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We present a general method for the implementation of quantum algorithms that optimizes both gate count and circuit depth. Our approach introduces connectivity-adapted CNOT-based building blocks called Parity Twine chains. It outperforms all known state-of-the art methods for implementing prominent quantum algorithms such as the quantum Fourier transform or the Quantum Approximate Optimization Algorithm across a wide range of quantum hardware, including linear, square-grid, hexagonal, ladder and all-to-all devices. For specific cases, we rigorously prove the optimality of our approach.

In recent years, the integration of deep learning techniques with remote sensing technology has revolutionized the way natural hazards, such as floods, are monitored and managed. However, existing methods for flood segmentation using remote sensing data often overlook the utility of correlative features among multispectral satellite information. In this study, we introduce a progressive cross attention network (ProCANet), a deep learning model that progressively applies both self- and cross-attention mechanisms to multispectral features, generating optimal feature combinations for flood segmentation. The proposed model was compared with state-of-the-art approaches using Sen1Floods11 dataset and our bespoke flood data generated for the Citarum River basin, Indonesia. Our model demonstrated superior performance with the highest Intersection over Union (IoU) score of 0.815. Our results in this study, coupled with the ablation assessment comparing scenarios with and without attention across various modalities, opens a promising path for enhancing the accuracy of flood analysis using remote sensing technology., Comment: 5 pages, 4 figures, published in IEEE Geoscience and Remote Sensing Letters

The degrees of freedom of Active Flux are cell averages and point values along the cell boundaries. These latter are shared between neighbouring cells, which gives rise to a globally continuous reconstruction. The semi-discrete Active Flux method uses its degrees of freedom to obtain Finite Difference approximations to the spatial derivatives which are used in the point value update. The averages are updated using a quadrature of the flux and making use of the point values as quadrature points. The integration in time employs standard Runge-Kutta methods. We show that this generalization of the Active Flux method in two and three spatial dimensions is stationarity preserving for linear acoustics on Cartesian grids, and present an analysis of numerical diffusion and stability.

This document is comprised of a collection of updated preliminary parameters for the key parts of the muon collider. The updated preliminary parameters follow on from the October 2023 Tentative Parameters Report. Particular attention has been given to regions of the facility that are believed to hold greater technical uncertainty in their design and that have a strong impact on the cost and power consumption of the facility. The data is collected from a collaborative spreadsheet and transferred to overleaf.

Active labour market policies are widely used by the Swiss government, enrolling more than half of unemployed individuals. This paper analyses whether the Swiss programmes increase future employment and earnings of the unemployed by using causal machine learning methods and leveraging an administrative dataset that captures the population of unemployed and their labour market histories. The findings indicate a small positive average effect on employment and earnings three years after starting a specific Temporary Wage Subsidy programme. In contrast, we find negative effects for Basic Courses, such as job application training, on both outcomes three years after starting the programme. We find no significant effect for Employment Programmes which are conducted outside the regular labour market and Training Courses, such as language and computer courses. The programmes are most effective for individuals with lower education levels and with a migration background from non-EU countries. Last, shallow policy trees provide practical guidance on how the allocation of individuals to programmes could be optimised.

Using the Parity Flow formalism, we show that physical SWAP gates can be eliminated in linear hardware architectures, without increasing the total number of two-qubit operations. This has a significant impact on the execution time of quantum circuits in linear Quantum Charge-Coupled Devices (QCCDs), where SWAP gates are implemented by physically changing the position of the ions. Because SWAP gates are one of the most time-consuming operations in QCCDs, our scheme considerably reduces the runtime of the quantum Fourier transform and the quantum approximate optimization algorithm on all-to-all spin models, compared to circuits generated with standard compilers (TKET and Qiskit). While increasing the problem size (and therefore the number of qubits) typically demands longer runtimes, which are constrained by coherence time, our runtime reduction enables a significant increase in the number of qubits at a given coherence time., Comment: 9 pages, 4 figures. Typos corrected

Carbyne, an infinite linear chain of carbon atoms, is the truly one-dimensional allotrope of carbon. While ideal carbyne and its fundamental properties have remained elusive, carbyne-like materials like carbyne chains confined inside carbon nanotubes are available for study. Here, we probe the longitudinal optical phonon (C-mode) of confined carbyne chains by Raman spectroscopy up to the third overtone. We observe a strong vibrational anharmonicity that increases with decreasing C-mode frequency, reaching up to 8% for the third overtone. Moreover, we find that the relation between vibrational anharmonicity and C-mode frequency is universal to carbyne-like materials, including ideal carbyne. This establishes experimentally that carbyne and related materials have pronounced anharmonic potential landscapes which must be included in the theoretical description of their structure and properties.

We present a framework for designing scores to summarize performance metrics. Our design has two multi-criteria objectives: (1) improving on scores should improve all performance metrics, and (2) achieving pareto-optimal scores should achieve pareto-optimal metrics. We formulate our design to minimize the dimensionality of scores while satisfying the objectives. We give algorithms to design scores, which are provably minimal under mild assumptions on the structure of performance metrics. This framework draws motivation from real-world practices in hospital rating systems, where misaligned scores and performance metrics lead to unintended consequences., Comment: A condensed version of this paper appeared at Foundations of Responsible Computing (FORC) 2024

We propose a scalable encoding of combinatorial optimization problems with arbitrary connectivity, including higher-order terms, on arrays of trapped neutral atoms requiring only a global laser drive. Our approach relies on modular arrangements of a small number of problem-independent gadgets. These gadgets represent maximum-weight independent set (MWIS) problems on unit-disk graphs, which are native to such devices. Instead of programming MWIS weights with site-dependent laser detunings, the scheme relies on systematic placements of auxiliary atoms. We show, that these auxiliary atoms can be simultaneously used for both problem-specific programming and the mitigation of unwanted effects originating from the tails of long-range interactions., Comment: 11 pages, 5 figures

Dwarf galaxies hold the key to crucial frontiers of astrophysics, however, their faintness renders spectroscopy challenging. Here we present the JWST Cycle 2 survey, All the Little Things (ALT, PID 3516), which is designed to seek late-forming Pop III stars and the drivers of reionization at $z\sim6-7$. ALT has acquired the deepest NIRCam grism spectroscopy yet (7-27 hr), at JWST's most sensitive wavelengths (3-4 $\mu$m), covering the powerful lensing cluster Abell 2744. Over the same 30 arcmin$^2$, ALT's ultra-deep F070W+F090W imaging ($\sim$30 mag) enables selection of very faint sources at $z>6$. We demonstrate the success of ALT's novel ``butterfly" mosaic to solve spectral confusion and contamination, and introduce the ``Allegro" method for emission line identification. By collecting spectra for every source in the field of view, ALT has measured precise ($R\sim1600$) redshifts for 1630 sources at $z=0.2-8.5$. This includes one of the largest samples of distant dwarf galaxies: [1015, 475, 50] sources less massive than the SMC, Fornax, and Sculptor with $\log(M_{*}/M_{\odot})<$[8.5, 7.5, 6.5]. We showcase ALT's discovery space with: (i) spatially resolved spectra of lensed clumps in galaxies as faint as $M_{\rm{UV}}\sim-15$; (ii) large-scale clustering -- overdensities at $z$=[2.50, 2.58, 3.97, 4.30, 5.66, 5.77, 6.33] hosting massive galaxies with striking Balmer breaks; (iii) small-scale clustering -- a system of satellites around a Milky Way analog at $z\sim6$; (iv) spectroscopically confirmed multiple images that help constrain the lensing model underlying all science in this legacy field; (v) sensitive star-formation maps based on dust-insensitive tracers such as Pa$\alpha$; (vi) direct spectroscopic discovery of rare sources such as AGN with ionized outflows. These results provide a powerful proof of concept for how grism surveys maximize the potential of strong lensing fields., Comment: Submitted to the Open Journal of Astrophysics. Figs. 6 and 10 illustrate the quality of the spectra and imaging, while Fig. 12 summarizes the yield of the survey. Comments warmly welcomed and greatly appreciated. The ALT DR1 catalog is available at https://zenodo.org/records/13871850

The practical implementation of quantum optimization algorithms on noisy intermediate-scale quantum devices requires accounting for their limited connectivity. As such, the Parity architecture was introduced to overcome this limitation by encoding binary optimization problems onto planar quantum chips. We investigate the performance of the Quantum Approximate Optimization Algorithm on the Parity architecture (Parity QAOA) for solving instances of the signed Max-Cut problem on complete and regular graphs. By comparing the algorithms at fixed circuit depth, we demonstrate that Parity QAOA outperforms conventional QAOA implementations based on SWAP networks. Our analysis utilizes Clifford circuits to estimate lower performance bounds for Parity QAOA for problem sizes that would be otherwise inaccessible on classical computers. For single layer circuits we additionally benchmark the recursive variant of the two algorithms, showing that their performance is equal.

Sterile neutrinos are a minimal extension of the Standard Model of particle physics and a promising candidate for dark matter if their mass is in the keV-range. The Karlsruhe Tritium Neutrino experiment (KATRIN), equipped with a novel multi-pixel silicon drift detector array, the TRISTAN detector, will be capable of searching for these keV-scale sterile neutrinos by investigating the kinematics of the tritium $\beta$-decay. This measurement will be performed after the completion of the neutrino mass measurement campaign. To detect a sterile neutrino signal with a high sensitivity, a profound understanding of the detector response is required. In this work, we report on the characterization of a 7-pixel TRISTAN prototype detector with a laser system. We present the experimental results obtained in high-resolution scans of the detector surface with a focused laser beam and demonstrate how the charge collection and the timing of the signals generated in the detector is related to the detector geometry. A comparison of the experimental data with simulations shows a good agreement., Comment: 23 pages, 12 figures

While Nb3Sn theoretically offers better superconducting RF cavity performance (Q0 and Eacc) to Nb at any given temperature, peak RF magnetic fields consistently fall short of the 400 mT prediction. The relatively rough topography of vapor-diffused Nb3Sn is widely conjectured to be one of the factors that limit the attainable performance of Nb3Sn-coated Nb cavities prepared via Sn vapor diffusion. Here we investigate the effect of coating duration on the topography of vapor-diffused Nb3Sn on Nb and calculate the associated magnetic field enhancement and superheating field suppression factors using atomic force microscopy topographies. It is shown that the thermally grooved grain boundaries are major defects which may contribute to a substantial decrease in the achievable accelerating field. The severity of these grooves increases with total coating duration due to the deepening of thermal grooves during the coating process., Comment: 16 pages, 5 figures

We present a formalism based on tracking the flow of parity quantum information to implement algorithms on devices with limited connectivity without qubit overhead, SWAP operations or shuttling. Instead, we leverage the fact that entangling gates not only manipulate quantum states but can also be exploited to transport quantum information. We demonstrate the effectiveness of this method by applying it to the quantum Fourier transform (QFT) and the Quantum Approximate Optimization Algorithm (QAOA) with $n$ qubits. This improves upon all state-of-the-art implementations of the QFT on a linear nearest-neighbor architecture, resulting in a total circuit depth of ${5n-3}$ and requiring ${n^2-1}$ CNOT gates. For the QAOA, our method outperforms SWAP networks, which are currently the most efficient implementation of the QAOA on a linear architecture. We further demonstrate the potential to balance qubit count against circuit depth by implementing the QAOA on twice the number of qubits using bi-linear connectivity, which approximately halves the circuit depth., Comment: 10 pages, 5 figures

The International Muon Collider Collaboration (IMCC) [1] was established in 2020 following the recommendations of the European Strategy for Particle Physics (ESPP) and the implementation of the European Strategy for Particle Physics-Accelerator R&D Roadmap by the Laboratory Directors Group [2], hereinafter referred to as the the European LDG roadmap. The Muon Collider Study (MuC) covers the accelerator complex, detectors and physics for a future muon collider. In 2023, European Commission support was obtained for a design study of a muon collider (MuCol) [3]. This project started on 1st March 2023, with work-packages aligned with the overall muon collider studies. In preparation of and during the 2021-22 U.S. Snowmass process, the muon collider project parameters, technical studies and physics performance studies were performed and presented in great detail. Recently, the P5 panel [4] in the U.S. recommended a muon collider R&D, proposed to join the IMCC and envisages that the U.S. should prepare to host a muon collider, calling this their "muon shot". In the past, the U.S. Muon Accelerator Programme (MAP) [5] has been instrumental in studies of concepts and technologies for a muon collider., Comment: This document summarises the International Muon Collider Collaboration (IMCC) progress and status of the Muon Collider R&D programme

We present a silicon drift detector (SDD) system for the spectroscopy focusing array (SFA) of the enhanced X-ray timing and polarimetry (eXTP) mission. The SFA focuses on fast timing (time resolution below 10 {\mu}s) and good spectroscopy capabilities (energy resolution better than 180 eV @ 6 keV). The sensor, consisting of 19 hexagonally shaped pixels with a total sensitive area of ${5.05}\, cm^{2}$, is connected to three high time resolution spectroscopy (HTRS) ASICs, allowing a fast readout of the detector signals. The detector works in a Charge- Sensitive Amplifier configuration. We assembled a prototype detector module and present here its mechanical design, describe the used sensor, and report about its performance., Comment: 9 pages, 5 figures; Conference: SPIE Space Telescopes and Instrumentation 2024: Ultraviolet to Gamma Ray

The depleted p-channel field effect transistor is the chosen sensor type for the Wide Field Imager of the Athena mission. It will be used in two types of cameras. One will enable observations of a field of view of 40' x 40' by using an array of four 512 x 512 pixel sensors in a 2 x 2 configuration. A second, small one is designed to investigate bright, point-like sources with a time resolution of up to 40 microseconds. Sensors of final size, layout, and technology were fabricated, assembled and characterised. Also, first results from the flight production are available and confirm the excellent performance. In order to be able to estimate the future performance of degraded detectors, a simulation was developed that takes into account the non-analytical threshold effects on the basis of measurement results. We present the measurement analysis and the comparison of simulated and measured values as well as first attempts to use the Monte Carlo simulation to predict performance results based on noise measurements., Comment: SPIE Space Telescopes and Instrumentation 2024: Ultraviolet to Gamma Ray

We examine the relationship between learnability and robust (or agnostic) learnability for the problem of distribution learning. We show that, contrary to other learning settings (e.g., PAC learning of function classes), realizable learnability of a class of probability distributions does not imply its agnostic learnability. We go on to examine what type of data corruption can disrupt the learnability of a distribution class and what is such learnability robust against. We show that realizable learnability of a class of distributions implies its robust learnability with respect to only additive corruption, but not against subtractive corruption. We also explore related implications in the context of compression schemes and differentially private learnability., Comment: In NeurIPS 2023

We initiate the study of computability requirements for adversarially robust learning. Adversarially robust PAC-type learnability is by now an established field of research. However, the effects of computability requirements in PAC-type frameworks are only just starting to emerge. We introduce the problem of robust computable PAC (robust CPAC) learning and provide some simple sufficient conditions for this. We then show that learnability in this setup is not implied by the combination of its components: classes that are both CPAC and robustly PAC learnable are not necessarily robustly CPAC learnable. Furthermore, we show that the novel framework exhibits some surprising effects: for robust CPAC learnability it is not required that the robust loss is computably evaluable! Towards understanding characterizing properties, we introduce a novel dimension, the computable robust shattering dimension. We prove that its finiteness is necessary, but not sufficient for robust CPAC learnability. This might yield novel insights for the corresponding phenomenon in the context of robust PAC learnability, where insufficiency of the robust shattering dimension for learnability has been conjectured, but so far a resolution has remained elusive., Comment: To appear in Conference on Learning Theory (COLT) 2024

Decision-making plays a pivotal role in shaping outcomes in various disciplines, such as medicine, economics, and business. This paper provides guidance to practitioners on how to implement a decision tree designed to address treatment assignment policies using an interpretable and non-parametric algorithm. Our Policy Tree is motivated on the method proposed by Zhou, Athey, and Wager (2023), distinguishing itself for the policy score calculation, incorporating constraints, and handling categorical and continuous variables. We demonstrate the usage of the Policy Tree for multiple, discrete treatments on data sets from different fields. The Policy Tree is available in Python's open-source package mcf (Modified Causal Forest).

The Muon Collider is one of the most promising future collider facilities with the potential to reach multi-TeV center-of-mass energy and high luminosity. Due to the significant Higgs boson production cross section in muon collisions at these high energies, the collider can be considered a Higgs factory. It holds the capability to significantly advance our understanding of the Higgs sector to an unprecedented level of precision. However, the presence of beam-induced background resulting from the decay of the beam muons poses unique challenges for detector development and event reconstruction. In this paper, the prospects for various measurements of the Higgs boson production cross sections at a $\sqrt{s}=3$ TeV collider are presented using a detailed detector simulation in a realistic environment. The study demonstrates the feasibility of achieving high precision measurements of the Higgs boson production cross sections with the current state-of-the-art detector design. In addition, the paper discusses the detector requirements necessary for obtaining such resolutions and for measuring the Higgs trilinear self-coupling.

One of the main bottlenecks in solving combinatorial optimization problems with quantum annealers is the qubit connectivity in the hardware. A possible solution for larger connectivty is minor embedding. This techniques makes the geometrical properties of the combinatorial optimization problem, encoded as a Hamiltonian, match the properties of the quantum annealing hardware. The embedding itself is a hard computational problem and therefore heuristic algorithms are required. In this work, we present fixed, modular and scalable embeddings that can be used to embed any combinatorial optimization problem described as an Ising Hamiltonian. These embeddings are the result of an extension of the well-known parity mapping, which has been used in the past to map higher-order Ising Hamiltonians to quadratic Hamiltonians, which are suitable for existing quantum hardware. We show how our new embeddings can be mapped to existing quantum annealers and that the embedded Hamiltonian physical properties match the original Hamiltonian properties.

Sterile neutrinos are hypothetical particles in the minimal extension of the Standard Model of Particle Physics. They could be viable dark matter candidates if they have a mass in the keV range. The Karlsruhe tritium neutrino (KATRIN) experiment, extended with a silicon drift detector focal plane array (TRISTAN), has the potential to search for keV-scale sterile neutrinos by measuring the kinematics of the tritium $\beta$-decay. The collaboration targets a sensitivity of $10^{-6}$ on the mixing amplitude $\sin^2{\Theta}$. For this challenging target, a precise understanding of the detector response is necessary. In this work, we report on the characterization of electron backscattering from the detector surface, which is one of the main effects that influence the shape of the observed energy spectrum. Measurements were performed with a tandem silicon drift detector system and a custom-designed electron source. The measured detector response and backscattering probability are in good agreement with dedicated backscattering simulations using the Geant4 simulation toolkit.

The effect of mid-T heat treatment on flux trapping sensitivity was measured on several 1.3 GHz single cell cavities subjected to vacuum annealing at temperature of 150 - 400 $^\circ$C for a duration of 3 hours. The cavity was cooldown with residual magnetic field $\sim$0 and $\sim$20 mG in the Dewar with cooldown condition of full flux trapping. The quality factor as a function of accelerating gradient was measured. The results show the correlation between the treatment temperature, quality factor, and sensitivity to flux trapping. Sensitivity increases with increasing heat treatment temperatures within the range of (200 - 325 $^\circ$C/3h). Moreover, variations in the effective penetration depth of the magnetic field and the density of quasi-particles can occur, influencing alterations in the cavity's electromagnetic response and resonance frequency., Comment: to be published in proceeding of IPAC2024

Uncovering causal effects at various levels of granularity provides substantial value to decision makers. Comprehensive machine learning approaches to causal effect estimation allow to use a single causal machine learning approach for estimation and inference of causal mean effects for all levels of granularity. Focusing on selection-on-observables, this paper compares three such approaches, the modified causal forest (mcf), the generalized random forest (grf), and double machine learning (dml). It also provides proven theoretical guarantees for the mcf and compares the theoretical properties of the approaches. The findings indicate that dml-based methods excel for average treatment effects at the population level (ATE) and group level (GATE) with few groups, when selection into treatment is not too strong. However, for finer causal heterogeneity, explicitly outcome-centred forest-based approaches are superior. The mcf has three additional benefits: (i) It is the most robust estimator in cases when dml-based approaches underperform because of substantial selectivity; (ii) it is the best estimator for GATEs when the number of groups gets larger; and (iii), it is the only estimator that is internally consistent, in the sense that low-dimensional causal ATEs and GATEs are obtained as aggregates of finer-grained causal parameters., Comment: arXiv admin note: text overlap with arXiv:2209.03744

The ASPECT-BET (An sdd-SPECTrometer for BETa decay studies) project aims to develop a novel technique for the precise measurement of forbidden $\beta$ spectra in the 10 keV - 1 MeV range. This technique uses a Silicon Drift Detector (SDD) as the main spectrometer, surrounded, if necessary, by a veto system to reject events with only partial energy deposition in the SDD. Accurate knowledge of the spectrometer's response to electrons is essential to reconstruct the theoretical shape of the $\beta$ spectrum. To compute this response, GEANT4 simulations optimized for low-energy electron interactions are used. In this article, we present the performance of these simulations in reconstructing the electron spectra, measured with SDDs, of a $^{109}$Cd monochromatic source, both in vacuum and in air. The allowed $\beta$ spectrum of a $^{14}$C source is also measured and analyzed, and it is shown that the experimental shape factor commonly used in the literature to reconstruct the measured spectrum is not necessary to explain the spectrum.

We approach designing a state-space model for deep learning applications through its dual representation, the transfer function, and uncover a highly efficient sequence parallel inference algorithm that is state-free: unlike other proposed algorithms, state-free inference does not incur any significant memory or computational cost with an increase in state size. We achieve this using properties of the proposed frequency domain transfer function parametrization, which enables direct computation of its corresponding convolutional kernel's spectrum via a single Fast Fourier Transform. Our experimental results across multiple sequence lengths and state sizes illustrates, on average, a 35% training speed improvement over S4 layers -- parametrized in time-domain -- on the Long Range Arena benchmark, while delivering state-of-the-art downstream performances over other attention-free approaches. Moreover, we report improved perplexity in language modeling over a long convolutional Hyena baseline, by simply introducing our transfer function parametrization. Our code is available at https://github.com/ruke1ire/RTF., Comment: Resubmission 02/06/2024: Fixed minor typo of recurrent form RTF

We present a fault-tolerant universal quantum computing architecture based on a code concatenation of noise-biased qubits and the parity architecture. The parity architecture can be understood as a LDPC code tailored specifically to obtain any desired logical connectivity from nearest neighbor physical interactions. The code layout can be dynamically adjusted to algorithmic requirements on-the-fly. This allows reaching arbitrary code distances and thereby exponential suppression of errors with a universal set of fault-tolerant gates. In addition to the previously explored tool-sets for concatenated cat codes, our approach features parallelizable interactions between arbitrary sets of qubits by directly addressing the parity qubits in the code. The proposed scheme enables codes with less physical qubit overhead compared to the repetition code with the same code distances, while requiring only weight-3 and weight-4 stabilizers and nearest neighbor 2D square-lattice connectivity., Comment: 8 pages

Collinear laser spectroscopy measurements were performed on $^{68-74}$Ge isotopes ($Z = 32$) at ISOLDE-CERN, by probing the $4s^2 4p^2 \, ^3\!P_1 \rightarrow 4s^2 4p 5s \, ^3\!P_1^o$ atomic transition (269~nm) of germanium. Nuclear charge radii are determined via the measured isotope shifts, revealing a larger local variation than the neighboring isotopic chains. Nuclear density functional theory with the Fayans functionals Fy($\Delta r$,HFB) and Fy(IVP), and the SV-min Skyrme describes the experimental data for the differential charge radii $\delta\langle r^{2} \rangle$ and charge radii $R_{\rm c}$ within the theoretical uncertainties. The observed large variation in the charge radii of germanium isotopes is better accounted for by theoretical models incorporating ground state quadrupole correlations. This suggests that the polarization effects due to pairing and deformation contribute to the observed large odd-even staggering in the charge radii of the Ge isotopic chain., Comment: 6 pages,5 figures

The TRISTAN detector is a new detector for electron spectroscopy at the Karlsruhe Tritium Neutrino (KATRIN) experiment. The semiconductor detector utilizes the silicon drift detector technology and will enable the precise measurement of the entire tritium beta decay electron spectrum. Thus, a significant fraction of the parameter space of potential neutrino mass eigenstates in the keV-mass regime can be probed. We developed a custom electron gun based on the effect of thermionic emission to characterize the TRISTAN detector modules with mono-energetic electrons before installation into the KATRIN beamline. The electron gun provides an electron beam with up to 25 keV kinetic energy and an electron rate in the order of 1E5 electrons per second. This manuscript gives an overview of the design and commissioning of the electron gun. In addition, we will shortly discuss a first measurement with the electron gun to characterize the electron response of the TRISTAN detector.

This article shows how coworker performance affects individual performance evaluation in a teamwork setting at the workplace. We use high-quality data on football matches to measure an important component of individual performance, shooting performance, isolated from collaborative effects. Employing causal machine learning methods, we address the assortative matching of workers and estimate both average and heterogeneous effects. There is substantial evidence for spillover effects in performance evaluations. Coworker shooting performance, meaningfully impacts both, manager decisions and third-party expert evaluations of individual performance. Our results underscore the significant role coworkers play in shaping career advancements and highlight a complementary channel, to productivity gains and learning effects, how coworkers impact career advancement. We characterize the groups of workers that are most and least affected by spillover effects and show that spillover effects are reference point dependent. While positive deviations from a reference point create positive spillover effects, negative deviations are not harmful for coworkers.

Motivated by the prospect of a two-dimensional square-lattice geometry for semiconductor spin qubits, we explore the realization of the Parity Architecture with quantum dots (QDs). We present sequences of spin shuttling and quantum gates that implement the Parity Quantum Approximate Optimization Algorithm (QAOA) on a lattice constructed of identical unit cells, such that the circuit depth is always constant. We further develop a detailed error model for a hardware-specific analysis of the Parity Architecture and we estimate the errors during one round of Parity QAOA. The model includes a general description of the shuttling errors as a function of the probability distribution function of the valley splitting, which is the main limitation for the performance. We compare our approach to a superconducting transmon qubit chip and we find that with high-fidelity spin shuttling the performance of the spin qubits is competitive or even exceeds the results of the transmons. Finally, we discuss the possibility of decoding the logical quantum state and of quantum error mitigation. We find that already with near-term spin qubit devices a sufficiently low physical error probability can be expected to reliably perform Parity QAOA with a short depth in a regime where the success probability compares favorably to standard QAOA., Comment: Supplemental Material attached, to view please download "Other formats / anc"

In the asymptotic analysis of regular sequences as defined by Allouche and Shallit, it is usually advisable to study their summatory function because the original sequence has a too fluctuating behaviour. It might be that the process of taking the summatory function has to be repeated if the sequence is fluctuating too much. In this paper we show that for all regular sequences except for some degenerate cases, repeating this process finitely many times leads to a ``nice'' asymptotic expansion containing periodic fluctuations whose Fourier coefficients can be computed using the results on the asymptotics of the summatory function of regular sequences by the first two authors of this paper. In a recent paper, Hwang, Janson, and Tsai perform a thorough investigation of divide-and-conquer recurrences. These can be seen as $2$-regular sequences. By considering them as the summatory function of their forward difference, the results on the asymptotics of the summatory function of regular sequences become applicable. We thoroughly investigate the case of a polynomial toll function.