Search

We study the set of intrinsic metrics on a given graph. This is a convex compact set and it carries a natural order. We investigate existence of largest elements with respect to this order. We show that the only locally finite graphs which admit a largest intrinsic metric are certain finite star graphs. In particular all infinite locally finite graphs do not admit a largest intrinsic metric. Moreover, we give a characterization for the existence of intrinsic metrics with finite balls for weakly spherically symmetric graphs.

The hydrogen Paschen lines are known activity indicators, but studies of them in M~dwarfs during quiescence are as rare as their reports in flare studies. This situation is mostly caused by a lack of observations, owing to their location in the near-infrared regime, which is covered by few high-resolution spectrographs. We study the Pa$\beta$ line, using a sample of 360 M~dwarfs observed by the CARMENES spectrograph. Descending the spectral sequence of inactive M~stars in quiescence, we find the Pa$\beta$ line to get shallower until about spectral type M3.5 V, after which a slight re-deepening is observed. Looking at the whole sample, for stars with H$\alpha$ in absorption, we find a loose anti-correlation between the (median) pseudo-equivalent widths (pEWs) of H$\alpha$ and Pa$\beta$ for stars of similar effective temperature. Looking instead at time series of individual stars, we often find correlation between pEW(H$\alpha$) and pEW(Pa$\beta$) for stars with H$\alpha$ in emission and an anti-correlation for stars with H$\alpha$ in absorption. Regarding flaring activity, we report the automatic detection of 35 Paschen line flares in 20 stars. Additionally we found visually six faint Paschen line flares in these stars plus 16 faint Paschen line flares in another 12 stars. In strong flares, Paschen lines can be observed up to Pa 14. Moreover, we find that Paschen line emission is almost always coupled to symmetric H$\alpha$ line broadening, which we ascribe to Stark broadening, indicating high pressure in the chromosphere. Finally we report a few Pa$\beta$ line asymmetries for flares that also exhibit strong H$\alpha$ line asymmetries., Comment: 21 pages, 22 figures, 7 tables, accepted to A&A

Optical measurements often exhibit mixed Poisson-Gaussian noise statistics, which hampers image quality, particularly under low signal-to-noise ratio (SNR) conditions. Computational imaging falls short in such situations when solely Poissonian noise statistics are assumed. In response to this challenge, we define a loss function that explicitly incorporates this mixed noise nature. By using maximum-likelihood estimation, we devise a practical method to account for camera readout noise in gradient-based ptychography optimization. Our results, based on both experimental and numerical data, demonstrate that this approach outperforms the conventional one, enabling enhanced image reconstruction quality under challenging noise conditions through a straightforward methodological adjustment., Comment: Contains main and supplementary documents

Models trained with empirical risk minimization (ERM) are known to learn to rely on spurious features, i.e., their prediction is based on undesired auxiliary features which are strongly correlated with class labels but lack causal reasoning. This behavior particularly degrades accuracy in groups of samples of the correlated class that are missing the spurious feature or samples of the opposite class but with the spurious feature present. The recently proposed Deep Feature Reweighting (DFR) method improves accuracy of these worst groups. Based on the main argument that ERM mods can learn core features sufficiently well, DFR only needs to retrain the last layer of the classification model with a small group-balanced data set. In this work, we examine the applicability of DFR to realistic data in the medical domain. Furthermore, we investigate the reasoning behind the effectiveness of last-layer retraining and show that even though DFR has the potential to improve the accuracy of the worst group, it remains susceptible to spurious correlations., Comment: Accepted at IJCAI Workshop on XAI 2023

Polymeric materials are widely used in industries ranging from automotive to biomedical. Their mechanical properties play a crucial role in their application and function and arise from the nanoscale structures and interactions of their constitutive polymer molecules. Polymeric materials behave viscoelastically, i.e. their mechanical responses depend on the time scale of the measurements; quantifying these time-dependent rheological properties at the nanoscale is relevant to develop, for example, accurate models and simulations of those materials, which are needed for advanced industrial applications. In this paper, an atomic force microscopy (AFM) method based on the photothermal actuation of an AFM cantilever is developed to quantify the nanoscale loss tangent, storage modulus, and loss modulus of polymeric materials. The method is then validated on a styrene-butadiene rubber (SBR), demonstrating the method's ability to quantify nanoscale viscoelasticity over a continuous frequency range up to five orders of magnitude (0.2 Hz to 20,200 Hz). Furthermore, this method is combined with AFM viscoelastic mapping obtained with amplitude-modulation frequency-modulation (AM-FM) AFM, enabling the extension of viscoelastic quantification over an even broader frequency range, and demonstrating that the novel technique synergizes with preexisting AFM techniques for quantitative measurement of viscoelastic properties. The method presented here introduces a way to characterize the viscoelasticity of polymeric materials, and soft matter in general at the nanoscale, for any application., Comment: The file includes Supporting information

Interpretable part-prototype models are computer vision models that are explainable by design. The models learn prototypical parts and recognise these components in an image, thereby combining classification and explanation. Despite the recent attention for intrinsically interpretable models, there is no comprehensive overview on evaluating the explanation quality of interpretable part-prototype models. Based on the Co-12 properties for explanation quality as introduced in arXiv:2201.08164 (e.g., correctness, completeness, compactness), we review existing work that evaluates part-prototype models, reveal research gaps and outline future approaches for evaluation of the explanation quality of part-prototype models. This paper, therefore, contributes to the progression and maturity of this relatively new research field on interpretable part-prototype models. We additionally provide a ``Co-12 cheat sheet'' that acts as a concise summary of our findings on evaluating part-prototype models., Comment: 24 pages, 1 image, accepted at the 1st World Conference on eXplainable Artificial Intelligence (xAI 2023)

Automatically summarizing radiology reports into a concise impression can reduce the manual burden of clinicians and improve the consistency of reporting. Previous work aimed to enhance content selection and factuality through guided abstractive summarization. However, two key issues persist. First, current methods heavily rely on domain-specific resources to extract the guidance signal, limiting their transferability to domains and languages where those resources are unavailable. Second, while automatic metrics like ROUGE show progress, we lack a good understanding of the errors and failure modes in this task. To bridge these gaps, we first propose a domain-agnostic guidance signal in form of variable-length extractive summaries. Our empirical results on two English benchmarks demonstrate that this guidance signal improves upon unguided summarization while being competitive with domain-specific methods. Additionally, we run an expert evaluation of four systems according to a taxonomy of 11 fine-grained errors. We find that the most pressing differences between automatic summaries and those of radiologists relate to content selection including omissions (up to 52%) and additions (up to 57%). We hypothesize that latent reporting factors and corpus-level inconsistencies may limit models to reliably learn content selection from the available data, presenting promising directions for future work., Comment: Accepted at INLG2023

Part-prototype models are explainable-by-design image classifiers, and a promising alternative to black box AI. This paper explores the applicability and potential of interpretable machine learning, in particular PIP-Net, for automated diagnosis support on real-world medical imaging data. PIP-Net learns human-understandable prototypical image parts and we evaluate its accuracy and interpretability for fracture detection and skin cancer diagnosis. We find that PIP-Net's decision making process is in line with medical classification standards, while only provided with image-level class labels. Because of PIP-Net's unsupervised pretraining of prototypes, data quality problems such as undesired text in an X-ray or labelling errors can be easily identified. Additionally, we are the first to show that humans can manually correct the reasoning of PIP-Net by directly disabling undesired prototypes. We conclude that part-prototype models are promising for medical applications due to their interpretability and potential for advanced model debugging., Comment: Accepted to the International Workshop on Explainable and Interpretable Machine Learning (XI-ML), co-located with ECAI 2023

In this work, we study a slave-rotor mean-field theory of an extended Hubbard model, applicable to transition metal dichalcogenide moir\'e systems, that captures both the formation of Wigner crystals as well as exotic spin states on top of these charge backgrounds. Phase diagrams are mapped out for different choices of long-range Coulomb repulsion strength, reproducing several experimentally found Wigner crystal states. Assuming unbroken time reversal symmetry, we find several spin liquid states as well as dimer states at fractional fillings. While spin dimer states are always found to have the lowest mean field energy, several spin liquid states are energetically competitive and may be stabilized by including gauge fluctuations or further interaction terms. We further discuss possible experimental signatures of these states pertinent to two-dimensional moir\'e heterostructures., Comment: 17 pages, 12 figures

Generating context specific data quality deficits is necessary to experimentally assess data quality of data-driven (artificial intelligence (AI) or machine learning (ML)) applications. In this paper we present badgers, an extensible open-source Python library to generate data quality deficits (outliers, imbalanced data, drift, etc.) for different modalities (tabular data, time-series, text, etc.). The documentation is accessible at https://fraunhofer-iese.github.io/badgers/ and the source code at https://github.com/Fraunhofer-IESE/badgers, Comment: 17 pages, 16 figures

The fidelity of quantum programs in the NISQ era is limited by high levels of device noise. To increase the fidelity of quantum programs running on NISQ devices, a variety of optimizations have been proposed. These include mapping passes, routing passes, scheduling methods and standalone optimisations which are usually incorporated into a transpiler as passes. Popular transpilers such as those proposed by Qiskit, Cirq and Cambridge Quantum Computing make use of these extensively. However, choosing the right set of transpiler passes and the right configuration for each pass is a challenging problem. Transpilers often make critical decisions using heuristics since the ideal choices are impossible to identify without knowing the target application outcome. Further, the transpiler also makes simplifying assumptions about device noise that often do not hold in the real world. As a result, we often see effects where the fidelity of a target application decreases despite using state-of-the-art optimisations. To overcome this challenge, we propose OPTRAN, a framework for Choosing an Optimal Pass Set for Quantum Transpilation. OPTRAN uses classically simulable quantum circuits composed entirely of Clifford gates, that resemble the target application, to estimate how different passes interact with each other in the context of the target application. OPTRAN then uses this information to choose the optimal combination of passes that maximizes the target application's fidelity when run on the actual device. Our experiments on IBM machines show that OPTRAN improves fidelity by 87.66% of the maximum possible limit over the baseline used by IBM Qiskit. We also propose low-cost variants of OPTRAN, called OPTRAN-E-3 and OPTRAN-E-1 that improve fidelity by 78.33% and 76.66% of the maximum permissible limit over the baseline at a 58.33% and 69.44% reduction in cost compared to OPTRAN respectively.

We demonstrate detection of broadband intense terahertz electromagnetic pulses by Zeeman-torque sampling (ZTS). Our approach is based on magneto-optic probing of the Zeeman torque the terahertz magnetic field exerts on the magnetization of a ferromagnet. Using an 8 nm thick iron film as sensor, we detect pulses from a silicon-based spintronic terahertz emitter with bandwidth 0.1-11 THz and peak field >0.1 MV/cm. Static calibration provides access to absolute transient THz field strengths. We show relevant added values of ZTS compared to electro-optic sampling (EOS): an absolute and echo-free transfer function with simple frequency dependence, linearity even at high terahertz field amplitudes, the straightforward calibration of EOS response functions and the modulation of the polarization-sensitive direction by an external AC magnetic field. Consequently, ZTS has interesting applications even beyond the accurate characterization of broadband high-field terahertz pulses for nonlinear terahertz spectroscopy.

Emergent gauge theories take a prominent role in the description of quantum matter, supporting deconfined phases with topological order and fractionalized excitations. A common construction of $\mathbb{Z}_2$ lattice gauge theories, first introduced by Wegner, involves Ising gauge spins placed on links and subject to a discrete $\mathbb{Z}_2$ Gauss law constraint. As shown by Kitaev, $\mathbb{Z}_2$ lattice gauge theories also emerge in the exact solution of certain spin systems with bond-dependent interactions. In this context, the $\mathbb{Z}_2$ gauge field is constructed from Majorana fermions, with gauge constraints given by the parity of Majorana fermions on each site. In this work, we provide an explicit Jordan-Wigner transformation that maps between these two formulations on the square lattice, where the Kitaev-type gauge theory emerges as the exact solution of a spin-orbital (Kugel-Khomskii) Hamiltonian. We then apply our mapping to study local perturbations to the spin-orbital Hamiltonian, which correspond to anisotropic interactions between electric-field variables in the $\mathbb{Z}_2$ gauge theory. These are shown to induce anisotropic confinement that is characterized by emergence of weakly-coupled one-dimensional spin chains. We study the nature of these phases and corresponding confinement transitions in both absence and presence of itinerant fermionic matter degrees of freedom. Finally, we discuss how our mapping can be applied to the Kitaev spin-1/2 model on the honeycomb lattice., Comment: 24+9 pages (single-column formatting), 7+1 figures; v2.5 (changes in blue, cosmetic changes in list of references)

Identifying the full entropy production of active particles is a challenging task. We introduce a microscopic, thermodynamically consistent model, which leads to active Ornstein-Uhlenbeck statistics in the continuum limit. Our minimal model consists of a particle with a fluctuating number of active reaction sites which contribute to its active self-propulsion on a lattice. In addition, the model also takes ordinary thermal noise into account. This approach allows us to identify the full entropy production stemming from both thermal diffusion and active driving. Extant methods based on the comparison of forward and time-reversed trajectory underestimate the physical entropy production when applied to the Langevin equations obtained from our model. Constructing microscopic Markovian models can thus provide a benchmark for determining the entropy production in non-Markovian active systems., Comment: 15 pages, 1 figure

We demonstrate the determination of anharmonic acoustic phonon properties via second-order Raman scattering exemplarily on copper iodide single crystals. The origin of multi-phonon features from the second-order Raman spectra was assigned by the support of the calculated 2-phonon density of states. In this way, the temperature dependence of acoustic phonons was determined down to 10\,K. To determine independently the harmonic contributions of respective acoustic phonons, density functional theory (DFT) in quasi-harmonic approximation was used. Finally, the anharmonic contributions were determined. The results are in agreement with earlier publications and extend CuI's determined acoustic phonon properties to lower temperatures with higher accuracy. This approach demonstrates that it is possible to characterize the acoustic anharmonicities via Raman scattering down to zero-temperature renormalization constants of at least 0.1\,cm$^{-1}$., Comment: 10 pages, 5 figures, 4 tables

The Merian survey is mapping $\sim$ 850 degrees$^2$ of the Hyper Suprime-Cam Strategic Survey Program (HSC-SSP) wide layer with two medium-band filters on the 4-meter Victor M. Blanco telescope at the Cerro Tololo Inter-American Observatory, with the goal of carrying the first high signal-to-noise (S/N) measurements of weak gravitational lensing around dwarf galaxies. This paper presents the design of the Merian filter set: N708 ($\lambda_c = 7080 \unicode{x212B}$, $\Delta\lambda = 275\unicode{x212B}$) and N540 ($\lambda_c = 5400\unicode{x212B}$, $\Delta\lambda = 210\unicode{x212B}$). The central wavelengths and filter widths of N708 and N540 were designed to detect the $\rm H\alpha$ and $\rm [OIII]$ emission lines of galaxies in the mass range $8<\rm \log M_*/M_\odot<9$ by comparing Merian fluxes with HSC broad-band fluxes. Our filter design takes into account the weak lensing S/N and photometric redshift performance. Our simulations predict that Merian will yield a sample of $\sim$ 85,000 star-forming dwarf galaxies with a photometric redshift accuracy of $\sigma_{\Delta z/(1+z)}\sim 0.01$ and an outlier fraction of $\eta=2.8\%$ over the redshift range $0.058

Zincblende copper iodide has attracted significant interest as a potential material for transparent electronics, thanks to its exceptional light transmission capabilities in the visible range and remarkable hole conductivity. However, remaining challenges hinder the utilization of copper iodide's unique properties in real-world applications. To address this, chalcogen doping has emerged as a viable approach to enhance the hole concentration in copper iodide. In search of further strategies to improve and tune the electronic properties of this transparent semiconductor, we investigate the ternary phase diagram of copper and iodine with sulphur or selenium by performing structure prediction calculations using the minima hopping method. As a result, we find 11 structures located on or near the convex hull, 9 of which are unreported. Based on our band structure calculations, it appears that sulphur and selenium are promising candidates for achieving ternary semiconductors suitable as $p$-type transparent conducting materials. Additionally, our study reveals the presence of unreported phases that exhibit intriguing topological properties. These findings broaden the scope of potential applications for these ternary systems, highlighting the possibility of harnessing their unique electronic characteristics in diverse electronic devices and systems.

We study femtosecond spin currents through MgO tunneling barriers in CoFeB(2 nm)|MgO($d$)|Pt(2 nm) stacks by terahertz emission spectroscopy. To obtain transport information independent of extrinsic experimental factors, we determine the complex-valued spin conductance $\tilde{G}_d (\omega)$ of the MgO layer (thickness d= 0-6 {\AA} over a wide frequency range $(\omega/2\pi=$ 0.5-8 THz). In the time $(t)$ domain,$ G_d (t)$ has an instantaneous and delayed component that point to (i) spin transport through Pt pinholes in MgO, (ii) coherent spin tunneling and (iii) incoherent resonant spin tunneling mediated by defect states in MgO. A remarkable signature of (iii) is its relaxation time that grows monotonically with $d$ to as much as 270 fs at $d= 6$ {\AA}, in full agreement with an analytical model. Our results indicate that terahertz spin conductance spectroscopy will yield new and relevant insights into ultrafast spin transport for a wide range of materials., Comment: 4 figures

Antiferromagnets have large potential for ultrafast coherent switching of magnetic order with minimum heat dissipation. In novel materials such as Mn$_2$Au and CuMnAs, electric rather than magnetic fields may control antiferromagnetic order by N\'eel spin-orbit torques (NSOTs), which have, however, not been observed on ultrafast time scales yet. Here, we excite Mn$_2$Au thin films with phase-locked single-cycle terahertz electromagnetic pulses and monitor the spin response with femtosecond magneto-optic probes. We observe signals whose symmetry, dynamics, terahertz-field scaling and dependence on sample structure are fully consistent with a uniform in-plane antiferromagnetic magnon driven by field-like terahertz NSOTs with a torkance of (150$\pm$50) cm$^2$/A s. At incident terahertz electric fields above 500 kV/cm, we find pronounced nonlinear dynamics with massive N\'eel-vector deflections by as much as 30{\deg}. Our data are in excellent agreement with a micromagnetic model which indicates that fully coherent N\'eel-vector switching by 90{\deg} within 1 ps is within close reach., Comment: 16 pages, 4 figures

Spintronic terahertz emitters promise terahertz sources with an unmatched broad frequency bandwidth that are easy to fabricate and operate, and therefore easy to scale at low cost. However, current experiments and proofs of concept rely on free-space ultrafast pump lasers and rather complex benchtop setups. This contrasts with the requirements of widespread industrial applications, where robust, compact, and safe designs are needed. To meet these requirements, we present a novel fiber-tip spintronic terahertz emitter solution that allows spintronic terahertz systems to be fully fiber-coupled. Using single-mode fiber waveguiding, the newly developed solution naturally leads to a simple and straightforward terahertz near-field imaging system with a 90%-10% knife-edge-response spatial resolution of 30 ${\mu}m$.

Trusted Platform Modules constitute an integral building block of modern security features. Moreover, as Windows 11 made a TPM 2.0 mandatory, they are subject to an ever-increasing academic challenge. While discrete TPMs - as found in higher-end systems - have been susceptible to attacks on their exposed communication interface, more common firmware TPMs (fTPMs) are immune to this attack vector as they do not communicate with the CPU via an exposed bus. In this paper, we analyze a new class of attacks against fTPMs: Attacking their Trusted Execution Environment can lead to a full TPM state compromise. We experimentally verify this attack by compromising the AMD Secure Processor, which constitutes the TEE for AMD's fTPMs. In contrast to previous dTPM sniffing attacks, this vulnerability exposes the complete internal TPM state of the fTPM. It allows us to extract any cryptographic material stored or sealed by the fTPM regardless of authentication mechanisms such as Platform Configuration Register validation or passphrases with anti-hammering protection. First, we demonstrate the impact of our findings by - to the best of our knowledge - enabling the first attack against Full Disk Encryption solutions backed by an fTPM. Furthermore, we lay out how any application relying solely on the security properties of the TPM - like Bitlocker's TPM- only protector - can be defeated by an attacker with 2-3 hours of physical access to the target device. Lastly, we analyze the impact of our attack on FDE solutions protected by a TPM and PIN strategy. While a naive implementation also leaves the disk completely unprotected, we find that BitLocker's FDE implementation withholds some protection depending on the complexity of the used PIN. Our results show that when an fTPM's internal state is compromised, a TPM and PIN strategy for FDE is less secure than TPM-less protection with a reasonable passphrase., Comment: The first two authors contributed equally. We publish all code necessary to mount the attack under https://github.com/PSPReverse/ftpm_attack. The repository further includes several intermediate results, e.g., flash memory dumps, to retrace the attack process without possessing the target boards and required hardware tools

Moir\'e heterostructures of transition metal dichalcogenides exhibit Mott-insulating behaviour both at half-filling as well as at fractional fillings, where electronic degrees of freedom form self-organized Wigner crystal states. An open question concerns magnetic states obtained by lifting the pseudospin-1/2 degeneracy of these states at lowest temperatures. While at half-filling virtual hopping is expected to induce (weak) antiferromagnetic exchange interactions, these are strongly suppressed when considering $\textit{dilute}$ filling fractions. We argue that instead a small concentration of doped electrons leads to the formation of spin-polarons, inducing ferromagnetic order at experimentally relevant temperatures. We predict explicit signatures of polaron-formation in the magnetization profile of the system., Comment: 6+12 pages, 3+3 figures; v3 (minor change)

Contemporary quantum computers encode and process quantum information in binary qubits (d = 2). However, many architectures include higher energy levels that are left as unused computational resources. We demonstrate a superconducting ququart (d = 4) processor and combine quantum optimal control with efficient gate decompositions to implement high-fidelity ququart gates. We distinguish between viewing the ququart as a generalized four-level qubit and an encoded pair of qubits, and characterize the resulting gates in each case. In randomized benchmarking experiments we observe gate fidelities greater 95% and identify coherence as the primary limiting factor. Our results validate ququarts as a viable tool for quantum information processing.

We construct and analyze families of periodic delay orbits for a class of delay differential equations in two dimensions depending on two real-valued functions. These families are parametrized by the delay parameter. It is possible to represent the dependency of these periodic delay orbits on the delay parameter by a curve in the plane, without loss of information. It turns out that the singularities of these curves necessarily are cusps in the non-degenerate case. After discussing degenerate situations in general, we explain how to glue different families of periodic delay orbits at degeneracies in the delay parameter., Comment: 21 pages, 11 figures

Random forest is a popular machine learning approach for the analysis of high-dimensional data because it is flexible and provides variable importance measures for the selection of relevant features. However, the complex relationships between the features are usually not considered for the selection and thus also neglected for the characterization of the analysed samples. Here we propose two novel approaches that focus on the mutual impact of features in random forests. Mutual forest impact (MFI) is a relation parameter that evaluates the mutual association of the featurs to the outcome and, hence, goes beyond the analysis of correlation coefficients. Mutual impurity reduction (MIR) is an importance measure that combines this relation parameter with the importance of the individual features. MIR and MFI are implemented together with testing procedures that generate p-values for the selection of related and important features. Applications to various simulated data sets and the comparison to other methods for feature selection and relation analysis show that MFI and MIR are very promising to shed light on the complex relationships between features and outcome. In addition, they are not affected by common biases, e.g. that features with many possible splits or high minor allele frequencies are prefered.

In single-molecule experiments, the dynamics of molecular motors are often observed indirectly by measuring the trajectory of an attached bead in a motor-bead assay. In this work, we propose a method to extract the step size and stalling force for a molecular motor without relying on external control parameters. We discuss this method for a generic hybrid model that describes bead and motor via continuous and discrete degrees of freedom, respectively. Our deductions are solely based on the observation of waiting times and transition statistics of the observable bead trajectory. Thus, the method is non-invasive, operationally accessible in experiments and can, in principle, be applied to any model describing the dynamics of molecular motors. We briefly discuss the relation of our results to recent advances in stochastic thermodynamics on inference from observable transitions. Our results are confirmed by extensive numerical simulations for parameters values of an experimentally realized F1-ATPase assay.

Extracting and identifying latent topics in large text corpora has gained increasing importance in Natural Language Processing (NLP). Most models, whether probabilistic models similar to Latent Dirichlet Allocation (LDA) or neural topic models, follow the same underlying approach of topic interpretability and topic extraction. We propose a method that incorporates a deeper understanding of both sentence and document themes, and goes beyond simply analyzing word frequencies in the data. This allows our model to detect latent topics that may include uncommon words or neologisms, as well as words not present in the documents themselves. Additionally, we propose several new evaluation metrics based on intruder words and similarity measures in the semantic space. We present correlation coefficients with human identification of intruder words and achieve near-human level results at the word-intrusion task. We demonstrate the competitive performance of our method with a large benchmark study, and achieve superior results compared to state-of-the-art topic modeling and document clustering models.

Superconducting quantum devices are a leading technology for quantum computation, but they suffer from several challenges. Gate errors, coherence errors and a lack of connectivity all contribute to low fidelity results. In particular, connectivity restrictions enforce a gate set that requires three-qubit gates to be decomposed into one- or two-qubit gates. This substantially increases the number of two-qubit gates that need to be executed. However, many quantum devices have access to higher energy levels. We can expand the qubit abstraction of $|0\rangle$ and $|1\rangle$ to a ququart which has access to the $|2\rangle$ and $|3\rangle$ state, but with shorter coherence times. This allows for two qubits to be encoded in one ququart, enabling increased virtual connectivity between physical units from two adjacent qubits to four fully connected qubits. This connectivity scheme allows us to more efficiently execute three-qubit gates natively between two physical devices. We present direct-to-pulse implementations of several three-qubit gates, synthesized via optimal control, for compilation of three-qubit gates onto a superconducting-based architecture with access to four-level devices with the first experimental demonstration of four-level ququart gates designed through optimal control. We demonstrate strategies that temporarily use higher level states to perform Toffoli gates and always use higher level states to improve fidelities for quantum circuits. We find that these methods improve expected fidelities with increases of 2x across circuit sizes using intermediate encoding, and increases of 3x for fully-encoded ququart compilation., Comment: 14 pages, 9 figures, to be published at ISCA 2023

Reducing the dimensions of ferroelectric materials down to the nanoscale has strong implications on the ferroelectric polarization pattern and on the ability to switch the polarization. As the size of ferroelectric domains shrinks to nanometer scale, the heterogeneity of the polarization pattern becomes increasingly pronounced, enabling a large variety of possible polar textures in nanocrystalline and nanocomposite materials. Critical to the understanding of fundamental physics of such materials and hence their applications in electronic nanodevices, is the ability to investigate their ferroelectric polarization at the nanoscale in a non-destructive way. We show that contact Kelvin probe force microscopy (cKPFM) combined with a k-means response clustering algorithm enables to measure the ferroelectric response at a mapping resolution of 8 nm. In a BaTiO3 thin film on silicon composed of tetragonal and hexagonal nanocrystals, we determine a nanoscale lateral distribution of discrete ferroelectric response clusters, fully consistent with the nanostructure determined by transmission electron microscopy. Moreover, we apply this data clustering method to the cKPFM responses measured at different temperatures, which allows us to follow the corresponding change in polarization pattern as the Curie temperature is approached and across the phase transition. This work opens up perspectives for mapping complex ferroelectric polarization textures such as curled/swirled polar textures that can be stabilized in epitaxial heterostructures and more generally mapping the polar domain distribution of any spatially-highly-heterogeneous ferroelectric materials.

We introduce a new class of random Gottesman-Kitaev-Preskill (GKP) codes derived from the cryptanalysis of the so-called NTRU cryptosystem. The derived codes are good in that they exhibit constant rate and average distance scaling $\Delta \propto \sqrt{n}$ with high probability, where $n$ is the number of bosonic modes, which is a distance scaling equivalent to that of a GKP code obtained by concatenating single mode GKP codes into a qubit-quantum error correcting code with linear distance. The derived class of NTRU-GKP codes has the additional property that decoding for a stochastic displacement noise model is equivalent to decrypting the NTRU cryptosystem, such that every random instance of the code naturally comes with an efficient decoder. This construction highlights how the GKP code bridges aspects of classical error correction, quantum error correction as well as post-quantum cryptography. We underscore this connection by discussing the computational hardness of decoding GKP codes and propose, as a new application, a simple public key quantum communication protocol with security inherited from the NTRU cryptosystem., Comment: 23 pages, 10 figures, comments welcome! The final contains added clarifications and an additional proof of the Gaussian heuristic for a class of NTRU-like lattices

Spectral properties of Schr\"odinger operators on compact metric graphs are studied and special emphasis is put on differences in the spectral behavior between different classes of vertex conditions. We survey recent results especially for $\delta$ and $\delta'$ couplings and demonstrate the spectral properties on many examples. Amongst other things, properties of the ground state eigenvalue and eigenfunction and the spectral behavior under various perturbations of the metric graph or the vertex conditions are considered., Comment: 36 pages

Quantum computing is in an era of limited resources. Current hardware lacks high fidelity gates, long coherence times, and the number of computational units required to perform meaningful computation. Contemporary quantum devices typically use a binary system, where each qubit exists in a superposition of the $\ket{0}$ and $\ket{1}$ states. However, it is often possible to access the $\ket{2}$ or even $\ket{3}$ states in the same physical unit by manipulating the system in different ways. In this work, we consider automatically encoding two qubits into one four-state qu\emph{quart} via a \emph{compression scheme}. We use quantum optimal control to design efficient proof-of-concept gates that fully replicate standard qubit computation on these encoded qubits. We extend qubit compilation schemes to efficiently route qubits on an arbitrary mixed-radix system consisting of both qubits and ququarts, reducing communication and minimizing excess circuit execution time introduced by longer-duration ququart gates. In conjunction with these compilation strategies, we introduce several methods to find beneficial compressions, reducing circuit error due to computation and communication by up to 50\%. These methods can increase the computational space available on a limited near-term machine by up to 2x while maintaining circuit fidelity., Comment: 14 pages, 13 figures, 1 table, to be published at ASPLOS 2023