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Breaking the error-threshold would mark a milestone in establishing quantum advantage for a wide range of relevant problems. One possible route is to encode information redundantly in a logical qubit by combining several noisy qubits, providing an increased robustness against external perturbations. We propose a setup for a logical qubit built from superconducting qubits (SCQs) coupled to a microwave cavity-mode. Our design is based on a recently discovered geometric stabilizing mechanism in the Bose-Hubbard wheel (BHW), which manifests as energetically well-separated clusters of many-body eigenstates. We investigate the impact of experimentally relevant perturbations between SCQs and the cavity on the spectral properties of the BHW. We show that even in the presence of typical fabrication uncertainties, the occurrence and separation of clustered many-body eigenstates is extremely robust. Introducing an additional, frequency-detuned SCQ coupled to the cavity yields duplicates of these clusters, that can be split up by an on-site potential. We show that this allows to (i) redundantly encode two logical qubit states that can be switched and read out efficiently and (ii) can be separated from the remaining many-body spectrum via geometric stabilization. We demonstrate at the example of an X-gate that the proposed logical qubit reaches single qubit-gate fidelities $>0.999$ in experimentally feasible temperature regimes $\sim10-20\,\mathrm{mK}$., Comment: 20 pages, 11 figures

We present a matrix-product state (MPS) based band-Lanczos method as solver for quantum cluster methods such as the variational cluster approximation (VCA). While a na\"ive implementation of MPS as cluster solver would barely improve its range of applicability, we show that our approach makes it possible to treat cluster geometries well beyond the reach of exact diagonalization methods. The key modifications we introduce are a continuous energy truncation combined with a convergence criterion that is more robust against approximation errors introduced by the MPS representation and provides a bound to deviations in the resulting Green's function. The potential of the resulting cluster solver is demonstrated by computing the self-energy functional for the single-band Hubbard model at half filling in the strongly correlated regime, on different cluster geometries. Here, we find that only when treating large cluster sizes, observables can be extrapolated to the thermodynamic limit, which we demonstrate at the example of the staggered magnetization. Treating clusters sizes with up to $6\times 6$ sites we obtain excellent agreement with quantum Monte-Carlo results., Comment: 12 pages, 8 figures and appendix; comments very welcome

Coarse-grained reconfigurable arrays (CGRAs) are domain-specific devices promising both the flexibility of FPGAs and the performance of ASICs. However, with restricted domains comes a danger: designing chips that cannot accelerate enough current and future software to justify the hardware cost. We introduce FlexC, the first flexible CGRA compiler, which allows CGRAs to be adapted to operations they do not natively support. FlexC uses dataflow rewriting, replacing unsupported regions of code with equivalent operations that are supported by the CGRA. We use equality saturation, a technique enabling efficient exploration of a large space of rewrite rules, to effectively search through the program-space for supported programs. We applied FlexC to over 2,000 loop kernels, compiling to four different research CGRAs and 300 generated CGRAs and demonstrate a 2.2$\times$ increase in the number of loop kernels accelerated leading to 3$\times$ speedup compared to an Arm A5 CPU on kernels that would otherwise be unsupported by the accelerator.

Handling entirely unknown data is a challenge for any deployed classifier. Classification models are typically trained on a static pre-defined dataset and are kept in the dark for the open unassigned feature space. As a result, they struggle to deal with out-of-distribution data during inference. Addressing this task on the class-level is termed open-set recognition (OSR). However, most OSR methods are inherently limited, as they train closed-set classifiers and only adapt the downstream predictions to OSR. This work presents LORD, a framework to Leverage Open-set Recognition by exploiting unknown Data. LORD explicitly models open space during classifier training and provides a systematic evaluation for such approaches. We identify three model-agnostic training strategies that exploit background data and applied them to well-established classifiers. Due to LORD's extensive evaluation protocol, we consistently demonstrate improved recognition of unknown data. The benchmarks facilitate in-depth analysis across various requirement levels. To mitigate dependency on extensive and costly background datasets, we explore mixup as an off-the-shelf data generation technique. Our experiments highlight mixup's effectiveness as a substitute for background datasets. Lightweight constraints on mixup synthesis further improve OSR performance., Comment: Accepted at ICCV 2023 Workshop (Out-Of-Distribution Generalization in Computer Vision)

Materials with strong electronic correlations may exhibit a superconducting (SC) phase when tuning some parameters, but they almost always also have multiple other phases, typically insulating ones, that are in close competition with SC. It is highly challenging to resolve this competition with quantitative numerics for the group of quasi-two-dimensional materials such as the cuprates. This is the case even for the simplified minimal models of these materials, the doped 2D Hubbard model with repulsive interactions, where clusters of sufficient size to determine the phase in the thermodynamic limit can be hard-to-impossible to treat in practice. The present work shows how quasi-one-dimensional systems, 2D and 3D arrays of weakly coupled 1D correlated electrons, are much more amenable to resolve the competition between SC and insulating orders on an equal footing using matrix-product states (MPS). Using the recently established MPS plus mean field (MPS+MF) approach for fermions, we demonstrate that large systems are readily reachable in these systems, and thus the thermodynamic regime by extrapolation. Focusing on basic model systems, 3D arrays of negative-U Hubbard chains with additional nearest-neighbor interaction V, we show that despite the MF component of the MPS+MF technique we can reproduce the expected coexistence of SC and charge-density wave at V=0 for density n=1. We then show how we can tune away from coexistence by both tuning V and doping the system. This work paves the way to deploy two-channel MPS+MF theory on some highly demanding high-$T_c$ SC systems, such as 3D arrays of repulsive-U doped Hubbard ladders, where we have recently characterized the properties of such arrays in single-channel MPS+MF calculations. The present approach could thus conclusively show that this SC order would actually be obtained, by explicitly comparing SC against its insulating competitors.

In high performance domains like image processing, physics simulation or machine learning, program performance is critical. Programmers called performance engineers are responsible for the challenging task of optimising programs. Two major challenges prevent modern compilers targeting heterogeneous architectures from reliably automating optimisation. First, domain-specific compilers such as Halide for image processing and TVM for machine learning are difficult to extend with the new optimisations required by new algorithms and hardware. Second, automatic optimisation is often unable to achieve the required performance, and performance engineers often fall back to painstaking manual optimisation. This thesis shows the potential of the Shine compiler to achieve domain-extensibility, controllable automation, and generate high performance code. Domain-extensibility facilitates adapting compilers to new algorithms and hardware. Controllable automation enables performance engineers to gradually take control of the optimisation process. The first research contribution is to add 3 code generation features to Shine, namely: synchronisation barrier insertion, kernel execution, and storage folding. The second research contribution is to demonstrate how extensibility and controllability are exploited to optimise a standard image processing pipeline for corner detection. The final research contribution is to introduce sketch-guided equality saturation, a semi-automated technique that allows performance engineers to guide program rewriting by specifying rewrite goals as sketches: program patterns that leave details unspecified., Comment: PhD Thesis made at the University of Glasgow, 163 pages

We combine matrix-product state (MPS) and Mean-Field (MF) methods to model the real-time evolution of a three-dimensional (3D) extended Hubbard system formed from one-dimensional (1D) chains arrayed in parallel with weak coupling in-between them. This approach allows us to treat much larger 3D systems of correlated fermions out-of-equilibrium over a much more extended real-time domain than previous numerical approaches. We deploy this technique to study the evolution of the system as its parameters are tuned from a charge-density wave (CDW) phase into the superconducting (SC) regime, which allows us to investigate the formation of transient non-equilibrium SC. In our ansatz, we use MPS solutions for chains as input for a self-consistent time-dependent MF scheme. In this way, the 3D problem is mapped onto an effective 1D Hamiltonian that allows us to use the MPS efficiently to perform the time evolution, and to measure the BCS order parameter as a function of time. Our results confirm previous findings for purely 1D systems that for such a scenario superconductivity forms in a transient state., Comment: Comments very welcome

Recent advances in numerical methods significantly pushed forward the understanding of electrons coupled to quantized lattice vibrations. At this stage, it becomes increasingly important to also account for the effects of physically inevitable environments. In particular, we study the transport properties of the Hubbard-Holstein Hamiltonian that models a large class of materials characterized by strong electron-phonon coupling, in contact with a dissipative environment. Even in the one-dimensional and isolated case, simulating the quantum dynamics of such a system with high accuracy is very challenging due to the infinite dimensionality of the phononic Hilbert spaces. For this reason, the effects of dissipation on the conductance properties of such systems have not been investigated systematically so far. We combine the non-Markovian hierarchy of pure states method and the Markovian quantum jumps method with the newly introduced projected purified density-matrix renormalization group, creating powerful tensor-network methods for dissipative quantum many-body systems. Investigating their numerical properties, we find a significant speedup up to a factor $\sim 30$ compared to conventional tensor-network techniques. We apply these methods to study dissipative quenches, aiming for an in-depth understanding of the formation, stability, and quasi-particle properties of bipolarons. Surprisingly, our results show that in the metallic phase dissipation localizes the bipolarons, which is reminiscent of an indirect quantum Zeno effect. However, the bipolaronic binding energy remains mainly unaffected, even in the presence of strong dissipation, exhibiting remarkable bipolaron stability. These findings shed light on the problem of designing real materials exhibiting phonon-mediated high-$T_\mathrm{C}$ superconductivity.

Correlated electron states are at the root of many important phenomena including unconventional superconductivity (USC), where electron-pairing arises from repulsive interactions. Computing the properties of correlated electrons, such as the critical temperature $T_c$ for the onset of USC, efficiently and reliably from the microscopic physics with quantitative methods remains a major challenge for almost all models and materials. In this theoretical work we combine matrix product states (MPS) with static mean field (MF) to provide a solution to this challenge for quasi-one-dimensional (Q1D) systems: Two- and three-dimensional (2D/3D) materials comprised of weakly coupled correlated 1D fermions. This MPS+MF framework for the ground state and thermal equilibrium properties of Q1D fermions is developed and validated for attractive Hubbard systems first, and further enhanced via analytical field theory. We then deploy it to compute $T_c$ for superconductivity in 3D arrays of weakly coupled, doped and repulsive Hubbard ladders. The MPS+MF framework thus enables the reliable, quantitative and unbiased study of USC and high-$T_c$ superconductivity - and potentially many more correlated phases - in fermionic Q1D systems from microscopic parameters, in ways inaccessible to previous methods. It opens the possibility of designing deliberately optimized Q1D superconductors, from experiments in ultracold gases to synthesizing new materials.

Dynamic environments require adaptive applications. One particular machine learning problem in dynamic environments is open world recognition. It characterizes a continuously changing domain where only some classes are seen in one batch of the training data and such batches can only be learned incrementally. Open world recognition is a demanding task that is, to the best of our knowledge, addressed by only a few methods. This work introduces a modification of the widely known Extreme Value Machine (EVM) to enable open world recognition. Our proposed method extends the EVM with a partial model fitting function by neglecting unaffected space during an update. This reduces the training time by a factor of 28. In addition, we provide a modified model reduction using weighted maximum K-set cover to strictly bound the model complexity and reduce the computational effort by a factor of 3.5 from 2.1 s to 0.6 s. In our experiments, we rigorously evaluate openness with two novel evaluation protocols. The proposed method achieves superior accuracy of about 12 % and computational efficiency in the tasks of image classification and face recognition., Comment: Accepted at ICPR 2022

Deep learning based computed tomography (CT) reconstruction has demonstrated outstanding performance on simulated 2D low-dose CT data. This applies in particular to domain adapted neural networks, which incorporate a handcrafted physics model for CT imaging. Empirical evidence shows that employing such architectures reduces the demand for training data and improves upon generalisation. However, their training requires large computational resources that quickly become prohibitive in 3D helical CT, which is the most common acquisition geometry used for medical imaging. Furthermore, clinical data also comes with other challenges not accounted for in simulations, like errors in flux measurement, resolution mismatch and, most importantly, the absence of the real ground truth. The necessity to have a computationally feasible training combined with the need to address these issues has made it difficult to evaluate deep learning based reconstruction on clinical 3D helical CT. This paper modifies a domain adapted neural network architecture, the Learned Primal-Dual (LPD), so that it can be trained and applied to reconstruction in this setting. We achieve this by splitting the helical trajectory into sections and applying the unrolled LPD iterations to those sections sequentially. To the best of our knowledge, this work is the first to apply an unrolled deep learning architecture for reconstruction on full-sized clinical data, like those in the Low dose CT image and projection data set (LDCT). Moreover, training and testing is done on a single GPU card with 24GB of memory.

The trend towards specialization of software and hardware - fuelled by the end of Moore's law and the still accelerating interest in domain-specific computing, such as machine learning - forces us to radically rethink our compiler designs. The era of a universal compiler framework built around a single one-size-fits-all intermediate representation (IR) is over. This realization has sparked the creation of the MLIR compiler framework that empowers compiler engineers to design and integrate IRs capturing specific abstractions. MLIR provides a generic framework for SSA-based IRs, but it doesn't help us to decide how we should design IRs that are easy to develop, to work with and to combine into working compilers. To address the challenge of IR design, we advocate for a language-oriented compiler design that understands IRs as formal programming languages and enforces their correct use via an accompanying type system. We argue that programming language techniques directly guide extensible IR designs and provide a formal framework to reason about transforming between multiple IRs. In this paper, we discuss the design of the Shine compiler that compiles the high-level functional pattern-based data-parallel language RISE via a hybrid functional-imperative intermediate language to C, OpenCL, and OpenMP. We compare our work directly with the closely related pattern-based Lift IR and compiler. We demonstrate that our language-oriented compiler design results in a more robust and predictable compiler that is extensible at various abstraction levels. Our experimental evaluation shows that this compiler design is able to generate high-performance GPU code.

Generating high-performance code for diverse hardware and application domains is challenging. Functional array programming languages with patterns like map and reduce have been successfully combined with term rewriting to define and explore optimization spaces. However, deciding what sequence of rewrites to apply is hard and has a huge impact on the performance of the rewritten program. Equality saturation avoids the issue by exploring many possible ways to apply rewrites, efficiently representing many equivalent programs in an e-graph data structure. Equality saturation has some limitations when rewriting functional language terms, as currently naive encodings of the lambda calculus are used. We present new techniques for encoding polymorphically typed lambda calculi, and show that the efficient encoding reduces the runtime and memory consumption of equality saturation by orders of magnitude. Moreover, equality saturation does not yet scale to complex compiler optimizations. These emerge from long rewrite sequences of thousands of rewrite steps, and may use pathological combinations of rewrite rules that cause the e-graph to quickly grow too large. This paper introduces \emph{sketch-guided equality saturation}, a semi-automatic technique that allows programmers to provide program sketches to guide rewriting. Sketch-guided equality saturation is evaluated for seven complex matrix multiplication optimizations, including loop blocking, vectorization, and multi-threading. Even with efficient lambda calculus encoding, unguided equality saturation can locate only the two simplest of these optimizations, the remaining five are undiscovered even with an hour of compilation time and 60GB of RAM. By specifying three or fewer sketch guides all seven optimizations are found in seconds of compilation time, using under 1GB of RAM, and generating high performance code., Comment: 23 pages excluding references, submitted to OOPLSA 2022

Fermion systems with flat bands can boost superconductivity by enhancing the density of states at the Fermi level. We use quasiexact numerical methods to show that repulsive interactions between spinless fermions in a one-dimensional (1D) flat-band system, the Creutz ladder, give a finite pairing energy that increases with repulsion, though charge quasi-order (QO) remains dominant. Adding an attractive component shifts the balance in favor of superconductivity and the interplay of two flat bands further yields a remarkable enhancement of superconductivity, well outside of known paradigms for 1D fermions.

This work presents an approach for image reconstruction in clinical low-dose tomography that combines principles from sparse signal processing with ideas from deep learning. First, we describe sparse signal representation in terms of dictionaries from a statistical perspective and interpret dictionary learning as a process of aligning distribution that arises from a generative model with empirical distribution of true signals. As a result we can see that sparse coding with learned dictionaries resembles a specific variational autoencoder, where the decoder is a linear function and the encoder is a sparse coding algorithm. Next, we show that dictionary learning can also benefit from computational advancements introduced in the context of deep learning, such as parallelism and as stochastic optimization. Finally, we show that regularization by dictionaries achieves competitive performance in computed tomography (CT) reconstruction comparing to state-of-the-art model based and data driven approaches., Comment: 34 pages, 5 figures

Lattice models consisting of high-dimensional local degrees of freedom without global particle-number conservation constitute an important problem class in the field of strongly correlated quantum many-body systems. For instance, they are realized in electron-phonon models, cavities, atom-molecule resonance models, or superconductors. In general, these systems elude a complete analytical treatment and need to be studied using numerical methods where matrix-product states (MPS) provide a flexible and generic ansatz class. Typically, MPS algorithms scale at least quadratic in the dimension of the local Hilbert spaces. Hence, tailored methods, which truncate this dimension, are required to allow for efficient simulations. Here, we describe and compare three state-of-the-art MPS methods each of which exploits a different approach to tackle the computational complexity. We analyze the properties of these methods for the example of the Holstein model, performing high-precision calculations as well as a finite-size-scaling analysis of relevant ground-state obervables. The calculations are performed at different points in the phase diagram yielding a comprehensive picture of the different approaches., Comment: ancillary data files provided

Visual inspection of solar modules is an important monitoring facility in photovoltaic power plants. Since a single measurement of fast CMOS sensors is limited in spatial resolution and often not sufficient to reliably detect small defects, we apply multi-frame super-resolution (MFSR) to a sequence of low resolution measurements. In addition, the rectification and removal of lens distortion simplifies subsequent analysis. Therefore, we propose to fuse this pre-processing with standard MFSR algorithms. This is advantageous, because we omit a separate processing step, the motion estimation becomes more stable and the spacing of high-resolution (HR) pixels on the rectified module image becomes uniform w. r. t. the module plane, regardless of perspective distortion. We present a comprehensive user study showing that MFSR is beneficial for defect recognition by human experts and that the proposed method performs better than the state of the art. Furthermore, we apply automated crack segmentation and show that the proposed method performs 3x better than bicubic upsampling and 2x better than the state of the art for automated inspection.

X-ray dark-field imaging enables a spatially-resolved visualization of ultra-small-angle X-ray scattering. Using phantom measurements, we demonstrate that a material's effective dark-field signal may be reduced by modification of the visibility spectrum by other dark-field-active objects in the beam. This is the dark-field equivalent of conventional beam-hardening, and is distinct from related, known effects, where the dark-field signal is modified by attenuation or phase shifts. We present a theoretical model for this group of effects and verify it by comparison to the measurements. These findings have significant implications for the interpretation of dark-field signal strength in polychromatic measurements., Comment: 13 pages, 6 figures. Submitted to IEEE Transactions on Medical Imaging

The atomic physic collaboration SPARC is a part of the APPA pillar at the future Facility for Antiproton and Ion Research. It aims for atomic-physics research across virtually the full range of atomic matter. A research area of the atomic physics experiments is the study of the collision dynamics in strong electro-magnetic fields as well as the fundamental interactions between electrons and heavy nuclei at the HESR. Here we give a short overview about the central instruments for SPARC experiments at this storage ring., Comment: 4 pages, 1 figures

Quantum lattice models with large local Hilbert spaces emerge across various fields in quantum many-body physics. Problems such as the interplay between fermions and phonons, the BCS-BEC crossover of interacting bosons, or decoherence in quantum simulators have been extensively studied both theoretically and experimentally. In recent years, tensor network methods have become one of the most successful tools to treat lattice systems numerically. Nevertheless, systems with large local Hilbert spaces remain challenging. Here, we introduce a mapping that allows to construct artificial $U(1)$ symmetries for any type of lattice model. Exploiting the generated symmetries, numerical expenses that are related to the local degrees of freedom decrease significantly. This allows for an efficient treatment of systems with large local dimensions. Further exploring this mapping, we reveal an intimate connection between the Schmidt values of the corresponding matrix-product-state representation and the single-site reduced density matrix. Our findings motivate an intuitive physical picture of the truncations occurring in typical algorithms and we give bounds on the numerical complexity in comparison to standard methods that do not exploit such artificial symmetries. We demonstrate this new mapping, provide an implementation recipe for an existing code, and perform example calculations for the Holstein model at half filling. We studied systems with a very large number of lattice sites up to $L=501$ while accounting for $N_{\rm ph}=63$ phonons per site with high precision in the CDW phase., Comment: updated to version published in SciPost Phys. 10, 058 (2021)

Optimizing programs to run efficiently on modern parallel hardware is hard but crucial for many applications. The predominantly used imperative languages - like C or OpenCL - force the programmer to intertwine the code describing functionality and optimizations. This results in a nightmare for portability which is particularly problematic given the accelerating trend towards specialized hardware devices to further increase efficiency. Many emerging DSLs used in performance demanding domains such as deep learning, automatic differentiation, or image processing attempt to simplify or even fully automate the optimization process. Using a high-level - often functional - language, programmers focus on describing functionality in a declarative way. In some systems such as Halide or TVM, a separate schedule specifies how the program should be optimized. Unfortunately, these schedules are not written in well-defined programming languages. Instead, they are implemented as a set of ad-hoc predefined APIs that the compiler writers have exposed. In this paper, we present Elevate: a functional language for describing optimization strategies. Elevate follows a tradition of prior systems used in different contexts that express optimization strategies as composition of rewrites. In contrast to systems with scheduling APIs, in Elevate programmers are not restricted to a set of built-in optimizations but define their own optimization strategies freely in a composable way. We show how user-defined optimization strategies in Elevate enable the effective optimization of programs expressed in a functional data-parallel language demonstrating competitive performance with Halide and TVM., Comment: https://elevate-lang.org/ https://github.com/elevate-lang

High dynamic range (HDR) imaging combines multiple images with different exposure times into a single high-quality image. The image signal processing pipeline (ISP) is a core component in digital cameras to perform these operations. It includes demosaicing of raw color filter array (CFA) data at different exposure times, alignment of the exposures, conversion to HDR domain, and exposure merging into an HDR image. Traditionally, such pipelines cascade algorithms that address these individual subtasks. However, cascaded designs suffer from error propagation, since simply combining multiple steps is not necessarily optimal for the entire imaging task. This paper proposes a multi-exposure HDR image signal processing pipeline (Merging-ISP) to jointly solve all these subtasks. Our pipeline is modeled by a deep neural network architecture. As such, it is end-to-end trainable, circumvents the use of hand-crafted and potentially complex algorithms, and mitigates error propagation. Merging-ISP enables direct reconstructions of HDR images of dynamic scenes from multiple raw CFA images with different exposures. We compare Merging-ISP against several state-of-the-art cascaded pipelines. The proposed method provides HDR reconstructions of high perceptual quality and it quantitatively outperforms competing ISPs by more than 1 dB in terms of PSNR., Comment: Computational Photography, DAGM GCPR 2021

Recent pump-probe experiments on underdoped cuprates and similar systems suggest the existence of a transient superconducting state above $\mathrm{T}_c$. This poses the question how to reliably identify the emergence of long-range order, in particular superconductivity, out-of-equilibrium. We investigate this point by studying a quantum quench in an extended Hubbard model and by computing various observables, which are used to identify (quasi-)long-range order in equilibrium. Our findings imply that, in contrast to current experimental studies, it does not suffice to study the time evolution of the optical conductivity to identify superconductivity. In turn, we suggest to utilize time-resolved ARPES experiments to probe for the formation of a condensate in the two-particle channel., Comment: Comments welcome

Matrix-product states have become the de facto standard for the representation of one-dimensional quantum many body states. During the last few years, numerous new methods have been introduced to evaluate the time evolution of a matrix-product state. Here, we will review and summarize the recent work on this topic as applied to finite quantum systems. We will explain and compare the different methods available to construct a time-evolved matrix-product state, namely the time-evolving block decimation, the MPO $W^\mathrm{II}$ method, the global Krylov method, the local Krylov method and the one- and two-site time-dependent variational principle. We will also apply these methods to four different representative examples of current problem settings in condensed matter physics., Comment: Content identical to final journal version, plus a table of contents and minus some formatting errors

The optical resolution of a digital camera is one of its most crucial parameters with broad relevance for consumer electronics, surveillance systems, remote sensing, or medical imaging. However, resolution is physically limited by the optics and sensor characteristics. In addition, practical and economic reasons often stipulate the use of out-dated or low-cost hardware. Super-resolution is a class of retrospective techniques that aims at high-resolution imagery by means of software. Multi-frame algorithms approach this task by fusing multiple low-resolution frames to reconstruct high-resolution images. This work covers novel super-resolution methods along with new applications in medical imaging., Comment: Ph.D. thesis at the Friedrich-Alexander-Universit\"at (FAU) Erlangen-N\"urnberg; source code is available at https://www5.cs.fau.de/de/forschung/software/multi-frame-super-resolution-toolbox/ . https://opus4.kobv.de/opus4-fau/frontdoor/index/index/docId/9145