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From biology and astronomy to quantum optics, there is a critical need for high frame rate, high quantum efficiency imaging. In practice, most cameras only satisfy one of these requirements. Here we introduce interlaced fast kinetics imaging, a technique that allows burst video acquisition at frame rates up to 3.33 Mfps using a commercial EMCCD camera with single-photon sensitivity. This approach leverages EMCCD's intrinsic fast row transfer dynamics by introducing a tilted lens array into the imaging path, creating a spatially distributed grid of exposed pixels, each aligned to its own column of the sensor. The remaining unexposed pixels serve as in-situ storage registers, allowing subsequent frames to be captured after just one row shift operation. Our interlaced fast kinetics camera maintains 50% contrast for square wave intensity modulation frequencies up to 1.61 MHz. We provide benchmarks of the video performance by capturing two dimensional videos of spatially evolving patterns that repeat every 2$\mu$s, with spatial resolution of 11$\times$15 pixels. Our approach is compatible with commercial EMCCDs and opens a new route to ultra-fast imaging at single-photon sensitivity with applications from fast fluorescence imaging to photon correlation measurement., Comment: 16 pages, 11 figures

Time series in natural sciences, such as hydrology and climatology, and other environmental applications, often consist of continuous observations constrained to the unit interval (0,1). Traditional Gaussian-based models fail to capture these bounds, requiring more flexible approaches. This paper introduces the Matsuoka Autoregressive Moving Average (MARMA) model, extending the GARMA framework by assuming a Matsuoka-distributed random component taking values in (0,1) and an ARMA-like systematic structure allowing for random time-dependent covariates. Parameter estimation is performed via partial maximum likelihood (PMLE), for which we present the asymptotic theory. It enables statistical inference, including confidence intervals and model selection. To construct prediction intervals, we propose a novel bootstrap-based method that accounts for dependence structure uncertainty. A comprehensive Monte Carlo simulation study assesses the finite sample performance of the proposed methodologies, while an application to forecasting the useful water volume of the Guarapiranga Reservoir in Brazil showcases their practical usefulness.

We present the first deep implicit 3D shape model of the female breast, building upon and improving the recently proposed Regensburg Breast Shape Model (RBSM). Compared to its PCA-based predecessor, our model employs implicit neural representations; hence, it can be trained on raw 3D breast scans and eliminates the need for computationally demanding non-rigid registration -- a task that is particularly difficult for feature-less breast shapes. The resulting model, dubbed iRBSM, captures detailed surface geometry including fine structures such as nipples and belly buttons, is highly expressive, and outperforms the RBSM on different surface reconstruction tasks. Finally, leveraging the iRBSM, we present a prototype application to 3D reconstruct breast shapes from just a single image. Model and code publicly available at https://rbsm.re-mic.de/implicit., Comment: 6 pages, 5 figures

Predictive synthesis of aqueous organic solutions with desired liquid-solid phase equilibria could drive progress in industrial chemistry, cryopreservation, and beyond, but is limited by the predictive power of current solution thermodynamics models. In particular, few analytical models enable accurate liquidus and eutectic prediction based only on bulk thermodynamic properties of the pure components, requiring instead either direct measurement or costly simulation of solution properties. In this work, we demonstrate that a simple modification to the canonical ideal solution theory accounting for the entopic effects of dissimilar molecule sizes can transform its predictive power, while offering new insight into the thermodynamic nature of aqueous organic solutions. Incorporating a Flory-style entropy of mixing term that includes both the mole and volume fractions of each component, we derive size-dependent equations for the ideal chemical potential and liquidus temperature, and use them to predict the binary phase diagrams of water and 10 organic solutes of varying sizes. We show that size-dependent prediction outperforms the ideal model in all cases, reducing average error in the predicted liquidus temperature by 59\%, eutectic temperature by 45\%, and eutectic composition by 43\%, as compared to experimental data. Furthermore, by retaining the ideal assumption that the enthalpy of mixing is zero, we demonstrate that for aqueous organic solutions, much of the deviation from ideality that is typically attributed to molecular interactions may in fact be explained by simple entropic size effects. These results suggest an underappreciated dominance of mixing entropy in these solutions, and provide a simple approach to predicting their phase equilibria., Comment: 7 pages, 3 figures

When employing deep neural networks (DNNs) for semantic segmentation in safety-critical applications like automotive perception or medical imaging, it is important to estimate their performance at runtime, e.g. via uncertainty estimates or prediction quality estimates. Previous works mostly performed uncertainty estimation on pixel-level. In a line of research, a connected-component-wise (segment-wise) perspective was taken, approaching uncertainty estimation on an object-level by performing so-called meta classification and regression to estimate uncertainty and prediction quality, respectively. In those works, each predicted segment is considered individually to estimate its uncertainty or prediction quality. However, the neighboring segments may provide additional hints on whether a given predicted segment is of high quality, which we study in the present work. On the basis of uncertainty indicating metrics on segment-level, we use graph neural networks (GNNs) to model the relationship of a given segment's quality as a function of the given segment's metrics as well as those of its neighboring segments. We compare different GNN architectures and achieve a notable performance improvement., Comment: 11 pages, 3 figures, submitted to BMVC "Workshop on Robust Recognition in the Open World" (https://rrow2024.github.io/call-for-papers)

Addressing the challenges posed by climate change, biodiversity loss, and environmental pollution requires comprehensive monitoring and effective data management strategies that are applicable across various scales in environmental system science. This paper introduces a versatile and transferable digital ecosystem for managing time series data, designed to adhere to the FAIR principles (Findable, Accessible, Interoperable, and Reusable). The system is highly adaptable, cloud-ready, and suitable for deployment in a wide range of settings, from small-scale projects to large-scale monitoring initiatives. The ecosystem comprises three core components: the Sensor Management System (SMS) for detailed metadata registration and management; time$.$IO, a platform for efficient time series data storage, transfer, and real-time visualization; and the System for Automated Quality Control (SaQC), which ensures data integrity through real-time analysis and quality assurance. The modular architecture, combined with standardized protocols and interfaces, ensures that the ecosystem can be easily transferred and deployed across different environments and institutions. This approach enhances data accessibility for a broad spectrum of stakeholders, including researchers, policymakers, and the public, while fostering collaboration and advancing scientific research in environmental monitoring.

While the blockchain-based smart contract has become a hot topic of research over the last decade, not the least in the context of Industry 4.0, it now has well-known legal and technical shortcomings that currently prohibit its real-world application. These shortcomings come from (1) that a smart contract is a computer program, not a document describing legal obligations, and (2) that blockchain-based systems are complicated to use and operate. In this paper, we present a refined and extended summary of our work taking key technologies from the blockchain sphere and applying them to the ricardian contract, which is a traditional contract in digital form with machine-readable parameters. By putting the ricardian contract in the context of our contract network architecture, we facilitate the infrastructure required for contracts to be offered, negotiated, performed, renegotiated and terminated in a completely digital and automatable fashion. Our architecture circumvents the legal issues of blockchains by facilitating an artifact very much alike a traditional contract, as well as its operational complexity by requiring consensus only between nodes representing directly involved parties. To demonstrate its utility, we also present how it could be used for (1) private data purchasing, (2) treasury management, (3) order-driven manufacturing and (4) automated device on-boarding., Comment: 11 pages, 9 figures

Electron-electron interactions in high-mobility conductors can give rise to transport signatures resembling those described by classical hydrodynamics. Using a nanoscale scanning magnetometer, we imaged a distinctive hydrodynamic transport pattern - stationary current vortices - in a monolayer graphene device at room temperature. By measuring devices with increasing characteristic size, we observed the disappearance of the current vortex and thus verify a prediction of the hydrodynamic model. We further observed that vortex flow is present for both hole- and electron-dominated transport regimes, while disappearing in the ambipolar regime. We attribute this effect to a reduction of the vorticity diffusion length near charge neutrality. Our work showcases the power of local imaging techniques for unveiling exotic mesoscopic transport phenomena., Comment: Main text and supplementary materials: 16 + 28 pages, 4 + 15 figures. This is the author's version of the work. It is posted here by permission of the AAAS for personal use, not for redistribution. The definitive version was published in Science on 25 April 2024, DOI: 10.1126/science.adj2167

The search for Majorana excitations has seen tremendous efforts in recent years, ultimately aiming for their individual controllability in future topological quantum computers. A promising framework to realize such exotic Majorana fermions are topologically ordered non-Abelian phases of matter, such as certain fractional quantum Hall states. Quantum simulators provide unprecedented controllability and versatility to investigate such states, and developing experimentally feasible schemes to realize and identify them is of immediate relevance. Motivated by recent experiments, we consider bosons on coupled chains, subjected to a magnetic flux and experiencing Hubbard repulsion. At magnetic filling factor $\nu=1$, similar systems on cylinders have been found to host the non-Abelian Moore-Read Pfaffian state in the bulk. Here, we address the question whether more realistic few-leg ladders can host this exotic state and its chiral Majorana edge states. To this end, we perform extensive DMRG simulations and determine the central charge of the ground state. While we do not find any evidence of gapless Majorana edge modes in systems of up to six legs, exact diagonalization of small systems reveals evidence for the Pfaffian state in the entanglement structure. By systematically varying the number of legs and monitoring the appearance and disappearance of this signal, our work highlights the importance of finite-size effects for the realization of exotic states in experimentally realistic systems.

We present an analysis method to search for exotic low-mass field (ELF) bursts generated during large energy astrophysical events such as supernovae, binary black hole or binary neutron star mergers, and fast radio bursts using the Global Network of Optical Magnetometers for Exotic physics searches (GNOME). In our model, the associated gravitational waves or electromagnetic signals herald the arrival of the ELF burst that interacts via coupling to the spin of fermions in the magnetometers. This enables GNOME to serve as a tool for multi-messenger astronomy. The algorithm employs a model-agnostic excess-power method to identify network-wide candidate events to be subjected to a model-dependent generalized likelihood-ratio test to determine their statistical significance. We perform the first search with this technique on GNOME data coincident with the binary black hole merger S200311bg detected by LIGO/Virgo on the 11th of March 2020 and find no significant events. We place the first lab-based limits on combinations of ELF production and coupling parameters.

From fundamental studies of light-matter interaction to applications in quantum networking and sensing, cavity quantum electrodynamics (QED) provides a platform-crossing toolbox to control interactions between atoms and photons. The coherence of such interactions is determined by the product of the single-pass atomic absorption and the number of photon round-trips. Reducing the cavity loss has enabled resonators supporting nearly 1-million optical roundtrips at the expense of severely limited optical material choices and increased alignment sensitivity. The single-pass absorption probability can be increased through the use of near-concentric, fiber or nanophotonic cavities, which reduce the mode waists at the expense of constrained optical access and exposure to surface fields. Here we present a new high numerical-aperture, lens-based resonator that pushes the single-atom-single-photon absorption probability per round trip close to its fundamental limit by reducing the mode size at the atom below a micron while keeping the atom mm-to-cm away from all optics. This resonator provides strong light-matter coupling in a cavity where the light circulates only ~ 10 times. We load a single 87Rb atom into such a cavity, observe strong coupling, demonstrate cavity-enhanced atom detection with imaging fidelity of 99.55(6) percent and survival probability of 99.89(4) percent in 130 microseconds, and leverage this new platform for a time-resolved exploration of cavity cooling. The resonator's loss-resilience paves the way to coupling of atoms to nonlinear and adaptive optical elements and provides a minimally invasive route to readout of defect centers. Introduction of intra-cavity imaging systems will enable the creation of cavity arrays compatible with Rydberg atom array computing technologies, vastly expanding the applicability of the cavity QED toolbox.

A seamless chip-to-world photonic interface enables wide-ranging advancements in optical ranging, display, communication, computation, imaging, and light-matter interaction. An optimal solution allows for 2D scanning of a diffraction-limited beam from anywhere on a photonic chip over a large number of beam-spots in free-space. Currently, devices with direct PIC integration rely on tiled apertures with poor mode qualities, large footprints, and complex control systems. Micro-mechanical beam scanners have good beam quality but lack direct PIC integration and are inertially-limited due to the use of bulk optical components or structures in which the optical aperture and actuator sizes are inextricably linked, resulting in trade-offs among resolution, speed, and footprint. Here, we overcome these limitations with the photonic "ski-jump": a nanoscale optical waveguide monolithically integrated atop a piezoelectrically actuated cantilever which passively curls ~90$^{\circ}$ out-of-plane in a footprint of <0.1 mm$^{2}$, emits sub-micron diffraction-limited optical modes, and exhibits kHz-rate mechanical resonances with quality factors exceeding 10,000. This enables two-dimensional beam-scanning with footprint-adjusted spot-rates of 68.6 mega-spots/(s$\cdot$mm$^{2}$) at CMOS-level voltages, which is equivalent to a 1 megapixel display at 100 Hz from a 1.5 mm$^{2}$ footprint, and exceeds the performance of state-of-the-art MEMS mirrors by >50$\times$. Using this device, we demonstrate image projection, video projection, and the initialization and readout of single photons from silicon vacancy centers in diamond waveguides. Based on current performance, we identify pathways for achieving >1 giga-spots at kHz-rates in a ~1 cm$^{2}$ area to provide a seamless, scalable optical pipeline between integrated photonic processors and the free-space world., Comment: 12 pages main text, 1 page methods, 10 pages supplementary information

Due to their immense representative power, neural network quantum states (NQS) have gained significant interest in current research. In recent advances in the field of NQS, it has been demonstrated that this approach can compete with state-of-the-art numerical techniques, making NQS a compelling alternative, in particular for the simulation of large, two-dimensional quantum systems. In this study, we show that recurrent neural network (RNN) wave functions can be employed to study systems relevant to current research in quantum many-body physics. Specifically, we employ a 2D tensorized gated RNN to explore the bosonic Hofstadter model with a variable local Hilbert space cut-off and long-range interactions. At first, we benchmark the RNN-NQS for the Hofstadter-Bose-Hubbard (HBH) Hamiltonian on a square lattice. We find that this method is, despite the complexity of the wave function, capable of efficiently identifying and representing most ground state properties. Afterwards, we apply the method to an even more challenging model for current methods, namely the Hofstadter model with long-range interactions. This model describes Rydberg-dressed atoms on a lattice subject to a synthetic magnetic field. We study systems of size up to $12 \times 12$ sites and identify three different regimes by tuning the interaction range and the filling fraction $\nu$. In addition to phases known from the HBH model at short-ranged interaction, we observe bubble crystals and Wigner crystals for long-ranged interactions. Especially interesting is the evidence of a bubble crystal phase on a lattice, as this gives experiments a starting point for the search of clustered liquid phases, possibly hosting non-Abelian anyon excitations. In our work we show that NQS are an efficient and reliable simulation method for quantum systems, which are the subject of current research., Comment: 11 pages, 8 figures + Appendix

Designing thermodynamic conditions to improve (or reduce) the stability of a target material is a key task in materials engineering. For example, during materials synthesis one aims to enhance the stability of a target phase relative to its precursors or competing byproduct phases. If an undesired phase forms in experiment, one aims to destabilize the undesired phase by dissolution or corrosion. When multiple thermodynamic knobs are available to engineer relative stability, it can be difficult to navigate the corresponding high-dimensional phase diagram to identify optimal pathways to promote or destabilize a target phase. We propose that instead of mapping the absolute phase boundaries of a target material, we can invoke a generalized Clausius-Clapeyron relation, which provides a 'compass' to point out which directions on a high-dimensional phase diagram are best to stabilize or destabilize a target phase. Phase boundaries on high-dimensional phase diagrams are also high-dimensional objects, and can represent phase coexistence between numerous phases simultaneously. On a 2D temperature-pressure phase diagram, phase boundaries are 1D lines separating two phases, with a slope given by the Clausius-Clapeyron relation, dP/dT = {\Delta}S/{\Delta}V. Here, we derive a parametric form of the Clausius-Clapeyron relation that readily scales to high-dimensional phase boundaries. The gradient of a phase boundary guides us on how to increase or decrease the relative stability of a target compound, meaning this generalized Clausius-Clapeyron relation enables us to engineer relative stability with respect to multiple thermodynamic conditions simultaneously. Using this approach, we analyze the acid stability of manganese oxide catalysts on a 4-dimensional Pourbaix diagram with axes of pH, redox potential, nanoparticle size, and aqueous [K+] ion concentration.

Modern materials are often synthesized or operated in complex chemical environments, where there can be numerous elemental species, competing phases, and reaction pathways. When analyzing reactions using the Gibbs free energy, which has a natural variable of composition, it is often cumbersome to solve for the equilibrium states of a complicated heterogeneous mixture of phases. However, if one is interested only in the stability of a single target material, it may be easier to reframe the boundary conditions around only the target material-of-interest, with boundary conditions open to chemical exchange with an external reservoir. The corresponding phase diagram would thus have a chemical potential axis for the open volatile species, rather than a composition axis. Here we discuss how to derive, compute, and interpret phase diagrams with chemical potential axes, which are dual to the more common composition phase diagram. In our ambition to construct high-dimensional phase diagrams featuring any thermodynamic variable on its axes, here we examine the duality between extensive and intensive conjugate variables in equilibrium thermodynamics. This duality manifests from the distinction between closed and open boundary conditions of a thermodynamic system, to the relationship between the Internal Energy and its Legendre transformations, to the point-line duality in calculating convex hulls versus half-space intersections. Here we focus on the duality relationships of chemical work, with extensive composition variables, N, and intensive chemical potentials, {\mu}. In particular, we explore mixed composition-chemical potential diagrams for oxynitride synthesis, lithium-ion cathode stability, and oxidation of high-entropy alloys. We further illustrate how chemical potential diagrams reveal the driving forces for non-equilibrium growth and dissolution kinetics.

Real-time computational speed and a high degree of precision are requirements for computer-assisted interventions. Applying a segmentation network to a medical video processing task can introduce significant inter-frame prediction noise. Existing approaches can reduce inconsistencies by including temporal information but often impose requirements on the architecture or dataset. This paper proposes a method to include temporal information in any segmentation model and, thus, a technique to improve video segmentation performance without alterations during training or additional labeling. With Motion-Corrected Moving Average, we refine the exponential moving average between the current and previous predictions. Using optical flow to estimate the movement between consecutive frames, we can shift the prior term in the moving-average calculation to align with the geometry of the current frame. The optical flow calculation does not require the output of the model and can therefore be performed in parallel, leading to no significant runtime penalty for our approach. We evaluate our approach on two publicly available segmentation datasets and two proprietary endoscopic datasets and show improvements over a baseline approach.

Phase stability, and the limits thereof, are a central concern of materials thermodynamics. However, the temperature limits of equilibrium liquid stability in chemical systems have only been widely characterized under constant (typically atmospheric) pressure conditions, whereunder the limit is represented by the eutectic. At higher pressures, this limit will shift in both temperature and chemical composition, opening a wide thermodynamic parameter space over which the absolute limit, i.e., the limit under arbitrary values of the thermodynamic forces at play (here pressure and concentration), might exist. In this work, we use isochoric freezing to measure this absolute limit for the first time in several binary aqueous brines, and, nodding to the etymology of "eutectic", we name this limit the "cenotectic" (from Greek " ", "universal-melt"). We observe that when no solute-bearing high-pressure phases exist, the cenotectic occurs consistently 22 +/- 2K below the 1 bar eutectic and at approximately 213 +/- 3 MPa, suggesting domination by the liquidus behaviors of the icy phases present. In charting the T-P evolution of each eutectic configuration, we also encounter several unreported high-pressure hydrates of NaHCO2, MgCl2, and NaCl, and we find that these high-pressure phases can produce complex multi-phase configurations involving the liquid that may remain metastable to significantly lower temperatures. We discuss the implications of these findings for ocean worlds of our solar system and cold ocean exoplanets; estimate thermodynamic limits on ice crust thickness and final ocean depth ("endgame") using the cenotectic pressure; and finally provide a generalized thermodynamic perspective on (and definition for) this fundamental thermodynamic invariant point.

The increasing pressure within VUCA (volatility, uncertainty, complexity and ambiguity) driven environments causes traditional, plan-driven Systems Engineering approaches to no longer suffice. Agility is then changing from a "nice-to-have" to a "must-have" capability for successful system developing organisations. The current state of the art, however, does not provide clear answers on how to map this need in terms of processes, methods, tools and competencies (PMTC) and how to successfully manage the transition within established industries. In this paper, we propose an agile Systems Engineering (SE) Framework for the automotive industry to meet the new agility demand. In addition to the methodological background, we present results of a pilot project in the chassis development department of a German automotive manufacturer and demonstrate the effectiveness of the newly proposed framework. By adopting the described agile SE Framework, companies can foster innovation and collaboration based on a learning, continuous improvement and self-reinforcing base., Comment: preprint of 2023 conference contribution to the German chapter (GfSE) of the International Council on Systems Engineering (INCOSE) annual conference held at VCC on 15-17 November 2023 in W\"urzburg to be published in final form within the German chapter (GfSE) of the International Council on Systems Engineering (INCOSE) annual conference 2023 proceedings

Resampling methods such as the bootstrap have proven invaluable in the field of machine learning. However, the applicability of traditional bootstrap methods is limited when dealing with large streams of dependent data, such as time series or spatially correlated observations. In this paper, we propose a novel bootstrap method that is designed to account for data dependencies and can be executed online, making it particularly suitable for real-time applications. This method is based on an autoregressive sequence of increasingly dependent resampling weights. We prove the theoretical validity of the proposed bootstrap scheme under general conditions. We demonstrate the effectiveness of our approach through extensive simulations and show that it provides reliable uncertainty quantification even in the presence of complex data dependencies. Our work bridges the gap between classical resampling techniques and the demands of modern data analysis, providing a valuable tool for researchers and practitioners in dynamic, data-rich environments.

Pound for pound, sea ice is the most important component of Earth's climate system. The changing conditions in which sea ice forms and exists are likely to affect the properties of sea ice itself, and potential climate feedbacks need to be identified and understood to improve future projections. Here we perform a set of idealised experiments which model sea ice growth under a range of ambient salinities, freezing temperatures, and freezing orientations. The results confirm existing theories; sea ice growth rate is largest for cooler freezing temperatures, fresher ambient salinities, and bottom oriented freezing configuration. Our primary metric of interest is the brine mass fraction (the mass ratio of brine inclusions to the total sea ice), which we quantify and determine the sensitivity of with respect to changes in freezing conditions. We find that the brine mass fraction of our model sea ice is most sensitive to freezing temperature, and increases 2.5% per 1oC increase of freezing temperature. This finding suggests that future sea ice in warmer climate states will retain more brine, with subsequent flow on effects for circulations driven by brine rejection in the high-latitude oceans.

The study of fractional Chern insulators and their exotic anyonic excitations poses a major challenge in current experimental and theoretical research. Quantum simulators, in particular ultracold atoms in optical lattices, provide a promising platform to realize, manipulate, and understand such systems with a high degree of controllability. Recently, an atomic $\nu=1/2$ Laughlin state has been realized experimentally for a small system of two particles on 4 by 4 sites. The next challenge concerns the preparation of Laughlin states in extended systems, ultimately giving access to anyonic braiding statistics or gapless chiral edge-states in systems with open boundaries. Here, we propose and analyze an experimentally feasible scheme to grow larger Laughlin states by connecting multiple copies of the already existing 4-by-4-system. First, we present a minimal setting obtained by coupling two of such patches, producing an extended 8-by-4-system with four particles. Then, we analyze different preparation schemes, setting the focus on two shapes for the extended system, and discuss their respective advantages: While growing strip-like lattices could give experimental access to the central charge, square-like geometries are advantageous for creating quasi-hole excitations in view of braiding protocols. We highlight the robust quantization of the fractional quasi-hole charge upon using our preparation protocol. We benchmark the performance of our patchwork preparation scheme by comparing it to a protocol based on coupling one-dimensional chains. We find that the patchwork approach consistently gives higher target-state fidelities, especially for elongated systems. The results presented here pave the way towards near-term implementations of extended Laughlin states in quantum gas microscopes and the subsequent exploration of exotic properties of topologically ordered systems in experiments., Comment: 18 pages, 21 figures

Topological phase transitions go beyond Ginzburg and Landau's paradigm of spontaneous symmetry breaking and occur without an associated local order parameter. Instead, such transitions can be characterized by the emergence of non-local order parameters, which require measurements on extensively many particles simultaneously - an impossible venture in real materials. On the other hand, quantum simulators have demonstrated such measurements, making them prime candidates for an experimental confirmation of non-local topological order. Here, building upon the recent advances in preparing few-particle fractional Chern insulators using ultracold atoms and photons, we propose a realistic scheme for detecting the hidden off-diagonal long-range order (HODLRO) characterizing Laughlin states. Furthermore, we demonstrate the existence of this hidden order in fractional Chern insulators, specifically for the $\nu=\frac{1}{2}$-Laughlin state in the isotropic Hofstadter-Bose-Hubbard model. This is achieved by large-scale numerical density matrix renormalization group (DMRG) simulations based on matrix product states, for which we formulate an efficient sampling procedure providing direct access to HODLRO in close analogy to the proposed experimental scheme. We confirm the characteristic power-law scaling of HODLRO, with an exponent $\frac{1}{\nu} = 2$, and show that its detection requires only a few thousand snapshots. This makes our scheme realistically achievable with current technology and paves the way for further analysis of non-local topological orders, e.g. in topological states with non-Abelian anyonic excitations., Comment: 13 + 5 pages, 7 + 3 figures