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Achieving fast and high-fidelity qubit operations is crucial for unlocking the potential of quantum computers. In particular, reaching low gate errors in two-qubit gates has been a long-standing challenge in the field of superconducting qubits due to their typically long duration relative to coherence times. To realize fast gates, we utilize the hybridization between fixed-frequency superconducting qubits with a strongly interacting coupler mode that is tunable in frequency. To reduce population leakage during required adiabatic passages through avoided level crossings, we employ a sensitivity-adaptive closed-loop optimization method to design complex pulse shapes. We compare the performance of Gaussian-square, Fourier-series, and piecewise-constant-slope (PiCoS) pulse parametrizations and are able to reach 99.9 % controlled-Z gate fidelity using a 64 ns long Fourier-series pulse defined by only seven parameters. These high-fidelity values are achieved by analyzing the optimized pulse shapes to identify and systematically mitigate signal-line distortions in the experiment. To improve the convergence speed of the optimization we implement an adaptive cost function, which continuously maximizes the sensitivity. The demonstrated method can be used for tune-up and recalibration of superconducting quantum processors.

The paper presents a new short proof of one of Adams's theorems and a $t$-trace-class theorem for parabolic Morrey spaces., Comment: 12 pages

The observation of a resonance structure in the opening angle of the electron-positron pairs in the $^{7}$Li(p,\ee) $^{8}$Be reaction was claimed and interpreted as the production and subsequent decay of a hypothetical particle (X17). Similar excesses, consistent with this particle, were later observed in processes involving $^{4}$He and $^{12}$C nuclei with the same experimental technique. The MEG II apparatus at PSI, designed to search for the $\mu^+ \rightarrow \mathrm{e}^+ \gamma$ decay, can be exploited to investigate the existence of this particle and study its nature. Protons from a Cockroft-Walton accelerator, with an energy up to 1.1 MeV, were delivered on a dedicated Li-based target. The $\gamma$ and the e$^{+}$e$^{-}$ pair emerging from the $^8\mathrm{Be}^*$ transitions were studied with calorimeters and a spectrometer, featuring a broader angular acceptance than previous experiments. We present in this paper the analysis of a four-week data-taking in 2023 with a beam energy of 1080 keV, resulting in the excitation of two different resonances with Q-value \SI{17.6}{\mega\electronvolt} and \SI{18.1}{\mega\electronvolt}. No significant signal was found, and limits at \SI{90}{\percent} C.L. on the branching ratios (relative to the $\gamma$ emission) of the two resonances to X17 were set, $R_{17.6} < 1.8 \times 10^{-6} $ and $R_{18.1} < 1.2 \times 10^{-5} $., Comment: 11 pages, 9 figures, submitted to EPJC

Let $G$ be a complex reductive algebraic group. In arxiv:2108.03453 Ivan Losev, Lucas mason-Brown and the third-named author suggested a symplectic duality between nilpotent Slodowy slices in $\mathfrak{g}^\vee$ and affinizations of certain $G$-equivariant covers of special nilpotent orbits. In this paper, we study the various versions of Hikita conjecture for this pair. We show that the original statement of the conjecture does not hold for the pairs in question and propose a refined version. We discuss the general approach towards the proof of the refined Hikita conjecture and prove this refined version for the parabolic Slodowy varieties, which includes many of the cases considered in arxiv:2108.03453 and more. Applied to the setting of arxiv:2108.03453, the refined Hikita conjecture explains the importance of special unipotent ideals from the symplectic duality point of view. We also discuss applications of our results. In the appendices, we discuss some classical questions in Lie theory that relate the refined version and the original version. We also explain how one can use our results to simplify some proofs of known results in the literature. As a combinatorial application of our results we observe an interesting relation between the geometry of Springer fibers and left Kazhdan-Lusztig cells in the corresponding Weyl group., Comment: 88 pages, comments are welcome!

We prove weak uniqueness for admissible solutions of It\^o's equations with uniformly nondegenerate $a$ which is almost in VMO and $b$ in a Morrey class of functions with low integrability property. If $b\in L_{d}$ any solution is admissible., Comment: 14 pages

Protecting qubits from environmental noise while maintaining strong coupling for fast high-fidelity control is a central challenge for quantum information processing. Here, we demonstrate a novel control scheme for superconducting fluxonium qubits that eliminates qubit decay through the control channel by reducing the environmental density of states at the transition frequency. Adding a low-pass filter on the flux line allows for flux-biasing and at the same time coherently controlling the fluxonium qubit by parametrically driving it at integer fractions of its transition frequency. We compare the filtered to the unfiltered configuration and find a five times longer $T_1$, and ten times improved $T_2$-echo time in the protected case. We demonstrate coherent control with up to 11-photon sub-harmonic drives, highlighting the strong non-linearity of the fluxonium potential. We experimentally determine Rabi frequencies and drive-induced frequency shifts in excellent agreement with numerical and analytical calculations. Furthermore, we show the equivalence of a 3-photon sub-harmonic drive to an on-resonance drive by benchmarking sub-harmonic gate fidelities above 99.94 %. These results open up a scalable path for full qubit control via a single protected channel, strongly suppressing qubit decoherence caused by control lines., Comment: 18 pages, 9 figures

Existence, uniqueness and stability of the solutions of linear stochastic evolution equations are investigated. The results obtained are used to prove theorems on solvability of linear second order stochastic partial differential equations in $L_{p}$-setting with singular lower order coefficients.

This research provides the theoretical feasibility study of a novel architecture of a MEMS differential resonant accelerometer, with switchable and tunable electrostatic transmission between the proof mass and the vibrating sensing beams. The same beams are used for sensing of the inertial force, while the transmission is switched ON, and for the device's calibration, when the transmission is OFF. Therefore, the beams' response in the OFF state is affected by the same factors (temperature, electronics, packaging) as in the ON state, with the only exception for the acceleration. This unique ability to physically disconnect the inertial force from the sensing elements opens possibilities for new schemes of the signal processing, including sensitivity tuning, zero-bias correction and on-the-fly self-calibration of the sensor. The device includes a proof mass (PM) and two force-transmitting frames that are attached to the substrate by the suspension springs, such that there is no direct mechanical connection between the PM and the frames. Two identical sensing beams are attached at their ends to the frames and the substrate. When the electrostatic transmission is switched ON by applying a voltage between the PM and frames, the force is transmitted from the PM through the frame to the beams. Disturbance in the electrostatic field, due to the acceleration-dependent displacement of the PM, results in the shift in the beam axial force and, therefore, in its resonant frequency, assuring the device's acceleration sensing. Furthermore, the change in the control voltage tunes the transmission of the input signal, and therefore the scale factor and the dynamic range of the sensor. An analytic model of the generic device is formulated and verified using finite elements analysis. The tunability of the device and the compensation of the scale factor thermal sensitivity are demonstrated using the model.

Diffusion models have demonstrated significant potential in achieving state-of-the-art performance across various text generation tasks. In this systematic study, we investigate their application to the table-to-text problem by adapting the diffusion model to the task and conducting an in-depth analysis. Our experiments cover multiple aspects of diffusion models training. We explore sampling strategy influence by inducing recent diffusion model accelerator DPM-Solver++ into our core model. We have tested different prediction aggregation methods, like ROVER and Minimum Bayes-Risk (MBR). Our studies cover the impact of the pre-training phase in diffusion models and the generation length constraints influence. We also have compared diffusion model generation with auto-regressive text-to-text models with different temperature settings for diversity evaluation. Our key observation is that diffusion models demonstrate the balance between quality and diversity while auto-regressive text-to-text models are not successful at handling both at the same time. Furthermore, we found out that to achieve the highest quality possible, it is preferable to use a regular sampler with the strictest length constraint to create multiple samples, and then use MBR to aggregate the predictions. However, if you are prepared to give up high level of diversity and to accelerate the process, you can also utilize a fast sampler DPM-Solver++. Our findings reveal that diffusion models achieve comparable results in the table-to-text domain, highlighting their viability in the table-to-text challenge as a promising research direction., Comment: IEEE Access

When $p(t)$ is a polynomial of degree $d$, $k$-th column of the Riordan array $\bigl(1/(1 - t^{d+1}), tp(t)\bigr)$ is an eventually periodic sequence with the repeating part beginning at the $1 + (k-1)(d+1)$-st term. The pre-periodic terms add up to the $(k-1)(d+1)$-st partial sum of the corresponding formal power series, and thus the Riordan array of $p(t)$ generates a sequence of column partial sums. We classify linear and quadratic polynomials, and present a particular family of polynomials of higher degrees, for which such sequences of column partial sums are eventually periodic., Comment: 34 pages, 6 figures

As quantum information technologies advance they face challenges in scaling and connectivity. In particular, two necessities remain independent of the technological implementation: the need for connectivity between distant qubits and the need for efficient generation of entanglement. Perfect State Transfer is a technique which realises the time optimal transfer of a quantum state between distant nodes of qubit lattices with only nearest-neighbour couplings, hence providing an important tool to improve device connectivity. Crucially, the transfer protocol results in effective parity-dependent non-local interactions, extending its utility to the efficient generation of entangled states. Here, we experimentally demonstrate Perfect State Transfer and the generation of multi-qubit entanglement on a chain of superconducting qubits. The system consists of six fixed-frequency transmon qubits connected by tunable couplers, where the couplings are controlled via parametric drives. By simultaneously activating all couplings and engineering their individual amplitudes and frequencies, we implement Perfect State Transfer on up to six qubits and observe the respective single-excitation dynamics for different initial states. We then apply the protocol in the presence of multiple excitations and verify its parity-dependent property, where the number of excitations within the chain controls the phase of the transferred state. Finally, we utilise this property to prepare a multi-qubit Greenberger-Horne-Zeilinger state using only a single transfer operation, demonstrating its application for efficient entanglement generation., Comment: 16 pages, 10 figures

We prove that a Coxeter group containing an element of finite order, which is generated by two non-commuting involutions, can not be embedded into the Riordan group., Comment: 13 pages

In recent years, several industrial solutions for the problem of multi-token code completion appeared, each making a great advance in the area but mostly focusing on cloud-based runtime and avoiding working on the end user's device. In this work, we describe our approach for building a multi-token code completion feature for the JetBrains' IntelliJ Platform, which we call Full Line Code Completion. The feature suggests only syntactically correct code and works fully locally, i.e., data querying and the generation of suggestions happens on the end user's machine. We share important time and memory-consumption restrictions, as well as design principles that a code completion engine should satisfy. Working entirely on the end user's device, our code completion engine enriches user experience while being not only fast and compact but also secure. We share a number of useful techniques to meet the stated development constraints and also describe offline and online evaluation pipelines that allowed us to make better decisions. Our online evaluation shows that the usage of the tool leads to 1.3 times more Python code in the IDE being produced by code completion. The described solution was initially started with a help of researchers and was then bundled into all JetBrains IDEs where it is now used by millions of users. Thus, we believe that this work is useful for bridging academia and industry, providing researchers with the knowledge of what happens when complex research-based solutions are integrated into real products., Comment: Published at ICSE'25. 12 pages, 4 figures

As systems for quantum computing keep growing in size and number of qubits, challenges in scaling the control capabilities are becoming increasingly relevant. Efficient schemes to simultaneously mediate coherent interactions between multiple quantum systems and to reduce decoherence errors can minimize the control overhead in next-generation quantum processors. Here, we present a superconducting qubit architecture based on tunable parametric interactions to perform two-qubit gates, reset, leakage recovery and to read out the qubits. In this architecture, parametrically driven multi-element couplers selectively couple qubits to resonators and neighbouring qubits, according to the frequency of the drive. We consider a system with two qubits and one readout resonator interacting via a single coupling circuit and experimentally demonstrate a controlled-Z gate with a fidelity of $98.30\pm 0.23 \%$, a reset operation that unconditionally prepares the qubit ground state with a fidelity of $99.80\pm 0.02 \%$ and a leakage recovery operation with a $98.5\pm 0.3 \%$ success probability. Furthermore, we implement a parametric readout with a single-shot assignment fidelity of $88.0\pm 0.4 \%$. These operations are all realized using a single tunable coupler, demonstrating the experimental feasibility of the proposed architecture and its potential for reducing the system complexity in scalable quantum processors., Comment: 19 pages, 14 figures

We present details on a new measurement of the muon magnetic anomaly, $a_\mu = (g_\mu -2)/2$. The result is based on positive muon data taken at Fermilab's Muon Campus during the 2019 and 2020 accelerator runs. The measurement uses $3.1$ GeV$/c$ polarized muons stored in a $7.1$-m-radius storage ring with a $1.45$ T uniform magnetic field. The value of $ a_{\mu}$ is determined from the measured difference between the muon spin precession frequency and its cyclotron frequency. This difference is normalized to the strength of the magnetic field, measured using Nuclear Magnetic Resonance (NMR). The ratio is then corrected for small contributions from beam motion, beam dispersion, and transient magnetic fields. We measure $a_\mu = 116 592 057 (25) \times 10^{-11}$ (0.21 ppm). This is the world's most precise measurement of this quantity and represents a factor of $2.2$ improvement over our previous result based on the 2018 dataset. In combination, the two datasets yield $a_\mu(\text{FNAL}) = 116 592 055 (24) \times 10^{-11}$ (0.20 ppm). Combining this with the measurements from Brookhaven National Laboratory for both positive and negative muons, the new world average is $a_\mu$(exp) $ = 116 592 059 (22) \times 10^{-11}$ (0.19 ppm)., Comment: 48 pages, 29 figures; 4 pages of Supplement Material; version accepted for publication in Physical Review D

Backpropagation, while effective for gradient computation, falls short in addressing memory consumption, limiting scalability. This work explores forward-mode gradient computation as an alternative in invertible networks, showing its potential to reduce the memory footprint without substantial drawbacks. We introduce a novel technique based on a vector-inverse-Jacobian product that accelerates the computation of forward gradients while retaining the advantages of memory reduction and preserving the fidelity of true gradients. Our method, Moonwalk, has a time complexity linear in the depth of the network, unlike the quadratic time complexity of na\"ive forward, and empirically reduces computation time by several orders of magnitude without allocating more memory. We further accelerate Moonwalk by combining it with reverse-mode differentiation to achieve time complexity comparable with backpropagation while maintaining a much smaller memory footprint. Finally, we showcase the robustness of our method across several architecture choices. Moonwalk is the first forward-based method to compute true gradients in invertible networks in computation time comparable to backpropagation and using significantly less memory.

Offline Reinforcement Learning (RL) addresses the problem of sequential decision-making by learning optimal policy through pre-collected data, without interacting with the environment. As yet, it has remained somewhat impractical, because one rarely knows the reward explicitly and it is hard to distill it retrospectively. Here, we show that an imitating agent can still learn the desired behavior merely from observing the expert, despite the absence of explicit rewards or action labels. In our method, AILOT (Aligned Imitation Learning via Optimal Transport), we involve special representation of states in a form of intents that incorporate pairwise spatial distances within the data. Given such representations, we define intrinsic reward function via optimal transport distance between the expert's and the agent's trajectories. We report that AILOT outperforms state-of-the art offline imitation learning algorithms on D4RL benchmarks and improves the performance of other offline RL algorithms by dense reward relabelling in the sparse-reward tasks.

Let $I(X,R)$ be the incidence algebra of the preordered set $X$ over the ring $R$. In the case of a finite connected partially ordered set $X$, we prove that the subgroup of inner multiplicative automorphisms is a direct factor of the group of multiplicative automorphisms of the algebra $I(X,R)$. As a consequence, we obtain several matching criteria of the subgroup of inner multiplicative automorphisms with the group of multiplicative automorphisms., Comment: arXiv admin note: substantial text overlap with arXiv:2305.02984

We extend the techniques in arXiv:2209.08865(1) to the non-simply-laced situation, and calculate explicit special values of parabolic affine inverse Kazhdan-Lusztig polynomials for subregular nilpotent orbits. We thus obtain explicit character formulas for certain irreducible representations of affine Lie algebras. As particular cases, we compute characters of simple vertex algebras $V_{k}(\mathfrak{g})$ for $k=-1,\ldots,-b$, where $b$ is the largest label of the highest short coroot $\theta^\vee$. Conjecturally, all ordinary modules over $V_{-b}(\mathfrak{g})$ are covered by our computations. As an application, we obtain the explicit formulas for flavoured Schur indices of rank one Argyres-Douglas 4d SCFTs with flavour symmetry $G_2$ and $B_3$. Our results are proved using the geometry of the Springer resolution. We identify the cell quotient of the anti-spherical module over $\widehat{W}$ corresponding to the subregular cell with a certain one-dimensional extension of a module defined by Lusztig. We describe the canonical basis in this module geometrically and present an explicit description of the corresponding objects in the derived category of equivariant coherent sheaves on the Springer resolution. They correspond to irreducible objects in the heart of a certain $t$-structure that we describe using an equivariant version of the derived McKay correspondence., Comment: 65 pages. With an appendix by Roman Bezrukavnikov, Vasily Krylov, and Kenta Suzuki

To control and measure the state of a quantum system it must necessarily be coupled to external degrees of freedom. This inevitably leads to spontaneous emission via the Purcell effect, photon-induced dephasing from measurement back-action, and errors caused by unwanted interactions with nearby quantum systems. To tackle this fundamental challenge, we make use of the design flexibility of superconducting quantum circuits to form a multi-mode element -- an artificial molecule -- with symmetry-protected modes. The proposed circuit consists of three superconducting islands coupled to a central island via Josephson junctions. It exhibits two essential non-linear modes, one of which is flux-insensitive and used as the protected qubit mode. The second mode is flux-tunable and serves via a cross-Kerr type coupling as a mediator to control the dispersive coupling of the qubit mode to the readout resonator. We demonstrate the Purcell protection of the qubit mode by measuring relaxation times that are independent of the mediated dispersive coupling. We show that the coherence of the qubit is not limited by photon-induced dephasing when detuning the mediator mode from the readout resonator and thereby reducing the dispersive coupling. The resulting highly protected qubit with tunable interactions may serve as a basic building block of a scalable quantum processor architecture, in which qubit decoherence is strongly suppressed.

We report on the piezoresistive method for detecting stability loss events in microelectromechanical (MEMS) sensors based on bifurcation. The method involves measuring the resistivity changes of an entire beam to detect snap-through transitions in an electrostatically actuated, bistable double-clamped crystalline Silicon (Si) microbeam. The applicability of the suggested approach in two types of sensors - an ambient air temperature sensor or a mean air velocity sensor, is demonstrated. In both cases the bistable beam, serving as the sensing element, is affected by the electrothermal Joule's heating and air cooling. The measured signal is obtained by monitoring the critical voltages of the snap-through transitions. Piezoresistive sensing is especially suitable for the response monitoring of the exposed to the environment, free-standing heated microbeam sensors, where optical, piezoelectric, or electrostatic interrogation methods are not applicable. The approach can be implemented in various bifurcation microsensors and for response monitoring of bistable actuators., Comment: 5 pages with 3 figures

We present the findings from an experimental study of a MEMS flow sensor in which an initially curved, double-clamped bistable microbeam is the primary sensing element. Our research explores how the overheat ratio, direct flow loading, and turbulence-induced vibration affect the sequential snap-through (ST) buckling and snap-back (SB) release of an electrostatically actuated beam heated by an electric current. The sensor is fabricated from highly doped single-crystal silicon using a silicon-on-insulator (SOI) wafer. Positioned at the chip's edge, the microbeam is exposed to airflow, enabling concurrent dynamic response measurements with a laser Doppler vibrometer and a video camera. Our research demonstrates that the overheat ratio can be significantly lower for this sensing principle than conventional thermal sensing elements, pointing to the potential for substantial energy savings. We also emphasize the significant impact of flow angles and vibrations on the critical ST and SB voltages, which are vital for the flow sensor's output. Additionally, we introduce the first direct experimental observation of the beam profile's time history during the snap-through /snap-back transition. The potential impact of this research lies in developing more robust MEMS flow sensors with enhanced sensitivity and a better understanding of their response to environmental factors, which could have broader applications in fields such as aerospace, environmental monitoring, and industrial process control., Comment: 38 pages, 11 figures

A key tool for the study of an affine Hecke algebra $\mathcal{H}$ is provided by Springer theory of the Langlands dual group via the realization of $\mathcal{H}$ as equivariant $K$-theory of the Steinberg variety. We prove a similar geometric description for Lusztig's asymptotic affine Hecke algebra $J$ identifying it with the sum of equivariant $K$-groups of the squares of ${\mathbb C}^*$-fixed points in the Springer fibers, as conjectured by Qiu and Xi (the same result was also obtained by Oron Popp using different methods). As an application, we give a new geometric proof of Lusztig's parametrization of irreducible representations of $J$. We also reprove Braverman-Kazhdan's spectral description of $J$. As another application, we prove a description of the cocenters of $\mathcal{H}$ and $J$ conjectured by the first author with Braverman, Kazhdan and Varshavsky. The proof is based on a new algebraic description of $J$, which may be of independent interest., Comment: 37 pages

We describe automorphisms and derivations of the incidence coalgebra $\text{Co}(X,F)$ of the partially ordered set $X$ over a field $F$. In this case, the fact is significantly used that the dual algebra of the coalgebra $\text{Co}(X,F)$ is isomorphic to the incidence algebra $I(X,F)$ of the partially ordered set $X$ over the field $F$.

Simulations of quantum chemistry and quantum materials are believed to be among the most important potential applications of quantum information processors, but realizing practical quantum advantage for such problems is challenging. Here, we introduce a simulation framework for strongly correlated quantum systems that can be represented by model spin Hamiltonians. Our approach leverages reconfigurable qubit architectures to programmably simulate real-time dynamics and introduces an algorithm for extracting chemically relevant spectral properties via classical co-processing of quantum measurement results. We develop a digital-analog simulation toolbox for efficient Hamiltonian time evolution utilizing digital Floquet engineering and hardware-optimized multi-qubit operations to accurately realize complex spin-spin interactions, and as an example present an implementation proposal based on Rydberg atom arrays. Then, we show how detailed spectral information can be extracted from these dynamics through snapshot measurements and single-ancilla control, enabling the evaluation of excitation energies and finite-temperature susceptibilities from a single-dataset. To illustrate the approach, we show how this method can be used to compute key properties of a polynuclear transition-metal catalyst and 2D magnetic materials., Comment: 21 pages and 11 figures, plus supplementary information

We consider parabolic equations with operators $\mathcal{L}=\partial_{t}+a^{ij}D_{ij}+b^{i}D_{i}-c$ with $a$ being almost in VMO, $b$ in a Morrey class containing $ L_{d+2}$ and $c $ in a Morrey class containing $L_{(d+2)/2}$. We prove the solvability in Sobolev spaces of $\mathcal{L} u=f\in L_{p}$ in bounded $C^{1,1}$-cylinders., Comment: 16 pages

The MEG II experiment, based at the Paul Scherrer Institut in Switzerland, reports the result of a search for the decay $\mu^+\to e^+\gamma$ from data taken in the first physics run in 2021. No excess of events over the expected background is observed, yielding an upper limit on the branching ratio of B($\mu^+\to e^+\gamma$) < $7.5 \times 10^{-13}$ (90% C.L.). The combination of this result and the limit obtained by MEG gives B($\mu^+\to e^+\gamma$) < $3.1 \times 10^{-13}$ (90% C.L.), which is the most stringent limit to date. A ten-fold larger sample of data is being collected during the years 2022-2023, and data-taking will continue in the coming years., Comment: 10 pages, 6 figures. To be published in EPJC

The MEG II experiment, located at the Paul Scherrer Institut (PSI) in Switzerland, is the successor to the MEG experiment, which completed data taking in 2013. MEG II started fully operational data taking in 2021, with the goal of improving the sensitivity of the mu+ -> e+ gamma decay down to 6e-14 almost an order of magnitude better than the current limit. In this paper, we describe the operation and performance of the experiment and give a new estimate of its sensitivity versus data acquisition time., Comment: 42 pages, 55 figures. Submitted to EPJC

In 1990 F. Chiarenza and M. Frasca published a paper in which they generalized a result of C. Fefferman on estimates of the integral of $|bu|^{p}$ through the integral of $|Du|^{p}$ for $p>1$. Formally their proof is valid only for $d\geq 3$. We present here further generalization with a different proof in which $D $ is replaced with the fractional power of the Laplacian for any dimension $d\geq 1$., Comment: 4 pages