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Let $C$ be a complete algebraically closed extension of $\mathbb{Q}_p$, and let $\mathfrak{X}$ be a smooth formal scheme over $\mathcal{O}_C$. By the work of Bhatt--Morrow--Scholze, it is known that when $\mathfrak{X}$ is proper, the length of the torsion in the integral $p$-adic \'etale cohomology of the generic fiber $\mathfrak{X}_C$ is bounded above by the length of the torsion in the crystalline cohomology of its special fiber. In this note, we focus on the non-proper case and observe that when $\mathfrak{X}$ is affine, the torsion in the integral $p$-adic \'etale cohomology of $\mathfrak{X}_C$ can even be expressed as a functor of the special fiber, unlike in the proper case. As a consequence, we show that, surprisingly, if $\mathfrak{X}$ is affine, the integral $p$-adic \'etale cohomology groups of $\mathfrak{X}_C$ have finite torsion subgroups. We discuss further applications and propose conjectures predicting the torsion in the integral $p$-adic \'etale cohomology of a broader class of rigid-analytic varieties over $C$., Comment: 14 pages. Comments are welcome!

Image processing is one of the most promising applications for quantum machine learning (QML). Quanvolutional Neural Networks with non-trainable parameters are the preferred solution to run on current and near future quantum devices. The typical input preprocessing pipeline for quanvolutional layers comprises of four steps: optional input binary quantization, encoding classical data into quantum states, processing the data to obtain the final quantum states, decoding quantum states back to classical outputs. In this paper we propose two ways to enhance the efficiency of quanvolutional models. First, we propose a flexible data quantization approach with memoization, applicable to any encoding method. This allows us to increase the number of quantization levels to retain more information or lower them to reduce the amount of circuit executions. Second, we introduce a new integrated encoding strategy, which combines the encoding and processing steps in a single circuit. This method allows great flexibility on several architectural parameters (e.g., number of qubits, filter size, and circuit depth) making them adjustable to quantum hardware requirements. We compare our proposed integrated model with a classical convolutional neural network and the well-known rotational encoding method, on two different classification tasks. The results demonstrate that our proposed model encoding exhibits a comparable or superior performance to the other models while requiring fewer quantum resources.

The strong spin-orbit interaction in silicon and germanium hole quantum dots enables all-electric microwave control of single spins but is unsuited for multi-spin exchange-only qubits that rely on scalable discrete signals to suppress cross-talk and heating effects in large quantum processors. Here, we propose an exchange-only spin-orbit qubit that utilizes spin-orbit interactions to implement qubit gates and keeps the beneficial properties of the original encoding. Our encoding is robust to significant local variability in hole spin properties and, because it operates with two degenerate states, it eliminates the need for the rotating frame, avoiding the technologically demanding constraints of fast clocks and precise signal calibration. Unlike current exchange-only qubits, which require complex multi-step sequences prone to leakage, our qubit design enables low-leakage two-qubit gates in a single step, addressing critical challenges in scaling spin qubits.

Quantum spintronics is an emerging field focused on developing novel applications by utilizing the quantum coherence of magnetic systems. Robust information transmission is crucial for achieving fully scalable spintronic devices. However, despite its significance, reliable long-range quantum information transmission in magnetic systems remains a challenging frontier. Here, we introduce a long-distance quantum transmission scheme based on topological spin textures in a hybrid system of a magnetic racetrack and spin qubits. We demonstrate this principle by employing the domain wall (DW)-the most fundamental texture-to transport quantum signal between distant qubits. In particular, we propose and analyze an efficient measurement-free protocol that leverages the DW mobility to enable robust entanglement generation between distant qubits. Strikingly, we find that this remote entanglement generation is not only fast and of high fidelity, but also remarkably tunable, capable of being easily turned on and off on-demand by switching the DW initial state. Furthermore, we show that, interestingly, spin qubits can serve as quantum stations for the racetrack, facilitating state transfer among fast-moving DWs on the same track. Our study provides a hybrid quantum platform for scalable quantum computation and opens the door to future explorations of topological textures for quantum information processing in spintronics architectures., Comment: 16 pages including supplemental material; 4 figures

The solution for non-linear, complex partial differential Equations (PDEs) is achieved through numerical approximations, which yield a linear system of equations. This approach is prevalent in Computational Fluid Dynamics (CFD), but it restricts the mesh size since the solution of the linear system becomes computationally intractable when the mesh resolution increases. The reliance on the ability of High-Performance Computers (HPC) to scale up and meet these requirements is myopic; such very high-fidelity simulations require a paradigm shift in computing. This paper presents an exploration of quantum methodologies aimed at achieving high accuracy in solving such a large system of equations. Leveraging recent works in Quantum Linear Solver Algorithms (QLSA) and variational algorithms suitable for Quantum Simulation in HPC, we aspire to push the boundaries of CFD-relevant problems that can be solved on hybrid quantum-classical framework. To this end, we consider the 2D, transient, incompressible, viscous, non-linear coupled Burgers equation as a test problem and investigate the accuracy of our approach by comparing results with a classical linear system of equation solvers, such as the Generalized Minimal RESidual method (GMRES). Through rigorous testing, our findings demonstrate that our quantum methods yield results comparable in accuracy to traditional approaches. Additionally, we demonstrate the accuracy, scalability, and consistency of our quantum method. Lastly, we present an insightful estimation of the resources our quantum algorithm needs to solve systems with nearly 2 billion mesh points.

Efficient control schemes that enable fast, high-fidelity operations are essential for any practical quantum computation. However, current optimization protocols are intractable due to stringent requirements imposed by the microscopic systems encoding the qubit, including dense energy level spectra and cross talk, and generally require a trade-off between speed and fidelity of the operation. Here, we address these challenges by developing a general framework for optimal control based on the quantum metric tensor. This framework allows for fast and high-fidelity adiabatic pulses, even for a dense energy spectrum, based solely on the Hamiltonian of the system instead of the full time evolution propagator and independent of the size of the underlying Hilbert space. Furthermore, the framework suppresses diabatic transitions and state-dependent crosstalk effects without the need for additional control fields. As an example, we study the adiabatic charge transfer in a double quantum dot to find optimal control pulses with improved performance. We show that for the geometric protocol, the transfer fidelites are lower bounded $F>99\%$ for ultrafast 20 ns pulses, regardless of the size of the anti-crossing., Comment: 16 pages, 12 figures

Hole spin qubits are rapidly emerging as the workhorse of semiconducting quantum processors because of their large spin-orbit interaction, enabling fast all-electric operations at low power. However, spin-orbit interaction also causes non-uniformities in devices, resulting in locally varying qubit energies and site-dependent anisotropies. While these anisotropies can be used to drive single-spins, if not properly harnessed, they can hinder the path toward large-scale quantum processors. Here, we report on a qubit in planar germanium, where we control the anisotropy of two spins in a double quantum dot. By characterising microwave-driven singlet-triplet qubits, we show two distinct operating regimes depending on the magnetic field direction. For in-plane fields, the two spins are largely anisotropic, enabling to measure all the available transitions; coherence times exceeding 3 $\mu$s are extracted. For out-of-plane fields, they have an isotropic response but preserve the substantial energy difference required to address the singlet-triplet qubit. Even in this field direction, where the qubit lifetime is strongly affected by nuclear spins, we find 400 ns coherence times. Our work adds a valuable tool to investigate and harness the anisotropy of spin qubits and can be implemented in any large-scale NxN device, facilitating the path towards scalable quantum processors.

In this paper we consider proper orthogonal decomposition (POD) methods that do not include difference quotients (DQs) of snapshots in the data set. The inclusion of DQs have been shown in the literature to be a key element in obtaining error bounds that do not degrade with the number of snapshots. More recently, the inclusion of DQs has allowed to obtain pointwise (as opposed to averaged) error bounds that decay with the same convergence rate (in terms of the POD singular values) as averaged ones. In the present paper, for POD methods not including DQs in their data set, we obtain error bounds that do not degrade with the number of snapshots if the function from where the snapshots are taken has certain degree of smoothness. Moreover, the rate of convergence is as close as that of methods including DQs as the smoothness of the function providing the snapshots allows. We do this by obtaining discrete counterparts of Agmon and interpolation inequalities in Sobolev spaces. Numerical experiments validating these estimates are also presented., Comment: 23 pages, 2 figures

We investigate the residual throughput penalty due to ISRS, after power-optimization, in multiband systems. We show it to be mild. We also revisit the launch power optimization 3-dB rule. We find that using it is possible but not advisable due to increased GSNR non-uniformity., Comment: The paper has been accepted for publication at ECOC 2024

We develop the fundamentals of a new theory of convex geometry -- which we call "broken line convex geometry". This is a theory of convexity where the ambient space is the rational tropicalization of a cluster variety, as opposed to an ambient vector space. In this theory, line segments are replaced by broken line segments, and we adopt the notion of convexity in [CMN21]. We state and prove broken line convex geometry versions of many standard results from usual convex geometry., Comment: 34 pages, 6 figures. Feedback welcome

The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown. Euclid is a medium-class mission in the Cosmic Vision 2015-2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14,000 deg^2 of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance., Comment: Accepted for publication in the A&A special issue`Euclid on Sky'

Qubits require a compromise between operation speed and coherence. Here, we demonstrate a compromise-free singlet-triplet (ST) qubit, where the qubit couples maximally to the driving field while simultaneously coupling minimally to the dominant noise sources. The qubit is implemented in a crystal-phase defined double-quantum dot in an InAs nanowire. Using a superconducting resonator, we measure the spin-orbit interaction (SOI) gap, the spin-photon coupling strength and the qubit decoherence rate as a function of the in-plane magnetic-field orientation. We demonstrate a spin qubit sweet spot maximizing the dipolar coupling and simultaneously minimizing the decoherence. Our theoretical description postulates phonons as the most likely dominant noise source. The compromise-free sweet spot originates from the SOI suggesting that it is not restricted to this material platform, but might find applications in any material with SOI. These findings pave the way for enhanced engineering of these nanomaterials for next-generation qubit technologies.

We present an in-depth analysis of the LISA Pathfinder differential acceleration performance over the entire course of its science operations, spanning approximately 500 days. We find that: 1) the evolution of the Brownian noise that dominates the acceleration amplitude spectral density (ASD), for frequencies $f\gtrsim 1\,\text{mHz}$, is consistent with the decaying pressure due to the outgassing of a single gaseous species. 2) between $f=36\,\mu\text{Hz}$ and $1\,\text{mHz}$, the acceleration ASD shows a $1/f$ tail in excess of the Brownian noise of almost constant amplitude, with $\simeq 20\%$ fluctuations over a period of a few days, with no particular time pattern over the course of the mission; 3) at the lowest considered frequency of $f=18\,\mu\text{Hz}$, the ASD significantly deviates from the $1/f$ behavior, because of temperature fluctuations that appear to modulate a quasi-static pressure gradient, sustained by the asymmetries of the outgassing pattern. We also present the results of a projection of the observed acceleration noise on the potential sources for which we had either a direct correlation measurement, or a quantitative estimate from dedicated experiments. These sources account for approximately $40\%$ of the noise power in the $1/f$ tail. Finally, we analyze the possible sources of the remaining unexplained fraction, and identify the possible measures that may be taken to keep those under control in LISA.

Iron (Fe) reduction is one of Earth's most ancient microbial metabolisms, but after atmosphere-ocean oxygenation, this anaerobic process was relegated to niche anoxic environments below the water and soil surface. However, new technologies to monitor redox processes at the microscale relevant to microbial cells have recently revealed that the oxygen (O2) concentrations controlling the distribution of aerobic and anaerobic metabolisms are more heterogeneous than previously believed. To explore how O2 levels regulate microbial Fe reduction, we cultivated a facultative Fe-reducing bacterium using a cutting-edge microfluidic reactor integrated with transparent planar O2 sensors. Contrary to expectations, microbial growth induced Fe(III)-oxide (ferrihydrite) reduction under fully oxygenated conditions without forming O2-depleted microsites. Batch incubations highlighted the importance of the process at a larger scale, fundamentally changing our understanding of Fe cycling from the conceptualization of metal and nutrient mobility in the subsurface to our interpretation of Fe mineralogy in the rock record.

The importance of considering contextual probabilities in shaping response patterns within psychological testing is underscored, despite the ubiquitous nature of order effects discussed extensively in methodological literature. Drawing from concepts such as path-dependency, first-order autocorrelation, state-dependency, and hysteresis, the present study is an attempt to address how earlier responses serve as an anchor for subsequent answers in tests, surveys, and questionnaires. Introducing the notion of non-commuting observables derived from quantum physics, I highlight their role in characterizing psychological processes and the impact of measurement instruments on participants' responses. We advocate for the utilization of first-order Markov chain modeling to capture and forecast sequential dependencies in survey and test responses. The employment of the first-order Markov chain model lies in individuals' propensity to exhibit partial focus to preceding responses, with recent items most likely exerting a substantial influence on subsequent response selection. This study contributes to advancing our understanding of the dynamics inherent in sequential data within psychological research and provides a methodological framework for conducting longitudinal analyses of response patterns of test and questionnaire., Comment: 20 pages, 1 figure, 3 tables, 25 equations/matrices. Part of this paper was presented to the XXIX AIP Congress, Experimental Psychology Section. September 18th-20th 2023, Lucca, Italy. Title of the talk: "Differentiating students with signs of ADHD or OCD based on hysteresis in responses to a mind-wandering test. A Study of Markov Chain Test Response Sequences"

This paper studies discretization of time-dependent partial differential equations (PDEs) by proper orthogonal decomposition reduced order models (POD-ROMs). Most of the analysis in the literature has been performed on fully-discrete methods using first order methods in time, typically the implicit Euler time integrator. Our aim is to show which kind of error bounds can be obtained using any time integrator, both in the full order model (FOM), applied to compute the snapshots, and in the POD-ROM method. To this end, we analyze in this paper the continuous-in-time case for both the FOM and POD-ROM methods, although the POD basis is obtained from snapshots taken at a discrete (i.e., not continuous) set times. Two cases for the set of snapshots are considered: The case in which the snapshots are based on first order divided differences in time and the case in which they are based on temporal derivatives. Optimal pointwise-in-time error bounds {between the FOM and the POD-ROM solutions} are proved for the $L^2(\Omega)$ norm of the error for a semilinear reaction-diffusion model problem. The dependency of the errors on the distance in time between two consecutive snapshots and on the tail of the POD eigenvalues is tracked. Our detailed analysis allows to show that, in some situations, a small number of snapshots in a given time interval might be sufficient to accurately approximate the solution in the full interval. Numerical studies support the error analysis.

Across a broad range of qubits, a pervasive trade-off becomes obvious: increased coherence seems to be only possible at the cost of qubit speed. This is consistent with the notion that protecting a qubit from its noisy surroundings also limits the control over it. Indeed, from ions to atoms, to superconductors and spins, the leading qubits share a similar Q-factor - the product of speed and coherence time - even though the speed and coherence of various qubits can differ by up to 8 orders of magnitude. This is the qubit speed-coherence dilemma: qubits are either coherent but slow or fast but short-lived. Here, we demonstrate a qubit for which we can triple the speed while simultaneously quadrupling the Hahn-echo coherence time when tuning a local electric field. In this way, the qubit speed and coherence scale together without compromise on either quantity, boosting the Q-factor by over an order of magnitude. Our qubit is a hole spin in a Ge/Si core/shell nanowire providing strong 1D confinement, resulting in the direct Rashba spin-orbit interaction. Due to Heavy-hole light-hole mixing a maximum of the spin-orbit strength is reached at finite electrical field. At the local maximum, charge fluctuations are decoupled from the qubit and coherence is enhanced, yet the drive speed becomes maximal. Our proof-of-concept experiment shows that a properly engineered qubit can be made faster and simultaneously more coherent, removing an important roadblock. Further, it demonstrates that through all-electrical control a qubit can be sped up, without coupling more strongly to the electrical noise environment. As charge fluctuators are unavoidable in semiconductors and all-electrical control is highly scalable, our results improve the prospects for quantum computing in Si and Ge., Comment: Main: 6 pages with 3 display items plus 2 pages for references and methods Supplementary: 12 pages with 7 display items

We consider nonlinear solvers for the incompressible, steady (or at a fixed time step for unsteady) Navier-Stokes equations in the setting where partial measurement data of the solution is available. The measurement data is incorporated/assimilated into the solution through a nudging term addition to the the Picard iteration that penalized the difference between the coarse mesh interpolants of the true solution and solver solution, analogous to how continuous data assimilation (CDA) is implemented for time dependent PDEs. This was considered in the paper [Li et al. {\it CMAME} 2023], and we extend the methodology by improving the analysis to be in the $L^2$ norm instead of a weighted $H^1$ norm where the weight depended on the coarse mesh width, and to the case of noisy measurement data. For noisy measurement data, we prove that the CDA-Picard method is stable and convergent, up to the size of the noise. Numerical tests illustrate the results, and show that a very good strategy when using noisy data is to use CDA-Picard to generate an initial guess for the classical Newton iteration.

Electrostatic force actuation is a key component of the system of geodesic reference test masses (TM) for the LISA orbiting gravitational wave observatory and in particular for performance at low frequencies, below 1 mHz, where the observatory sensitivity is limited by stray force noise. The system needs to apply forces of order 10$^{-9}$ N while limiting fluctuations in the measurement band to levels approaching 10$^{-15}$ N/Hz$^{1/2}$. We present here the LISA actuation system design, based on audio-frequency voltage carrier signals, and results of its in-flight performance test with the LISA Pathfinder test mission. In LISA, TM force actuation is used to align the otherwise free-falling TM to the spacecraft-mounted optical metrology system, without any forcing along the critical gravitational wave-sensitive interferometry axes. In LISA Pathfinder, on the other hand, the actuation was used also to stabilize the TM along the critical $x$ axis joining the two TM, with the commanded actuation force entering directly into the mission's main differential acceleration science observable. The mission allowed demonstration of the full compatibility of the electrostatic actuation system with the LISA observatory requirements, including dedicated measurement campaigns to amplify, isolate, and quantify the two main force noise contributions from the actuation system, from actuator gain noise and from low frequency ``in band'' voltage fluctuations. These campaigns have shown actuation force noise to be a relevant, but not dominant, noise source in LISA Pathfinder and have allowed performance projections for the conditions expected in the LISA mission.