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Quantum machine learning has gained considerable attention as quantum technology advances, presenting a promising approach for efficiently learning complex data patterns. Despite this promise, most contemporary quantum methods require significant resources for variational parameter optimization and face issues with vanishing gradients, leading to experiments that are either limited in scale or lack potential for quantum advantage. To address this, we develop a general-purpose, gradient-free, and scalable quantum reservoir learning algorithm that harnesses the quantum dynamics of neutral-atom analog quantum computers to process data. We experimentally implement the algorithm, achieving competitive performance across various categories of machine learning tasks, including binary and multi-class classification, as well as timeseries prediction. Effective and improving learning is observed with increasing system sizes of up to 108 qubits, demonstrating the largest quantum machine learning experiment to date. We further observe comparative quantum kernel advantage in learning tasks by constructing synthetic datasets based on the geometric differences between generated quantum and classical data kernels. Our findings demonstrate the potential of utilizing classically intractable quantum correlations for effective machine learning. We expect these results to stimulate further extensions to different quantum hardware and machine learning paradigms, including early fault-tolerant hardware and generative machine learning tasks., Comment: 10 + 14 pages, 4 + 7 figures

Quandles are right-invertible, right-self distributive (and idempotent) algebraic structures. Therefore, right translations are quandle automorphisms. It has been interesting to look into finite quandles by way of the cycle structures their right translations may have. For each quandle, the list of these cycle structures is known as the profile of the quandle. For a connected quandle, any two right translations are conjugate so there is essentially one cycle structure per connected quandle - which we thus identify with the profile. Hayashi conjectured that, for a connected quandle, each length of its profile divides the longest length. In the present article we introduce Super Hayashi Quandles (SHQ). An SHQ is a finite connected quandle such that any two lengths in its profile are (i) distinct, and (ii) the shorter one divides the longer one. The SHQ's are latin quandles and we prove that their profiles depend only on the second shortest length and on the number of cycles. Furthermore, we prove that SHQ's have SHQ's alone for subquandles (with the same second shortest length but fewer cycles). Finally, we construct infinitely many SHQ's.

A quandle is an algebraic structure whose binary operation is idempotent, right-invertible and right self-distributive. Right-invertibility ensures right translations are permutations and right self-distributivity ensures further they are automorphisms. For finite connected quandles, all right translations have the same cycle structure, called the profile of the connected quandle. Hayashi conjectured that the longest length in the profile of a finite connected quandle is a multiple of the remaining lengths. We prove that this conjecture is true for profiles with at most five lengths.

Metastable states arise in a range of quantum systems and can be observed in various dynamical scenarios, including decay, bubble nucleation, and long-lived oscillations. The phenomenology of metastable states has been examined in quantum many-body systems, notably in 1D ferromagnetic Ising spin systems and superfluids. In this paper, we study long-lived oscillations of metastable and ground states in 1D antiferromagnetic neutral atom chains with long-range Rydberg interactions. We use a staggered local detuning field to achieve confinement. Using theoretical and numerical models, we identify novel spectral signatures of quasiparticle oscillations distinct to antiferromagnetic neutral atom systems and interpret them using a classical energy model of short-range meson repulsion. Finally, we evaluate the experimental accessibility of our proposed setup on current neutral-atom platforms and discuss experimental feasibility and constraints., Comment: 15 pages, 5 figures

Metastable states of quantum many-body systems with confinement offer a means to simulate false vacuum phenomenology, including non-equilibrium dynamical processes like decay by nucleation, in truncated limits. Recent work has examined the decay process in 1D ferromagnetic Ising spins and superfluids. In this paper, we study nucleation dynamics in 1D antiferromagnetic neutral atom chains with Rydberg interactions, using both numerical simulations and analytic modeling. We apply a staggered local detuning field to generate the metastable and ground states. Our efforts focus on two dynamical regimes: decay and annealing. In the first, we corroborate the phenomenological decay rate scaling and determine the associated parameter range for the decay process; in the second, we uncover and elucidate a procedure to anneal the metastable state from the initial to the final system, with intermediate nucleation events. We further propose experimental protocols to prepare the required states and perform quenches on near-term neutral atom quantum simulators, examining the experimental feasibility of our proposed setup and parameter regime., Comment: 15 pages, 8 figures

Aquila, an analog quantum simulation platform developed by QuEra Computing, supports control of the position and coherent evolution of up to 256 neutral atoms. This study details novel experimental protocols designed for analog quantum simulators that generate Bell state entanglement far away from the blockade regime, construct a $Z_2$ state with a defect induced by an ancilla, and optimize the driving fields schedule to prepare excited states with enhanced fidelity. We additionally evaluate the effectiveness of readout error mitigation techniques in improving the fidelity of measurement results. All experiments were executed on Aquila from QuEra and facilitated by the AWS Braket interface. Our experimental results closely align with theoretical predictions and numerical simulations. The insights gained from this study showcase Aquila's capabilities in handling complex quantum simulations and computations, and also pave the way for new avenues of research in quantum information processing and physics that employ programmable analog hardware platforms., Comment: 7 pages, 6 figures, IEEE QCE24 - QTEM Best Paper Award - 1st Place

We investigate the topological phase transitions driven by band warping and a transverse magnetic field, for three-dimensional Weyl semimetals. First, we use the Chern number as a mathematical tool to derive the topological phase diagram. Next, we associate each of the topological sectors to a given angular momentum state of a rotating wave packet. Then we show how the position of the Weyl nodes can be manipulated by a transverse external magnetic field that ultimately quenches the wave packet rotation, first partially and then completely, thus resulting in a sequence of field-induced topological phase transitions. Finally, we calculate the current-induced magnetization and the anomalous Hall conductivity of a prototypical warped Weyl material. Both observables reflect the topological transitions associated with the wave packet rotation and can help to identify the elusive 3D quantum anomalous Hall effect in three-dimensional, warped Weyl materials., Comment: 6 pages, 5 figures

The Vera C. Rubin Observatory will undertake the Legacy Survey of Space and Time, providing an unprecedented, volume-limited catalog of star clusters in the Southern Sky, including Galactic and extragalactic star clusters. The Star Clusters subgroup of the Stars, Milky Way and Local Volume Working Group has identified key areas where Rubin Observatory will enable significant progress in star cluster research. This roadmap represents our science cases and preparation for studies of all kinds of star clusters from the Milky Way out to distances of tens of megaparsecs., Comment: accepted to PASP

We investigate the physical properties of $G_2$-symmetric integrable chains with local degrees of freedom in the fundamental representation; given the typical connection between integrability and critical points, we test the model's properties against a hypothesis of conformal-invariant long-distance behavior. Leveraging an embedding between the $G_2$ exceptional Lie algebra and $SU(2)$-symmetric chains with local spin-3 representations, we perform numerical analyses via exact diagonalization (ED) targeted at specific spin sectors, as well as via non-Abelian density-matrix renormalization group (DMRG). A basic study of the momentum-resolved ED spectrum suggests the low-energy system is effectively described by a $(G_2)_1$ Wess--Zumino--Witten (WZW) theory, but we find challenges in further numerical characterization of conformal data. The study and control of the phenomenology of this model may have implications for the development of accessible models for Fibonacci anyons., Comment: 13 pages, 5 figures

With the emergence of the Node.js ecosystem, JavaScript has become a widely-used programming language for implementing server-side web applications. In this paper, we present the first empirical study of static code analysis tools for detecting vulnerabilities in Node.js code. To conduct a comprehensive tool evaluation, we created the largest known curated dataset of Node.js code vulnerabilities. We characterized and annotated a set of 957 vulnerabilities by analyzing information contained in npm advisory reports. We tested nine different tools and found that many important vulnerabilities appearing in the OWASP Top-10 are not detected by any tool. The three best performing tools combined only detect up to 57.6% of all vulnerabilities in the dataset, but at a very low precision of 0.11%. Our curated dataset offers a new benchmark to help characterize existing Node.js code vulnerabilities and foster the development of better vulnerability detection tools for Node.js code.

Quandles are self-distributive, right-invertible, idempotent algebras. A group with conjugation for binary operation is an example of a quandle. Given a quandle $(Q, \ast)$ and a positive integer $n$, define $a\ast_n b = (\cdots (a\ast \underbrace{b)\ast \cdots )\ast b}_{n}$, where $a, b \in Q$. Then, $(Q, \ast_n)$ is again a quandle. We set forth the following problem. ``Find $(Q, \ast)$ such that the sequence $\{(Q, \ast_n)\, :\, n\in \mathbb{Z}^+ \}$ is made up of pairwise non-isomorphic quandles.'' In this article we find such a quandle $(Q, \ast)$. We study the general linear group of $2$-by-$2$ matrices over $\mathbb{C}$ as a quandle under conjugation. Its (algebraically) connected components, that is, its conjugacy classes, are subquandles of it. We show the latter are connected as quandles and prove rigidity results about them such as the dihedral quandle of order $3$ is not a subquandle for most of them. Then we consider the quandle which is the projective linear group of $2$-by-$2$ matrices over $\mathbb{C}$ with conjugation, and prove it solves the problem above. In the course of this work we prove a sufficient and necessary condition for a quandle to be latin. This will reduce significantly the complexity of algorithms for ascertaining if a quandle is latin., Comment: 25 pages

Architectures for quantum computing based on neutral atoms have risen to prominence as candidates for both near and long-term applications. These devices are particularly well suited to solve independent set problems, as the combinatorial constraints can be naturally encoded in the low-energy Hilbert space due to the Rydberg blockade mechanism. Here, we approach this connection with a focus on a particular device architecture and explore the ubiquity and utility of independent set problems by providing examples of real-world applications. After a pedagogical introduction of basic graph theory concepts of relevance, we briefly discuss how to encode independent set problems in Rydberg Hamiltonians. We then outline the major classes of independent set problems and include associated example applications with industry and social relevance. We determine a wide range of sectors that could benefit from efficient solutions of independent set problems -- from telecommunications and logistics to finance and strategic planning -- and display some general strategies for efficient problem encoding and implementation on neutral-atom platforms., Comment: 30 pages, 10 example applications

WebAssembly is a new binary instruction format that allows targeted compiled code written in high-level languages to be executed with near-native speed by the browser's JavaScript engine. However, given that WebAssembly binaries can be compiled from unsafe languages like C/C++, classical code vulnerabilities such as buffer overflows or format strings can be transferred over from the original programs down to the cross-compiled binaries. As a result, this possibility of incorporating vulnerabilities in WebAssembly modules has widened the attack surface of modern web applications. This paper presents Wasmati, a static analysis tool for finding security vulnerabilities in WebAssembly binaries. It is based on the generation of a code property graph (CPG), a program representation previously adopted for detecting vulnerabilities in various languages but hitherto unapplied to WebAssembly. We formalize the definition of CPG for WebAssembly, introduce techniques to generate CPG for complex WebAssembly, and present four different query specification languages for finding vulnerabilities by traversing a program's CPG. We implemented ten queries capturing different vulnerability types and extensively tested Wasmati on four heterogeneous datasets. We show that Wasmati can scale the generation of CPGs for large real-world applications and can efficiently find vulnerabilities for all our query types. We have also tested our tool on WebAssembly binaries collected in the wild and identified several potential vulnerabilities, some of which we have manually confirmed to exist unless the enclosing application properly sanitizes the interaction with such affected binaries., Comment: Computers & Security

We consider the Cahn-Hilliard equation on manifolds with conical singularities and prove existence of global attractors in higher order Mellin-Sobolev spaces with asymptotics. We also show convergence of solutions in the same spaces to an equilibrium point and provide asymptotic behavior of the equilibrium near the conical tips in terms of the local geometry., Comment: 21 pages

We prove Euler's theorem of number theory developing an argument based on quandles. A quandle is an algebraic structure whose axioms mimic the three Reidemeister moves of knot theory., Comment: 6 pages

Importance: Lower-resource areas in Africa and Asia face a unique set of healthcare challenges: the dual high burden of communicable and non-communicable diseases; a paucity of highly trained primary healthcare providers in both rural and densely populated urban areas; and a lack of reliable, inexpensive internet connections. Objective: To address these challenges, we designed an artificial intelligence assistant to help primary healthcare providers in lower-resource areas document demographic and medical sign/symptom data and to record and share diagnostic data in real-time with a centralized database. Design: We trained our system using multiple data sets, including US-based electronic medical records (EMRs) and open-source medical literature and developed an adaptive, general medical assistant system based on machine learning algorithms. Main outcomes and Measure: The application collects basic information from patients and provides primary care providers with diagnoses and prescriptions suggestions. The application is unique from existing systems in that it covers a wide range of common diseases, signs, and medication typical in lower-resource countries; the application works with or without an active internet connection. Results: We have built and implemented an adaptive learning system that assists trained primary care professionals by means of an Android smartphone application, which interacts with a central database and collects real-time data. The application has been tested by dozens of primary care providers. Conclusions and Relevance: Our application would provide primary healthcare providers in lower-resource areas with a tool that enables faster and more accurate documentation of medical encounters. This application could be leveraged to automatically populate local or national EMR systems.

The multichannel Kondo model supports effective anyons on the partially screened impurity, as suggested by its fractional impurity entropy. It was recently demonstrated for the multi-impurity chiral Kondo model, that scattering of an electron through the impurities depends on the anyon's total fusion channel. Here we study the correlation between impurity-spins. We argue, based on a combination of conformal field theory, a perturbative limit with a large number of channels $k$, and the exactly solvable two-channel case, that the inter-impurity spin correlation probes the anyon fusion of the pair of correlated impurities. This may allow, using measurement-only topological quantum computing protocols, to braid the multichannel Kondo anyons via consecutive measurements.

It was proposed in [(https://doi.org/10.1103/PhysRevLett.114.145301){Chen et al., Phys. Rev. Lett. $\mathbf{114}$, 145301 (2015)}] that spin-2 chains display an extended critical phase with enhanced SU$(3)$ symmetry. This hypothesis is highly unexpected for a spin-2 system and, as we argue, would imply an unconventional mechanism for symmetry emergence. Yet, the absence of convenient critical points for renormalization group perturbative expansions, allied with the usual difficulty in the convergence of numerical methods in critical or small-gapped phases, renders the verification of this hypothetical SU$(3)$-symmetric phase a non-trivial matter. By tracing parallels with the well-understood phase diagram of spin-1 chains and searching for signatures robust against finite-size effects, we draw criticism on the existence of this phase. We perform non-Abelian density matrix renormalization group studies of multipolar static correlation function, energy spectrum scaling, single-mode approximation, and entanglement spectrum to shed light on the problem. We determine that the hypothetical SU$(3)$ spin-2 phase is, in fact, dominated by ferro-octupolar correlations and also observe a lack of Luttinger-liquid-like behavior in correlation functions that suggests that is perhaps not critical. We further construct an infinite family of spin-$S$ systems with similar ferro-octupolar-dominated quasi-SU$(3)$-like phenomenology; curiously, we note that the spin-3 version of the problem is located in a subspace of exact G$_2$ symmetry, making this a point of interest for search of Fibonacci topological properties in magnetic systems., Comment: 13 pages, 9 figures

A quandle is an algebraic structure satisfying three axioms: idempotency, right-invertibility and right self-distributivity. In quandles, right translations are permutations. The profile of a quandle is the list of cycle structures, one per right translation in the quandle. In this note we prove that if, for each cycle structure in the profile of a quandle, no two cycle lengths are equal, then the quandle is latin -- this is the sufficient condition mentioned in the title., Comment: 8 pages

Amplifiers based on Josephson junctions allow for a fast and noninvasive readout of superconducting qubits. Motivated by the ongoing progress toward the realization of fault-tolerant qubits based on Majorana bound states, we investigate the topological counterpart of the Josephson bifurcation amplifier. We predict that the bifurcation dynamics of a topological Josephson junction driven in the appropriate parameter regime may be used as an additional tool to detect the emergence of Majorana bound states., Comment: 16 pages, 11 figures

In this paper we study an abstract framework for computing shape derivatives of functionals subject to PDE constraints. We revisit the Lagrangian approach using the implicit function theorem in an abstract setting tailored for applications to shape optimization. This abstract framework yields practical formulae to compute the derivative of a shape functional, the material derivative of the state, and the adjoint state. Furthermore, it allows to gain insight on the duality between the material derivative of the state and the adjoint state. We show several applications of our main result to the computation of distributed shape derivatives for problems involving linear elliptic, nonlinear elliptic, parabolic PDEs and distributions. We compare our approach with other techniques for computing shape derivatives including the material derivative method and the averaged adjoint method.

This article is based upon previous work by Sousa Ramos and his collaborators. They first prove that the existence of only one orbit associated with the Collatz conjecture is equivalent to the determinant of each matrix of a certain sequence of matrices to have the same value. These matrices are called Collatz matrices. The second step in their work would be to calculate this determinant for each of the Collatz matrices. Having calculated this determinant for the first few terms of the sequence of matrices, their plan was to prove the determinant of the current term equals the determinant of the previous one. Unfortunately, they could not prove it for the cases where the dimensions of the matrices are 26+54l or 44+54l, where l is a positive integer. In the current article we improve on these results., Comment: 10 pages, typos corrected