Search

We obtain a bound on the girth g of a quaternion unit gain graph in terms of the rank r of its adjacency matrix. In particular, we show that g <= r + 2 and characterize all quaternion unit gain graphs for which g = r+2. This extends corresponding results for (ordinary) graphs, signed graphs, and complex unit gain graphs., Comment: 6 pages

Transitioning from quantum computation on physical qubits to quantum computation on encoded, logical qubits can improve the error rate of operations, and will be essential for realizing valuable quantum computational advantages. Using a neutral atom quantum processor with 256 qubits, each an individual Ytterbium atom, we demonstrate the entanglement of 24 logical qubits using the distance-two [[4,2,2]] code, simultaneously detecting errors and correcting for lost qubits. We also implement the Bernstein-Vazirani algorithm with up to 28 logical qubits encoded in the [[4,1,2]] code, showing better-than-physical error rates. We demonstrate fault-tolerant quantum computation in our approach, guided by the proposal of Gottesman (2016), by performing repeated loss correction for both structured and random circuits encoded in the [[4,2,2]] code. Finally, since distance-two codes can correct qubit loss, but not other errors, we show repeated loss and error correction using the distance-three [[9,1,3]] Bacon-Shor code. These results begin to clear a path for achieving scientific quantum advantage with a programmable neutral atom quantum processor., Comment: 17 pages, 16 figures

Satellite-based quantum repeaters are a promising means to reach global distances in quantum networking due to the polynomial decrease of optical transmission with distance in free space, in contrast to the exponential decrease in optical fibers. We propose a satellite-based quantum repeater architecture with trapped individual atomic qubits, which can serve both as quantum memories and true single photon sources. This hardware allows for nearly deterministic Bell measurements and exhibits long coherence times without the need for costly cryogenic technology in space. We develop a detailed analytical model of the repeater, which includes the main imperfections of the quantum hardware and the optical link, allowing us to estimate that high-rate and high-fidelity entanglement distribution can be achieved over inter-continental distances. In particular, we find that high fidelity entanglement distribution over thousands of kilometres at a rate of 100 Hz can be achieved with orders of magnitude fewer memory modes than conventional architectures based on optical Bell state measurements., Comment: 10 pages, 4 figures

We demonstrate the first end-to-end integration of high-performance computing (HPC), reliable quantum computing, and AI in a case study on catalytic reactions producing chiral molecules. We present a hybrid computation workflow to determine the strongly correlated reaction configurations and estimate, for one such configuration, its active site's ground state energy. We combine 1) the use of HPC tools like AutoRXN and AutoCAS to systematically identify the strongly correlated chemistry within a large chemical space with 2) the use of logical qubits in the quantum computing stage to prepare the quantum ground state of the strongly correlated active site, demonstrating the advantage of logical qubits compared to physical qubits, and 3) the use of optimized quantum measurements of the logical qubits with so-called classical shadows to accurately predict various properties of the ground state including energies. The combination of HPC, reliable quantum computing, and AI in this demonstration serves as a proof of principle of how future hybrid chemistry applications will require integration of large-scale quantum computers with classical computing to be able to provide a measurable quantum advantage., Comment: 15 pages, 9 figures

A critical milestone for quantum computers is to demonstrate fault-tolerant computation that outperforms computation on physical qubits. The tesseract subsystem color code protects four logical qubits in 16 physical qubits, to distance four. Using the tesseract code on Quantinuum's trapped-ion quantum computers, we prepare high-fidelity encoded graph states on up to 12 logical qubits, beneficially combining for the first time fault-tolerant error correction and computation. We also protect encoded states through up to five rounds of error correction. Using performant quantum software and hardware together allows moderate-depth logical quantum circuits to have an order of magnitude less error than the equivalent unencoded circuits., Comment: 12 pages, 13 figures

Obtaining reliable and precise estimates of wildlife species abundance and distribution is essential for the conservation and management of animal populations and natural reserves. Remote sensors such as camera traps are increasingly employed to gather data on uniquely identifiable individuals. Spatial capture-recapture (SCR) models provide estimates of population and spatial density from such data. These models introduce spatial correlation between observations of the same individual through a latent activity center. However SCR models assume that observations are independent over time and space, conditional on their given activity center, so that observed sightings at a given time and location do not influence the probability of being seen at future times and/or locations. With detectors like camera traps, this is ecologically unrealistic given the smooth movement of animals over space through time. We propose a new continuous-time modeling framework that incorporates both an individual's (latent) activity center and (known) previous location and time of detection. We demonstrate that standard SCR models can produce substantially biased density estimates when there is correlation in the times and locations of detections, and that our new model performs substantially better than standard SCR models on data simulated through a movement model as well as in a real camera trap study of American martens where an improvement in model fit is observed when incorporating the observed locations and times of previous observations., Comment: 20 pages, 4 figures

Direct imaging of exoplanets allows us to measure positions and chemical signatures of exoplanets. Given the limited resources for space observations where the atmosphere is absent, we want to make these measurements from the ground. However, it is difficult from the ground because it requires an adaptive optics system to provide an extremely well corrected wavefront to enable coronographic techniques. Currently only natural guide star AO systems have demonstrated the necessary wavefront correction for direct imaging of exoplanets. However, using a stellar source as the guide star for wavefront sensing limits the number of exoplanet systems we can directly image because it requires a relatively bright V~10 mag star. To increase the number of observable targets, we need to push the limit of natural guide stars to fainter magnitudes with high Strehl ratio correction. We propose to combine laser guide star (LGS) and natural guide star (NGS) wavefront sensing to achieve the high Strehl correction with fainter natural guide stars. We call this approach Hybrid Atmospheric Phase Analysis (HAPA); 'hapa' in Hawaiian means 'half' or 'of mixed ethnic heritage'. The relatively bright LGS is used for higher order correction, whereas the NGS is used for high accuracy lower order correction. We focus on demonstrating this approach using Robo-AO-2 at the UH 2.2m telescope on Maunakea with a UV Rayleigh laser at 355 nm. The laser focuses at 10 km altitude and has an equivalent magnitude of m_U~8. In this report specifically, we present simulated results of HAPA employed at Robo-AO-2, with the LGS system having a single configuration of 16x16 subaperture Shack-Hartmann wavefront sensor and the NGS system having 6 different configurations -- 16x16, 8x8, 5x5, 4x4, 2x2 and 1x1. We also discuss the on-sky experiments we plan to carry out with HAPA at the UH 2.2m telescope., Comment: 11 pages, 4 figures, 8 tables, SPIE Astronomical Telescopes + Instrumentation 2024

We installed the next-generation automated laser adaptive optics system, Robo-AO-2, on the University of Hawaii 2.2-m telescope on Maunakea in 2023. We engineered Robo-AO-2 to deliver robotic, diffraction-limited observations at visible and near-infrared wavelengths in unprecedented numbers. This new instrument takes advantage of upgraded components, manufacturing techniques and control; and includes a parallel reconfigurable natural guide star wavefront sensor with which to explore hybrid wavefront sensing techniques. We present the results of commissioning in 2023 and 2024., Comment: Proceedings of SPIE, 13097-15

We consider Hoffman's program about the limit points of the spectral radius of the Hermitian adjacency matrix of mixed graphs. In particular, we determine all mixed graphs without negative $4$-cycle whose spectral radius does not exceed $\sqrt{2+\sqrt{5}}$, and identify all limit points of spectral radii of mixed graphs., Comment: 17 pages, 12 figures

We study the Patient Assignment Scheduling (PAS) problem in a random environment that arises in the management of patient flow in the hospital systems, due to the stochastic nature of the arrivals as well as the Length of Stay distribution. We develop a Markov Decision Process (MDP) which aims to assign the newly arrived patients in an optimal way so as to minimise the total expected long-run cost per unit time over an infinite horizon. We assume Poisson arrival rates that depend on patient types, and Length of Stay distributions that depend on whether patients stay in their primary wards or not. Since the instances of realistic size of this problem are not easy to solve, we develop numerical methods based on Approximate Dynamic Programming. We illustrate the theory with numerical examples with parameters obtained by fitting to data from a tertiary referral hospital in Australia, and demonstrate the application potential of our methodology under practical considerations., Comment: Submitted to Annals of Operations Research

Based on \cite{H}, it is well known that the rescaled two point correlation functions \[ \sqrt{N} \langle \sigma_i ; \sigma_j\rangle = \sqrt{N} \big( \langle \sigma_i \sigma_j\rangle -\langle \sigma_i\rangle \langle \sigma_j\rangle\big) \] in the Sherrington-Kirkpatrick spin glass model with non-zero external field admit at sufficiently high temperature an explicit non-Gaussian distributional limit as $N\to \infty$. Inspired by recent results from \cite{ABSY, BSXY, BXY}, we provide a novel proof of the distributional convergence which is based on expanding $\langle \sigma_i ; \sigma_j\rangle$ into a sum over suitable weights of self-avoiding paths from vertex $i$ to $j$. Compared to \cite{H}, our key observation is that the path representation of $\langle \sigma_i ; \sigma_j\rangle$ provides a direct explanation of the specific form of the limiting distribution of $\sqrt{N} \langle \sigma_i ; \sigma_j\rangle$., Comment: 17 pages

Context. Time-series photometry has given astronomers the tools to study time-dependent astrophysical phenomena, from stellar activity to fast radio bursts and exoplanet transits. Transit events in particular are focused primarily on planetary transits, and eclipsing binaries with eclipse geometries that are parameterised with a few variables, while more complex light curves caused by substructure within the transiting object require customized analysis code. Aims. We present Beyond Circular Eclipsers (BeyonCE), which reduces the parameter space encompassed by the transit of circum-secondary disc (CSD) systems with azimuthally symmetric non-uniform optical depth profiles. By rejecting disc geometries that cannot reproduce the measured gradients within their light curves, we can constrain the size and orientation of discs with complex sub-structure. Methods. We map out all the possible geometries of a disc, calculate the gradients for rings crossing the star, then reject those configurations where the measured gradient of the light curve is greater than the theoretical gradient from the given disc orientation. Results. We present the fitting code BeyonCE and demonstrate its effectiveness in considerably reducing the parameter space of discs that contain azimuthally symmetric structure by analyzing the light curves seen towards J1407 and PDS 110 which are attributed to CSD transits., Comment: Beyonce program can be found at https://github.com/dmvandamt/beyonce

An association scheme is called amorphic if every possible fusion of relations gives rise to a fusion scheme. We call a pair of relations fusing if fusing that pair gives rise to a fusion scheme. We define the fusing-relations graph on the set of relations, where a pair forms an edge if it fuses. We show that if the fusing-relations graph is connected but not a path, then the association scheme is amorphic. As a side result, we show that an association scheme in which at most one relation is not strongly regular of (negative) Latin square type, is amorphic.

Language model-based code completion models have quickly grown in use, helping thousands of developers write code in many different programming languages. However, research on code completion models typically focuses on imperative languages such as Python and JavaScript, which results in a lack of representation for functional programming languages. Consequently, these models often perform poorly on functional languages such as Haskell. To investigate whether this can be alleviated, we evaluate the performance of two language models for code, CodeGPT and UniXcoder, on the functional programming language Haskell. We fine-tune and evaluate the models on Haskell functions sourced from a publicly accessible Haskell dataset on HuggingFace. Additionally, we manually evaluate the models using our novel translated HumanEval dataset. Our automatic evaluation shows that knowledge of imperative programming languages in the pre-training of LLMs may not transfer well to functional languages, but that code completion on functional languages is feasible. Consequently, this shows the need for more high-quality Haskell datasets. A manual evaluation on HumanEval-Haskell indicates CodeGPT frequently generates empty predictions and extra comments, while UniXcoder more often produces incomplete or incorrect predictions. Finally, we release HumanEval-Haskell, along with the fine-tuned models and all code required to reproduce our experiments on GitHub (https://github.com/AISE-TUDelft/HaskellCCEval)., Comment: To appear in the First Special Event on AI Foundation Models and Software Engineering (FORGE 2024)

In blind quantum computing, a user with a simple client device can perform a quantum computation on a remote quantum server such that the server cannot gain knowledge about the computation. Here, we numerically investigate hardware requirements for verifiable blind quantum computing using an ion trap as server and a distant measurement-only client. While the client has no direct access to quantum-computing resources, it can remotely execute quantum programs on the server by measuring photons emitted by the trapped ion. We introduce a numerical model for trapped-ion quantum devices in NetSquid, a discrete-event simulator for quantum networks. Using this, we determine the minimal hardware requirements on a per-parameter basis to perform the verifiable blind quantum computing protocol. We benchmark these for a five-qubit linear graph state, with which any single-qubit rotation can be performed, where client and server are separated by 50 km. Current state-of-the-art ion traps satisfy the minimal requirements on a per-parameter basis, but all current imperfections combined make it impossible to perform the blind computation securely over 50 km using existing technology. Using a genetic algorithm, we determine the set of hardware parameters that minimises the total improvements required, finding directions along which to improve hardware to reach our threshold error probability that would enable experimental demonstration. In this way, we lay a path for the near-term experimental progress required to realise the implementation of verifiable blind quantum computing over a 50 km distance.

Transformer-based language models for automatic code completion have shown great promise so far, yet the evaluation of these models rarely uses real data. This study provides both quantitative and qualitative assessments of three public code language models when completing real-world code. We first developed an open-source IDE extension, Code4Me, for the online evaluation of the models. We collected real auto-completion usage data for over a year from more than 1200 users, resulting in over 600K valid completions. These models were then evaluated using six standard metrics across twelve programming languages. Next, we conducted a qualitative study of 1690 real-world completion requests to identify the reasons behind the poor model performance. A comparative analysis of the models' performance in online and offline settings was also performed, using benchmark synthetic datasets and two masking strategies. Our findings suggest that while developers utilize code completion across various languages, the best results are achieved for mainstream languages such as Python and Java. InCoder outperformed the other models across all programming languages, highlighting the significance of training data and objectives. Our study also revealed that offline evaluations do not accurately reflect real-world scenarios. Upon qualitative analysis of the model's predictions, we found that 66.3% of failures were due to the models' limitations, 24.4% occurred due to inappropriate model usage in a development context, and 9.3% were valid requests that developers overwrote. Given these findings, we propose several strategies to overcome the current limitations. These include refining training objectives, improving resilience to typographical errors, adopting hybrid approaches, and enhancing implementations and usability., Comment: To be published in the proceedings of the 46th IEEE/ACM International Conference on Software Engineering (ICSE 2024)

Electronic structure theory provides a foundation for understanding chemical transformations and processes in complex chemical environments. Our work is focused on the NWChemEx project that has selected two interrelated science challenges that address the production of advanced biomass-derived fuels and other value-added chemical compounds. One of which is the dehydration of 2-propanol over a zeolite catalyst. Aqueous phase dehydration of 2-propanol was investigated using density functional theory (DFT) calculations. We considered and analyzed the thermochemistry of the dehydration of 2-propanol using NWChem calculations while the NWChemEx code is still under development. Realistically modeling the reaction in this study properly requires simulations using extended atomistic models. We validated our computational models by comparing the predicted outcomes for 2-propanol dehydration with the calculated results from 1-propanol dehydration studies. We used the first-principles DFT calculations to investigate aqueous phase dehydration of 2-propanol, examine the enthalpy of the 2-propanol reaction and computed the energy for geometry optimization for increasingly better basis sets: cc-pVDZ, cc-pVTZ, cc-pVQZ, cc-pV5Z, and cc-pV6Z. The various transition states and minima along the reaction pathway are critical to inform the NWChemEx science challenge calculations. In this work, we established how the accuracy of the calculations depends on the basis sets, and we determined what basis sets are needed to achieve sufficient accurate results. We also calculated the reaction free energy as a function of temperature as thermodynamic parameter. We found that at low temperature the reaction is thermodynamically unfavorable. Nevertheless, dehydrating 2-propanol increases entropy, underscoring the need for high temperatures to facilitate the reaction., Comment: Added page numbers

Detecting abrupt changes in real-time data streams from scientific simulations presents a challenging task, demanding the deployment of accurate and efficient algorithms. Identifying change points in live data stream involves continuous scrutiny of incoming observations for deviations in their statistical characteristics, particularly in high-volume data scenarios. Maintaining a balance between sudden change detection and minimizing false alarms is vital. Many existing algorithms for this purpose rely on known probability distributions, limiting their feasibility. In this study, we introduce the Kernel-based Cumulative Sum (KCUSUM) algorithm, a non-parametric extension of the traditional Cumulative Sum (CUSUM) method, which has gained prominence for its efficacy in online change point detection under less restrictive conditions. KCUSUM splits itself by comparing incoming samples directly with reference samples and computes a statistic grounded in the Maximum Mean Discrepancy (MMD) non-parametric framework. This approach extends KCUSUM's pertinence to scenarios where only reference samples are available, such as atomic trajectories of proteins in vacuum, facilitating the detection of deviations from the reference sample without prior knowledge of the data's underlying distribution. Furthermore, by harnessing MMD's inherent random-walk structure, we can theoretically analyze KCUSUM's performance across various use cases, including metrics like expected delay and mean runtime to false alarms. Finally, we discuss real-world use cases from scientific simulations such as NWChem CODAR and protein folding data, demonstrating KCUSUM's practical effectiveness in online change point detection., Comment: 16 pages. arXiv admin note: text overlap with arXiv:1903.01661

Let $\mathcal{G}=\{G_1,\ldots,G_n \}$ be a family of graphs of order $n$ with the same vertex set. A rainbow Hamiltonian cycle in $\mathcal{G}$ is a cycle that visits each vertex precisely once such that any two edges belong to different graphs of $\mathcal{G}$. We obtain a rainbow version of Ore's size condition of Hamiltonicity, and pose a related problem. Towards a solution of that problem, we give a sufficient condition for the existence of a rainbow Hamiltonian cycle in terms of the spectral radii of the graphs in $\mathcal{G}$ and completely characterize the corresponding extremal graphs.

The resource estimation tools provided by Azure Quantum and Azure Quantum Development Kit are described. Using these tools one can automatically evaluate the logical and physical resources required to run algorithms on fault-tolerant quantum computers. An example is given of obtaining resource estimates for quantum fault-tolerant implementations of three different multiplication algorithms., Comment: 6 pages, 4 figures; updated to reflect Azure Quantum Development Kit release