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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 have 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 1.5 times more code in the IDE being produced by code completion. The described solution was initially started with the help of researchers and was bundled into two JetBrains' IDEs - PyCharm Pro and DataSpell - at the end of 2023, so 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: 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 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 [BKK] 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. To do so, 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 in [Lus83]. 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: 63 pages

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. 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: 32 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

The magnetic dilution of Vanadyl phthalocyanine (VOPc) within the isostructural diamagnetic Titanyl phthalocyanine (TiOPc) affords promising molecular spin qubit platforms for solid-state quantum computing. The development of quantitative methods for determining how the interactions with a supporting substrate impact the electronic structure of the system are fundamental to determine their potential integration in physical devices. In this work we propose a combined approach based on X-ray absorption spectroscopy (XAS), atomic multiplet calculations, and density functional theory (DFT) to investigate the 3d orbital level structure of VOPc on TiOPc/Ag(100). We characterize VOPc in different molecular environments realized by changing the thickness of TiOPc interlayer and adsorption configuration on Ag(100). Depending on the molecular film structure, we find characteristic XAS features that we analyze using atomic multiplet calculations. We use a Bayesian optimization algorithm to accelerate the parameter search process in the multiplet calculations and identify the ground state properties, such as the 3d orbital occupancy and splitting, as well as intra-atomic interactions. Our analysis indicates that VOPc retains its spin S = 1/2 character in all configurations. Conversely, the energy separation and sequence of the unoccupied V 3d orbitals sensitively depend on the interaction with the surface and TiOPc interlayer. We validate the atomic orbital picture obtained from the multiplet model by comparison with DFT, which further allows us to understand the VOPc electronic properties using a molecular orbital description., Comment: https://journals.aps.org/prb/accepted/fa07aO95X4f10b4334a769f8107f50ef629b9b212

Conventional semiconductor-based integrated circuits are gradually approaching fundamental scaling limits. Many prospective solutions have recently emerged to supplement or replace both the technology on which basic devices are built and the architecture of data processing. Neuromorphic circuits are a promising approach to computing where techniques used by the brain to achieve high efficiency are exploited. Many existing neuromorphic circuits rely on unconventional and useful properties of novel technologies to better mimic the operation of the brain. One such technology is single flux quantum (SFQ) logic -- a cryogenic superconductive technology in which the data are represented by quanta of magnetic flux (fluxons) produced and processed by Josephson junctions embedded within inductive loops. The movement of a fluxon within a circuit produces a quantized voltage pulse (SFQ pulse), resembling a neuronal spiking event. These circuits routinely operate at clock frequencies of tens to hundreds of gigahertz, making SFQ a natural technology for processing high frequency pulse trains. Prior proposals for SFQ neural networks often require energy-expensive fluxon conversions, involve heterogeneous technologies, or exclusively focus on device level behavior. In this paper, a design methodology for deep single flux quantum neuromorphic networks is presented. Synaptic and neuronal circuits based on SFQ technology are presented and characterized. Based on these primitives, a deep neuromorphic XOR network is evaluated as a case study, both at the architectural and circuit levels, achieving wide classification margins. The proposed methodology does not employ unconventional superconductive devices or semiconductor transistors. The resulting networks are tunable by an external current, making this proposed system an effective approach for scalable cryogenic neuromorphic computing.

We introduce a new subclass of Fano varieties (Casagrande-Druel varieties), that are $n$-dimensional varieties constructed from Fano double covers of dimension $n-1$. We conjecture that a Casagrande-Druel variety is K-polystable if the double cover and its base space are K-polystable. We prove this for smoothable Casagrande-Druel threefolds, and for Casagrande-Druel varieties constructed from double covers of $\mathbb{P}^{n-1}$ ramified over smooth hypersurfaces of degree $2d$ with $n>d>\frac{n}{2}>1$. As an application, we describe the connected components of the K-moduli space parametrizing smoothable K-polystable Fano threefolds in the families 3.9 and 4.2 in the Mori-Mukai classification., Comment: 58 pages

Lithium battery industry is booming, and this fast growth should be supported by developing industry friendly tools to control the quality of positive and negative electrode materials. Raman spectroscopy was shown to be a cost effective and sensitive instrument to study defects and heterogeneities in lithium titanate, popular negative electrode material for high power applications, but there are still some points to be clarified. This work presents a detailed thermal Raman study for lithium titanate and discusses the difference of the number of predicted and experimentally observed Raman-active bands. The low temperature study and the analysis of thermal shifts of bands positions during heating let us to conclude about advantages of the proposed approach with surplus bands and recommend using shifts of major band to estimate the sample heating.

We present a new measurement of the positive muon magnetic anomaly, $a_\mu \equiv (g_\mu - 2)/2$, from the Fermilab Muon $g\!-\!2$ Experiment using data collected in 2019 and 2020. We have analyzed more than 4 times the number of positrons from muon decay than in our previous result from 2018 data. The systematic error is reduced by more than a factor of 2 due to better running conditions, a more stable beam, and improved knowledge of the magnetic field weighted by the muon distribution, $\tilde{\omega}'^{}_p$, and of the anomalous precession frequency corrected for beam dynamics effects, $\omega_a$. From the ratio $\omega_a / \tilde{\omega}'^{}_p$, together with precisely determined external parameters, we determine $a_\mu = 116\,592\,057(25) \times 10^{-11}$ (0.21 ppm). Combining this result with our previous result from the 2018 data, we obtain $a_\mu\text{(FNAL)} = 116\,592\,055(24) \times 10^{-11}$ (0.20 ppm). The new experimental world average is $a_\mu (\text{Exp}) = 116\,592\,059(22)\times 10^{-11}$ (0.19 ppm), which represents a factor of 2 improvement in precision., Comment: 8 pages, 3 figures

We consider Riordan arrays $\bigl(1/(1-t^{d+1}), ~ tp(t)\bigr)$. These are infinite lower triangular matrices determined by the formal power series $1/(1-t^{d+1})$ and a polynomial $p(t)$ of degree $d$. Columns of such matrix are eventually periodic sequences with a period of $d + 1$, and circulant matrices are used to describe the long term behavior of such periodicity when the column's index grows indefinitely. We also discuss some combinatorially interesting sequences that appear through the corresponding A - and Z - sequences of such Riordan arrays., Comment: 25 pages, 7 figures

Automated design of analog and radio-frequency circuits using supervised or reinforcement learning from simulation data has recently been studied as an alternative to manual expert design. It is straightforward for a design agent to learn an inverse function from desired performance metrics to circuit parameters. However, it is more common for a user to have threshold performance criteria rather than an exact target vector of feasible performance measures. In this work, we propose a method for generating from simulation data a dataset on which a system can be trained via supervised learning to design circuits to meet threshold specifications. We moreover perform the to-date most extensive evaluation of automated analog circuit design, including experimenting in a significantly more diverse set of circuits than in prior work, covering linear, nonlinear, and autonomous circuit configurations, and show that our method consistently reaches success rate better than 90% at 5% error margin, while also improving data efficiency by upward of an order of magnitude. A demo of this system is available at circuits.streamlit.app, Comment: in proceedings of ICML 23

We present the theory for the evaluation of non-adiabatic couplings (NACs) involving resonance states within the complex absorbing potential equation-of-motion coupled-cluster (CAP-EOM-CC) framework implemented within the singles and doubles approximation. Resonance states are embedded in the continuum and undergo rapid decay through autodetachment. In addition, nuclear motions can facilitate transitions between different resonances and between resonances and bound states. These non-adiabatic transitions affect the chemical fate of resonances and have distinct spectroscopic signatures. The NAC vector is a central quantity needed to model such effects. In the CAP-EOM-CC framework, resonance states are treated on the same footing as bound states. Using the example of fumaronitrile, which supports a bound radical anion and several anionic resonances, we analyze the non-adiabatic coupling between bound states and pseudocontinuum states, between bound states and resonances and between two resonances. We find that the NAC between a bound state and a resonance is nearly independent of the CAP strength and thus straightforward to evaluate whereas the NAC between two resonance states or between a bound state and a pseudocontinuum state is more difficult to evaluate.

We classify non-factorial nodal Fano threefolds with $1$ node and class group of rank $2$., Comment: 14 pages. Minor changes; improved exposition

We propose a pipeline for combined multi-class object geolocation and height estimation from street level RGB imagery, which is considered as a single available input data modality. Our solution is formulated via Markov Random Field optimization with deterministic output. The proposed technique uses image metadata along with coordinates of objects detected in the image plane as found by a custom-trained Convolutional Neural Network. Computing the object height using our methodology, in addition to object geolocation, has negligible effect on the overall computational cost. Accuracy is demonstrated experimentally for water drains and road signs on which we achieve average elevation estimation error lower than 20cm.

We study automorphisms, isomorphisms, and derivations of the incidence algebra $I(X,R)$, where $X$ is preordered set and $R$ is an algebra over some commutative ring $T$.