gel. Our model provides a solid foundation for future studies that incorporate hydrodynamic erosion and tackle industrially relevant geometries.

The Cellular Potts model, also known as Glazier-Graner-Hogeweg model, is a lattice-based approach, by which biological tissues at the level of individual cells can be numerically studied. Traditionally, a square or hexagonal underlying lattice structure is assumed for two-dimensional systems and this is known to introduce artifacts in the structure and dynamics of the model tissues. Here, we developed a new variant of this method that can be applied to a broad class of (ir)regular lattices. We show that on an irregular lattice, deriving from a fluid-like configuration, two types of artifacts can be removed. We further report on the transition between a fluid-like disordered and a solid-like hexagonally ordered phase present for monodisperse confluent cells as a function of their surface tension. This transition shows the hallmarks of a first-order phase transition, and is different from the glass/jamming transitions commonly reported for the vertex and Voronoi models. We emphasize this by analyzing the distribution of shape parameters found in our state space. Our analysis provides a useful reference for the future study of epithelia using the (ir)regular Cellular Potts model.

We present a computational approach to determine the space of almost-inner derivations of a finite dimensional Lie algebra given by a structure constant table. We also present an example of a Lie algebra for which the quotient algebra of the almost-inner derivations modulo the inner derivations is non-abelian. This answers a question of Kunyavskii and Ostapenko.

Concurrent structural and electronic transformations in VO2 thin films are of twofold importance: enabling fine-tuning of the emergent electrical properties in functional devices, yet creating an intricate interfacial domain structure of transitional phases. Despite the importance of understanding the structure of VO2 thin films, a detailed real space atomic structure analysis in which also the oxygen atomic columns are resolved is lacking. Moreover, intermediate atomic structures have remained elusive due to the lack of robust atomically resolved quantitative analysis. Here, we directly resolve both V and O atomic columns and discover the presence of the strain-stabilized intermediate monoclinic (M2) phase nanolayers (less than 2 nm thick) in epitaxially grown VO2 films on a TiO2 (001) substrate, where the dominant part of VO2 undergoes a transition from the tetragonal (rutile) phase to the monoclinic M1 phase. We unfold the crucial role of imaging the spatial configurations of the oxygen anions (in addition to V cations) utilizing atomic-resolution electron microscopy. Our approach sets a direct pathway to unravel the structural transitions in wide range of correlated oxides, offering substantial implications for e.g. optoelectronics and ferroelectrics., Comment: 17 pages, 4 figures

Self-stimulated echoes have recently been reported in the high cooperativity and inhomogeneous coupling regime of spin ensembles with superconducting resonators. In this work, we study their relative amplitudes using echo-silencing made possible by a fast frequency tunable resonator. The highly anisotropic spin linewidth of Er$^{3+}$ electron spins in the CaWO$_4$ crystal also allows to study the dependence on spin-resonator ensemble cooperativity. It is demonstrated that self-stimulated echoes primarily result from a combination of two large control pulses and the echo preceding it.

Purpose: Common to most MRSI techniques, the spatial resolution and the minimal scan duration of Deuterium Metabolic Imaging (DMI) are limited by the achievable SNR. This work presents a deep learning method for sensitivity enhancement of DMI. Methods: A convolutional neural network (CNN) was designed to estimate the 2H-labeled metabolite concentrations from low SNR and distorted DMI FIDs. The CNN was trained with synthetic data that represent a range of SNR levels typically encountered in vivo. The estimation precision was further improved by fine-tuning the CNN with MRI-based edge-preserving regularization for each DMI dataset. The proposed processing method, PReserved Edge ConvolutIonal neural network for Sensitivity Enhanced DMI (PRECISE-DMI), was applied to simulation studies and in vivo experiments to evaluate the anticipated improvements in SNR and investigate the potential for inaccuracies. Results: PRECISE-DMI visually improved the metabolic maps of low SNR datasets, and quantitatively provided higher precision than the standard Fourier reconstruction. Processing of DMI data acquired in rat brain tumor models resulted in more precise determination of 2H-labeled lactate and glutamate + glutamine levels, at increased spatial resolution (from >8 to 2 $\mu$L) or shortened scan time (from 32 to 4 min) compared to standard acquisitions. However, rigorous SD-bias analyses showed that overuse of the edge-preserving regularization can compromise the accuracy of the results. Conclusion: PRECISE-DMI allows a flexible trade-off between enhancing the sensitivity of DMI and minimizing the inaccuracies. With typical settings, the DMI sensitivity can be improved by 3-fold while retaining the capability to detect local signal variations.

We classify the non-degenerate two-step nilpotent Lie algebras of dimension 8 over the field of real numbers, using known results over complex numbers. We write explicit structure constants for these real Lie algebras., Comment: 21 pages

Hydrogen is a promising energy carrier that can push forward the energy transition because of its high energy density (142 MJ kg-1), variety of potential sources, low weight and low environmental impact, but its storage for automotive applications remains a formidable challenge. MgH2, with its high gravimetric and volumetric density, presents a compelling platform for hydrogen storage; however, its utilization is hindered by the sluggish kinetics of hydrogen uptake/release and high temperature operation. Herein we show that a novel layered heterostructure of reduced graphene oxide and organosilica with high specific surface area and narrow pore size distribution can serve as a scaffold to host MgH2 nanoparticles with a narrow diameter distribution around ~2.5 nm and superior hydrogen storage properties to bulk MgH2. Desorption studies showed that hydrogen release starts at 50 {\deg}C, with a maximum at 348 {\deg}C and kinetics dependent on particle size. Reversibility tests demonstrated that the dehydrogenation kinetics and re-hydrogenation capacity of the system remains stable at 1.62 wt.% over four cycles at 200 {\deg}C. Our results prove that MgH2 confinement in a nanoporous scaffold is an efficient way to constrain the size of the hydride particles, avoid aggregation and improve kinetics for hydrogen release and recharging.

Due to their high energy density (2600 Wh/kg), low cost, and low environmental impact, lithium-sulfur batteries are considered a promising alternative to lithium-ion batteries. However, their commercial viability remains a formidable scientific challenge mainly because of the sluggish reaction kinetics at the cathode and the so-called "shuttling effect" of soluble polysulfides, which results in capacity decay and a shortened lifespan. Herein, molecular imprinting with Li$_2$S$_8$ as a target molecule in combination with a two-dimensional material, MXene, is proposed to overcome these issues. Molecularly imprinted polymer-coated nitrogen-doped Ti-based MXene was successfully synthesized and demonstrated to exhibit an appealing electrochemical performance, namely a high specific capacity of 1095 mAh/g at 0.1 C and an extended cycling stability (300 mAh/g at 1.0 C after 300 cycles). X-ray photoelectron spectroscopy was applied to elucidate the underlying mechanisms and proved that Li$_2$S$_8$-imprinted polymer polyacrylamide serves as a polysulfide trap through strong chemical affinity towards the long-chain lithium polysulfides, while N-doped Ti-based MXene promotes the redox kinetics by accelerating the conversion of lithium polysulfides. This distinct interfacial strategy is expected to result in more effective and stable Li-S batteries.

Let G be a linear algebraic group, not necessarily connected or reductive, over the field of real numbers R. We describe a method, implemented on computer, to find the first Galois cohomology set H^1(R,G). The output is a list of 1-cocycles in G. Moreover, we have an implemented algorithm that, given a 1-cocycle z in Z^1(R,G), finds the cocycle in the computed list to which z is equivalent, together with an element of G(C) realizing the equivalence., Comment: V1: 41 pages. V2: 45 pages, the final version to appear in J. London Math. Soc

A critical challenge in developing scalable error-corrected quantum systems is the accumulation of errors while performing operations and measurements. One promising approach is to design a system where errors can be detected and converted into erasures. Such a system utilizing erasure qubits are known to have relaxed requirements for quantum error correction. A recent proposal aims to do this using a dual-rail encoding with superconducting cavities. However, experimental characterization and demonstration of a dual-rail cavity qubit has not yet been realized. In this work, we implement such a dual-rail cavity qubit; we demonstrate a projective logical measurement with integrated erasure detection and use it to measure dual-rail qubit idling errors. We measure logical state preparation and measurement errors at the $0.01\%$-level and detect over $99\%$ of cavity decay events as erasures. We use the precision of this new measurement protocol to distinguish different types of errors in this system, finding that while decay errors occur with probability $\sim 0.2\%$ per microsecond, phase errors occur 6 times less frequently and bit flips occur at least 140 times less frequently. These findings represent the first confirmation of the expected error hierarchy necessary to concatenate dual-rail erasure qubits into a highly efficient erasure code.

Colloidal gels are elasto-plastic materials composed of an out-of-equilibrium, self-assembled network of micron-sized (solid) particles suspended in a fluid. Recent work has shown that far-field hydrodynamic interactions do not change gel structure, only the rate at which the network forms and ages. However, during gel formation, the interplay between short-ranged attractions leading to gelation and equally short-ranged hydrodynamic lubrication interactions remains poorly understood. Here, we therefore study gelation using a range of hydrodynamic descriptions: from single-body (Brownian Dynamics), to pairwise (Rotne-Prager-Yamakawa), to (non-)lubrication-corrected many-body (Stokesian Dynamics). We confirm the current understanding informed by simulations accurate in the far-field. Yet, we find that accounting for lubrication can strongly impact structure at low colloid volume fraction. Counterintuitively, strongly dissipative lubrication interactions also accelerate the aging of a gel, irrespective of colloid volume fraction. Both elements can be explained by lubrication forces facilitating collective dynamics and therefore phase-separation. Our findings indicate that despite the computational cost, lubricated hydrodynamic modeling with many-body far-field interactions is needed to accurately capture the evolution of the gel structure.

Exploring the interplay between topological phases and photons opens new avenues for investigating novel quantum states. Here we show that superconducting resonators can serve as sensitive probes for properties of topological insulator nanowires (TINWs) embedded within them. By combining a static, controllable magnetic flux threading the TINW with an additional oscillating electromagnetic field applied perpendicularly, we show that orbital resonances can be generated and are reflected in periodic changes of the Q-factor of the resonator as a function of the flux. This response probes the confinement of the two-dimensional Dirac orbitals on the surface of the TINW, revealing their density of states and specific transition rules, as well as their dependence on the applied flux. Our approach represents a promising cross-disciplinary strategy for probing topological solid-state materials using state-of-the-art photonic cavities, which would avoid the need for attaching contacts, thereby enabling access to electronic properties closer to the pristine topological states.

In this paper we classify the orbits of the group SL(3,F)^3 on the space F^3\otimes F^3\otimes F^3 for F=C and F=R. This is known as the classification of complex and real 3-qutrit states. We also give an overview of physical theories where these classifications are relevant.