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Direct-ink writing leverages the rheological complexity of yield-stress fluids to construct complex geometries, particularly those with large gaps across internal structures. However, extensional rheological properties have rarely been considered in work that studies rheology-printability correlations. Here, we test our hypothesis that extensional properties correlate with drawability, a key indicator of printability that signifies speed robustness, printing resolution, and gap-spanning performance. We formulated cementitious suspensions using hydroxyapatite (HAp) particles, independently tuning them for yield stress and extensibility, two crucial rheological properties, and test-printed. To enhance extensibility, we incorporated hydroxypropyl methylcellulose as a polymeric modifier, but this enhancement may decrease as yield stress increases, presenting a challenge in materials design. We modulated particle interactions to achieve a wide range of yield stress and extensibility, allowing for rigorous testing of our hypothesis. This approach created inks with high extensibility and high yield stress, generally considered mutually exclusive properties. We evaluated correlations between drawability and key rheological properties, finding the strongest positive correlation with extensional failure strains (strain-to-break) rather than yield stress. We establish a bijective property-manufacturing relationship (one-on-one mapping of shear yield stress to buildability and extensional strain-to-break to drawability) by combining our findings on drawability with previous studies on buildability. This relationship provides a comprehensive framework for designing high-performance inks that can be self-supporting, capable of high-speed printing, and allow gap-spanning features.

We introduce the pseudorandom quantum authentication scheme (PQAS), an efficient method for encrypting quantum states that relies solely on the existence of pseudorandom unitaries (PRUs). The scheme guarantees that for any eavesdropper with quantum polynomial-time (QPT) computational power, the encrypted states are indistinguishable from the maximally mixed state. Furthermore, the receiver can verify that the state has not been tampered with and recover the original state with asymptotically unit fidelity. Our scheme is cost-effective, requiring only polylogarithmic circuit depth and a single shared key to encrypt a polynomial number of states. Notably, the PQAS can potentially exist even without quantum-secure one-way functions, requiring fundamentally weaker computational assumptions than semantic classical cryptography. Additionally, PQAS is secure against attacks that plague protocols based on QPT indistinguishability from Haar random states, such as chosen-plaintext attacks (CPAs) and attacks that reveal meta-information such as quantum resources. We relate the amount of meta-information that is leaked to quantum pseudoresources, giving the concept a practical meaning. As an application, we construct important cryptographic primitives, such as verifiable pseudorandom density matrices (VPRDMs), which are QPT-indistinguishable from random mixed states while being efficiently verifiable via a secret key, as well as verifiable noise-robust EFI pairs and one-way state generators (OWSGs). Our results establish a new paradigm of quantum information processing with weaker computational assumptions., Comment: 7 + 21 pages, 2 figures

Position exchange of non-Abelian anyons affects the quantum state of their system in a topologically-protected way. Their expected manifestations in even-denominator fractional quantum Hall (FQH) systems offer the opportunity to directly study their unique statistical properties in interference experiments. In this work, we present the observation of coherent Aharonov-Bohm interference at two even-denominator states in high-mobility bilayer graphene-based van der Waals heterostructures by employing the Fabry-P\'erot interferometry (FPI) technique. Operating the interferometer at a constant filling factor, we observe an oscillation period corresponding to two flux quanta inside the interference loop, $\Delta\Phi=2\Phi_0$, at which the interference does not carry signatures of non-Abelian statistics. The absence of the expected periodicity of $\Delta\Phi=4\Phi_0$ may indicate that the interfering quasiparticles carry the charge $e^* = \frac{1}{2}e$ or that interference of $e^* = \frac{1}{4}e$ quasiparticles is thermally smeared. Interestingly, at two hole-conjugate states, we also observe oscillation periods of half the expected value, indicating interference of $e^* = \frac{2}{3}e$ quasiparticles instead of $e^* = \frac{1}{3}e$. To probe statistical phase contributions, we operated the FPI with controlled deviations of the filling factor, thereby introducing fractional quasiparticles inside the interference loop. The resulting changes to the interference patterns at both half-filled states indicate that the additional bulk quasiparticles carry the fundamental charge $e^*=\frac{1}{4}e$, as expected for non-Abelian anyons.

Quantum dots (QDs) are pivotal for the development of quantum technologies, with applications ranging from single-photon sources for secure communication to quantum computing infrastructures. Understanding the electron dynamics within these QDs is essential for characterizing their properties and functionality. Here, we show how by virtue of the recently introduced quantum polyspectral analysis of transport measurements, the complex transport measurements of multi-electron QD systems can be analyzed. This method directly relates higher-order temporal correlations of a raw quantum point contact (QPC) current measurement to the Liouvillian of the measured quantum system. By applying this method to the two-level switching dynamics of a double QD system, we reveal a hidden third state, without relying on the identification of quantum jumps or prior assumptions about the number of involved quantum states. We show that the statistics of the QPC current measurement can identically be described by different three-state Markov models, each with significantly different transition rates. Furthermore, we compare our method to a traditional analysis via waiting-time distributions for which we prove that the statistics of a three-state Markov model is fully described without multi-time waiting-time distributions even in the case of two level switching dynamics. Both methods yield the same parameters with a similar accuracy. The quantum polyspectra method, however, stays applicable in scenarios with low signal-to-noise, where the traditional full counting statistics falters. Our approach challenges previous assumptions and models, offering a more nuanced understanding of QD dynamics and paving the way for the optimization of quantum devices.

We introduce a nonstabilizerness monotone which we name basis-minimised stabilizerness asymmetry (BMSA). It is based on the notion of $G$-asymmetry, a measure of how much a certain state deviates from being symmetric with respect to a symmetry group $G$. For pure states, we show that the BMSA is a strong monotone for magic-state resource theory, while it can be extended to mixed states via the convex roof construction. We discuss its relation with other magic monotones, first showing that the BMSA coincides with the recently introduced basis-minimized measurement entropy, thereby establishing the strong monotonicity of the latter. Next, we provide inequalities between the BMSA and other nonstabilizerness measures known in the literature. Finally, we present numerical methods to compute the BMSA, highlighting its advantages and drawbacks compared to other nonstabilizerness measures in the context of pure many-body quantum states. We also discuss the importance of additivity and strong monotonicity for measures of nonstabilizerness in many-body physics, motivating the search for additional computable nonstabilizerness monotones., Comment: 19 pages, 3 figures

Angular integrals arise in a wide range of perturbative quantum field theory calculations. In this work we investigate angular integrals with three denominators in $d=4-2\varepsilon$ dimensions. We derive integration-by-parts relations for this class of integrals, leading to explicit recursion relations and a reduction to a small set of master integrals. Using a differential equation approach we establish results up to order $\varepsilon$ for general integer exponents and masses. Here, reduction identities for the number of masses, known results for two-denominator integrals, and a general dimensional-shift identity for angular integrals considerably reduce the required amount of work. For the first time we find for angular integrals a term contributing proportional to a Euclidean Gram determinant in the $\varepsilon$-expansion. This coefficient is expressed as a sum of Clausen functions with intriguing connections to Euclidean, spherical, and hyperbolic geometry. The results of this manuscript are applicable to phase-space calculations with multiple observed final-state particles., Comment: 26 pages, 4 figures, 1 ancillary Mathematica notebook

Persistent currents flowing in spatially closed tracks define one of the most iconic concepts in mesoscopic physics. They have been studied in solid-state platforms such as superfluids, superconductors and metals. Cold atoms trapped in magneto-optical toroidal circuits and driven by suitable artificial gauge fields allow us to study persistent currents with unprecedented control and flexibility of the system's physical conditions. Here, we review persistent currents of ultracold matter. Capitalizing on the remarkable progress in driving different atomic species to quantum degeneracy, persistent currents of single or multicomponent bosons/fermions, and their mixtures can be addressed within the present experimental know-how. This way, fundamental concepts of quantum science and many-body physics, like macroscopic quantum coherence, solitons, vortex dynamics, fermionic pairing and BEC-BCS crossover can be studied from a novel perspective. Finally, we discuss how persistent currents can form the basis of new technological applications like matter-wave gyroscopes and interferometers.

Quantum many-body systems provide a unique platform for exploring the rich interplay between chaos, randomness, and complexity. In a recently proposed paradigm known as deep thermalization, random quantum states of system A are generated by performing projective measurements on system B following chaotic Hamiltonian evolution acting jointly on AB. In this scheme, the randomness of the projected state ensemble arises from the intrinsic randomness of the outcomes when B is measured. Here we propose a modified scheme, in which classical randomness injected during the protocol is converted by quantum chaos into quantum randomness of the resulting state ensemble. We show that for generic chaotic systems this conversion is optimal in that each bit of injected classical entropy generates as much additional quantum randomness as adding an extra qubit to B. This significantly enhances the randomness of the projected ensemble without imposing additional demands on the quantum hardware. Our scheme can be easily implemented on typical analog quantum simulators, providing a more scalable route for generating quantum randomness valuable for many applications. In particular, we demonstrate that the accuracy of a shadow tomography protocol can be substantially improved., Comment: 6 pages, 3 figures

Quantum error correction (QEC) is essential for operating quantum computers in the presence of noise. Here, we accurately decode arbitrary Calderbank-Shor-Steane (CSS) codes via the maximum satisfiability (MaxSAT) problem. We show how to map quantum maximum likelihood problem of CSS codes of arbitrary geometry and parity check weight into MaxSAT problems. We incorporate the syndrome measurements as hard clauses, while qubit and measurement error probabilities, including biased and non-uniform, are encoded as soft MaxSAT clauses. For the code capacity of color codes on a hexagonal lattice, our decoder has a higher threshold and superior scaling in noise suppression compared to belief propagation with ordered statistics post-processing (BP-OSD), while showing similar scaling in computational cost. Further, we decode surface codes and recently proposed bivariate quantum low-density parity check (QLDPC) codes where we find lower error rates than BP-OSD. Finally, we connect the complexity of MaxSAT decoding to a computational phase transition controlled by the clause density of the MaxSAT problem, where we show that our mapping is always in the computationally ''easy`` phase. Our MaxSAT decoder can be further parallelised or implemented on ASICs and FPGAs, promising potential further speedups of several orders of magnitude. Our work provides a flexible platform towards practical applications on quantum computers., Comment: 11 pages including appendix, 7 figures

Quantum annealing and quantum approximate optimization algorithms hold a great potential to speed-up optimization problems. This could be game-changing for a plethora of applications. Yet, in order to hope to beat classical solvers, quantum circuits must scale up to sizes and performances much beyond current hardware. In that quest, intense experimental effort has been recently devoted to optimizations on 3-regular graphs, which are computationally hard but experimentally relatively amenable. However, even there, the amount and quality of quantum resources required for quantum solvers to outperform classical ones is unclear. Here, we show that quantum annealing for 3-regular graphs can be classically simulated even at scales of 1000 qubits and 5000000 two-qubit gates with all-to-all connectivity. To this end, we develop a graph tensor-network quantum annealer (GTQA) able of high-precision simulations of Trotterized circuits of near-adiabatic evolutions. Based on a recently proposed belief-propagation technique for tensor canonicalization, GTQA is equipped with re-gauging and truncation primitives that keep approximation errors small in spite of the circuits generating significant amounts of entanglement. As a result, even with a maximal bond dimension as low as 4, GTQA produces solutions competitive with those of state-of-the-art classical solvers. For non-degenerate instances, the unique solution can be read out from the final reduced single-qubit states. In contrast, for degenerate problems, such as MaxCut, we introduce an approximate measurement simulation algorithm for graph tensor-network states. On one hand, our findings showcase the potential of GTQA as a powerful quantum-inspired optimizer. On the other hand, they considerably raise the bar required for experimental demonstrations of quantum speed-ups in combinatorial optimizations.

Artificial intelligence (AI) permeates all fields of life, which resulted in new challenges in requirements engineering for artificial intelligence (RE4AI), e.g., the difficulty in specifying and validating requirements for AI or considering new quality requirements due to emerging ethical implications. It is currently unclear if existing RE methods are sufficient or if new ones are needed to address these challenges. Therefore, our goal is to provide a comprehensive overview of RE4AI to researchers and practitioners. What has been achieved so far, i.e., what practices are available, and what research gaps and challenges still need to be addressed? To achieve this, we conducted a systematic mapping study combining query string search and extensive snowballing. The extracted data was aggregated, and results were synthesized using thematic analysis. Our selection process led to the inclusion of 126 primary studies. Existing RE4AI research focuses mainly on requirements analysis and elicitation, with most practices applied in these areas. Furthermore, we identified requirements specification, explainability, and the gap between machine learning engineers and end-users as the most prevalent challenges, along with a few others. Additionally, we proposed seven potential research directions to address these challenges. Practitioners can use our results to identify and select suitable RE methods for working on their AI-based systems, while researchers can build on the identified gaps and research directions to push the field forward., Comment: Accepted in Requirements Engineering Journal, 2024

Sign Language Assessment (SLA) tools are useful to aid in language learning and are underdeveloped. Previous work has focused on isolated signs or comparison against a single reference video to assess Sign Languages (SL). This paper introduces a novel SLA tool designed to evaluate the comprehensibility of SL by modelling the natural distribution of human motion. We train our pipeline on data from native signers and evaluate it using SL learners. We compare our results to ratings from a human raters study and find strong correlation between human ratings and our tool. We visually demonstrate our tools ability to detect anomalous results spatio-temporally, providing actionable feedback to aid in SL learning and assessment., Comment: Accepted to Twelfth International Workshop on Assistive Computer Vision and Robotics at ECCV 2024

Autonomous driving for urban and highway driving applications often requires High Definition (HD) maps to generate a navigation plan. Nevertheless, various challenges arise when generating and maintaining HD maps at scale. While recent online mapping methods have started to emerge, their performance especially for longer ranges is limited by heavy occlusion in dynamic environments. With these considerations in mind, our work focuses on leveraging lightweight and scalable priors-Standard Definition (SD) maps-in the development of online vectorized HD map representations. We first examine the integration of prototypical rasterized SD map representations into various online mapping architectures. Furthermore, to identify lightweight strategies, we extend the OpenLane-V2 dataset with OpenStreetMaps and evaluate the benefits of graphical SD map representations. A key finding from designing SD map integration components is that SD map encoders are model agnostic and can be quickly adapted to new architectures that utilize bird's eye view (BEV) encoders. Our results show that making use of SD maps as priors for the online mapping task can significantly speed up convergence and boost the performance of the online centerline perception task by 30% (mAP). Furthermore, we show that the introduction of the SD maps leads to a reduction of the number of parameters in the perception and reasoning task by leveraging SD map graphs while improving the overall performance. Project Page: https://henryzhangzhy.github.io/sdhdmap/., Comment: Accepted by the 2024 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2024)

Pseudorandom states (PRSs) are state ensembles that cannot be distinguished from Haar random states by any efficient quantum algorithm. However, the definition of PRSs has been limited to pure states and lacks robustness against noise. In this work, we introduce pseudorandom density matrices (PRDMs), ensembles of $n$-qubit states that are computationally indistinguishable from the generalized Hilbert-Schmidt ensemble, which is constructed from $(n+m)$-qubit Haar random states with $m$ qubits traced out. For a mixedness parameter $m=0$, PRDMs are equivalent to PRSs, whereas for $m=\omega(\log n)$, PRDMs are computationally indistinguishable from the maximally mixed state. In contrast to PRSs, PRDMs with $m=\omega(\log n)$ are robust to unital noise channels and a recently introduced $\mathsf{PostBQP}$ attack. Further, we construct pseudomagic and pseudocoherent state ensembles, which possess near-maximal magic and coherence, but are computationally indistinguishable from states with zero magic and coherence. PRDMs can exhibit a pseudoresource gap of $\Theta(n)$ vs $0$, surpassing previously found gaps. We introduce noise-robust EFI pairs, which are state ensembles that are computationally indistinguishable yet statistically far, even when subject to noise. We show that testing entanglement, magic and coherence is not efficient. Further, we prove that black-box resource distillation requires a superpolynomial number of copies. We also establish lower bounds on the purity needed for efficient testing and black-box distillation. Finally, we introduce memoryless PRSs, a noise-robust notion of PRS which are indistinguishable to Haar random states for efficient algorithms without quantum memory. Our work provides a comprehensive framework of pseudorandomness for mixed states, which yields powerful quantum cryptographic primitives and fundamental bounds on quantum resource theories., Comment: 34 pages, 2 figures

Quantum error correction suppresses noise in quantum systems to allow for high-precision computations. In this work, we introduce Multivariate Bicycle (MB) Quantum Low-Density Parity-Check (QLDPC) codes, via an extension of the framework developed by Bravyi et al. [Nature, 627, 778-782 (2024)] and particularly focus on Trivariate Bicycle (TB) codes. Unlike the weight-6 codes proposed in their study, we offer concrete examples of weight-4 and weight-5 TB-QLDPC codes which promise to be more amenable to near-term experimental setups. We show that our TB-QLDPC codes up to weight-6 have a bi-planar structure. Further, most of our new codes can also be arranged in a two-dimensional toric layout, and have substantially better encoding rates than comparable surface codes while offering similar error suppression capabilities. For example, we can encode 4 logical qubits with distance 5 into 30 physical qubits with weight-5 check measurements, while a surface code with these parameters requires 100 physical qubits. The high encoding rate and compact layout make our codes highly suitable candidates for near-term hardware implementations, paving the way for a realizable quantum error correction protocol., Comment: 4 + 14 pages, 17 figures

This paper introduces the Bosch street dataset (BSD), a novel multi-modal large-scale dataset aimed at promoting highly automated driving (HAD) and advanced driver-assistance systems (ADAS) research. Unlike existing datasets, BSD offers a unique integration of high-resolution imaging radar, lidar, and camera sensors, providing unprecedented 360-degree coverage to bridge the current gap in high-resolution radar data availability. Spanning urban, rural, and highway environments, BSD enables detailed exploration into radar-based object detection and sensor fusion techniques. The dataset is aimed at facilitating academic and research collaborations between Bosch and current and future partners. This aims to foster joint efforts in developing cutting-edge HAD and ADAS technologies. The paper describes the dataset's key attributes, including its scalability, radar resolution, and labeling methodology. Key offerings also include initial benchmarks for sensor modalities and a development kit tailored for extensive data analysis and performance evaluation, underscoring our commitment to contributing valuable resources to the HAD and ADAS research community.

We consider prescribed mean curvature equations whose solutions are minimal surfaces, constant mean curvature surfaces, or capillary surfaces. We consider both Dirichlet boundary conditions for Plateau problems and nonlinear Neumann boundary conditions for capillary problems and we consider domains in $\mathbf{R}^2$ to be rectangles, disks, or annuli. We present spectral methods for approximating solutions of the associated boundary value problems. These are either based on Chebyshev or Chebyshev-Fourier methods depending on the geometry of the domain. The non-linearity in the prescribed mean curvature equations is treated with a Newton method. The algorithms are designed to be adaptive; if the prescribed tolerances are not met then the resolution of the solution is increased until the tolerances are achieved. 22, Comment: 22 pages, 10 figures

Nonstabilizerness or `magic' is a key resource for quantum computing and a necessary condition for quantum advantage. Non-Clifford operations turn stabilizer states into resourceful states, where the amount of nonstabilizerness is quantified by resource measures such as stabilizer R\'enyi entropies (SREs). Here, we show that SREs saturate their maximum value at a critical number of non-Clifford operations. Close to the critical point SREs show universal behavior. Remarkably, the derivative of the SRE crosses at the same point independent of the number of qubits and can be rescaled onto a single curve. We find that the critical point depends non-trivially on R\'enyi index $\alpha$. For random Clifford circuits doped with T-gates, the critical T-gate density scales independently of $\alpha$. In contrast, for random Hamiltonian evolution, the critical time scales linearly with qubit number for $\alpha>1$, while is a constant for $\alpha<1$. This highlights that $\alpha$-SREs reveal fundamentally different aspects of nonstabilizerness depending on $\alpha$: $\alpha$-SREs with $\alpha<1$ relate to Clifford simulation complexity, while $\alpha>1$ probe the distance to the closest stabilizer state and approximate state certification cost via Pauli measurements. As technical contributions, we observe that the Pauli spectrum of random evolution can be approximated by two highly concentrated peaks which allows us to compute its SRE. Further, we introduce a class of random evolution that can be expressed as random Clifford circuits and rotations, where we provide its exact SRE. Our results opens up new approaches to characterize the complexity of quantum systems., Comment: 14 pages, 9 figures

Bilayer graphene has emerged as a key platform for non-Abelian fractional quantum Hall (FQH) states, exhibiting multiple half-filled plateaus with large energy gaps. Here, we report four unexpected quarter-filled states and complete the sequence of half-filled plateaus by observing the previously missing $\nu=-\frac{3}{2}$ and $\nu=\frac{1}{2}$ states. Identifying the half-filled plateaus according to their Levin--Halperin daughter states, we reveal an alternating pattern of non-Abelian topological orders. Whenever a pair of $N=1$ Landau levels cross, anti-Pfaffian and Pfaffian develop in the lower and higher levels, respectively. Surprisingly, quarter states occur in $N=0$ levels and are also accompanied by daughters. The mutual exclusion of half- and quarter-filled states indicates a robust competition between the interactions favoring paired states of either two-flux or four-flux composite fermions. Finally, we observe several FQH states that require strong interactions between composite fermions. The systematic pattern of non-Abelian states across two generations of even denominators strengthens the identification of their topological orders and suggests a universal origin., Comment: 17 pages, 5 figures

The tunneling of interacting charges in nanostructures is a random and noisy process, which gives rise to a variety of intriguing physical phenomena, including Coulomb blockade, the Kondo effect, and Fermi-edge singularities. Such correlation effects are visible in low-frequency measurements of the electric current or the shot noise, however, they are also expected to leave clear fingerprints in the tunneling times of individual charges. Here, we experimentally demonstrate the real-time detection and control of correlated charge tunneling in a dynamically driven quantum dot. To this end, we measure the joint distribution of waiting times between tunneling charges, and we show that subsequent waiting times are strongly correlated due to the Coulomb interactions between the tunneling charges and the external periodic drive. Our measurements are in excellent agreement with a theoretical model that allows us to develop a detailed understanding of the correlated tunneling events. We also demonstrate that the degree of correlations can be controlled by the external drive. Our experiment paves the way for systematic real-time investigations of correlated electron transport in low-dimensional nanostructures with potential applications in metrology and sensing., Comment: 7 pages, 5 figures

In autonomous driving, accurately interpreting the movements of other road users and leveraging this knowledge to forecast future trajectories is crucial. This is typically achieved through the integration of map data and tracked trajectories of various agents. Numerous methodologies combine this information into a singular embedding for each agent, which is then utilized to predict future behavior. However, these approaches have a notable drawback in that they may lose exact location information during the encoding process. The encoding still includes general map information. However, the generation of valid and consistent trajectories is not guaranteed. This can cause the predicted trajectories to stray from the actual lanes. This paper introduces a new refinement module designed to project the predicted trajectories back onto the actual map, rectifying these discrepancies and leading towards more consistent predictions. This versatile module can be readily incorporated into a wide range of architectures. Additionally, we propose a novel scene encoder that handles all relations between agents and their environment in a single unified heterogeneous graph attention network. By analyzing the attention values on the different edges in this graph, we can gain unique insights into the neural network's inner workings leading towards a more explainable prediction.

Nonstabilizerness, or `magic', is a critical quantum resource that, together with entanglement, characterizes the non-classical complexity of quantum states. Here, we address the problem of quantifying the average nonstabilizerness of random Matrix Product States (RMPS). RMPS represent a generalization of random product states featuring bounded entanglement that scales logarithmically with the bond dimension $\chi$. We demonstrate that the $2$-Stabilizer R\'enyi Entropy converges to that of Haar random states as $N/\chi^2$, where $N$ is the system size. This indicates that MPS with a modest bond dimension are as magical as generic states. Subsequently, we introduce the ensemble of Clifford enhanced Matrix Product States ($\mathcal{C}$MPS), built by the action of Clifford unitaries on RMPS. Leveraging our previous result, we show that $\mathcal{C}$MPS can approximate $4$-spherical designs with arbitrary accuracy. Specifically, for a constant $N$, $\mathcal{C}$MPS become close to $4$-designs with a scaling as $\chi^{-2}$. Our findings indicate that combining Clifford unitaries with polynomially complex tensor network states can generate highly non-trivial quantum states.

We present a novel semi-analytical method for parton evolution. It is based on constructing a family of analytic functions spanning $x$-space which is closed under the considered evolution equation. Using these functions as a basis, the original integro-differential evolution equation transforms into a system of coupled ordinary differential equations, which can be solved numerically by restriction to a suitably chosen finite subsystem. The evolved distributions are obtained as analytic functions in $x$ with numerically obtained coefficients, providing insight into the analytic behavior of the evolved parton distributions. As a proof-of-principle, we apply our method to the leading order non-singlet and singlet DGLAP equation. Comparing our results to traditional Mellin-space methods, we find good agreement. The method is implemented in the code $\texttt{POMPOM}$ in $\texttt{Mathematica}$ as well as in $\texttt{Python}$., Comment: 29 pages, 11 figures, ancillary files with Mathematica and Python implementations of POMPOM, updated to match journal version, typos in appendix A corrected

Quasi-particles in fractional quantum Hall states are collective excitations that carry fractional charge and anyonic statistics. While the fractional charge affects semi-classical characteristics such as shot noise and charging energies, the anyonic statistics is most notable in quantum interference phenomena. In this study, we utilize a versatile bilayer graphene-based Fabry-P\'erot Interferometer (FPI) that facilitates the study of a broad spectrum of operating regimes, from Coulomb-dominated to Aharonov-Bohm, for both integer and fractional quantum Hall states. Focusing on the $\nu$=$1 \over 3$ fractional quantum Hall state, we study the Aharonov-Bohm interference of quasi-particles when the magnetic flux through an interference loop and the charge density within the loop are independently varied. When their combined variation is such that the Landau filling remains $1 \over 3$ we observe pristine Aharonov-Bohm oscillations with a period of three flux quanta, as is expected from the interference of quasi-particles of one-third of the electron charge. When the combined variation is such that it leads to quasi-particles addition or removal from the loop, phase jumps emerge, and alter the phase evolution. Notably, across all cases, the average phase consistently increases by 2$\pi$ with each addition of one electron to the loop.

The 2nd generation VLTI instrument GRAVITY is a two-field infrared interferometer operating in the K band between 1.97 and 2.43 $\mu$m with either the four 8 m or the four 1.8 m telescopes of the Very Large Telescope (VLT). Beams collected by the telescopes are corrected with adaptive optics systems and the fringes are stabilized with a fringe-tracking system. A metrology system allows the measurement of internal path lengths in order to achieve high-accuracy astrometry. High sensitivity and high interferometric accuracy are achieved thanks to (i) correction of the turbulent phase, (ii) the use of low-noise detectors, and (iii) the optimization of photometric and coherence throughput. Beam combination and most of the beam transport are performed with single-mode waveguides in vacuum and at low temperature. In this paper, we present the functions and performance achieved with weakly birefringent standard single-mode fiber systems in GRAVITY. Fibered differential delay lines (FDDLs) are used to dynamically compensate for up to 6 mm of delay between the science and reference targets. Fibered polarization rotators allow us to align polarizations in the instrument and make the single-mode beam combiner close to polarization neutral. The single-mode fiber system exhibits very low birefringence (less than 23{\deg}), very low attenuation (3.6-7 dB/km across the K band), and optimized differential dispersion (less than 2.04 $\mu$rad cm2 at zero extension of the FDDLs). As a consequence, the typical fringe contrast losses due to the single-mode fibers are 6% to 10% in the lowest-resolution mode and 5% in the medium- and high-resolution modes of the instrument for a photometric throughput of the fiber chain of the order of 90%. There is no equivalent of this fiber system to route and modally filter beams with delay and polarization control in any other K-band beamcombiner., Comment: 14 pages including 2 appendices, 8 figures in the main text plus 2 figures in the appendices, final version published in A&A