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Realizing universal fault-tolerant quantum computation is a key goal in quantum information science. By encoding quantum information into logical qubits utilizing quantum error correcting codes, physical errors can be detected and corrected, enabling substantial reduction in logical error rates. However, the set of logical operations that can be easily implemented on such encoded qubits is often constrained, necessitating the use of special resource states known as 'magic states' to implement universal, classically hard circuits. A key method to prepare high-fidelity magic states is to perform 'distillation', creating them from multiple lower fidelity inputs. Here we present the experimental realization of magic state distillation with logical qubits on a neutral-atom quantum computer. Our approach makes use of a dynamically reconfigurable architecture to encode and perform quantum operations on many logical qubits in parallel. We demonstrate the distillation of magic states encoded in d=3 and d=5 color codes, observing improvements of the logical fidelity of the output magic states compared to the input logical magic states. These experiments demonstrate a key building block of universal fault-tolerant quantum computation, and represent an important step towards large-scale logical quantum processors., Comment: 8+11 pages, 4+4 figures

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

The industrial manufacturing of chemicals consumes a significant amount of energy and raw materials. In principle, the development of new catalysts could greatly improve the efficiency of chemical production. However, the discovery of viable catalysts can be exceedingly challenging because it is difficult to know the efficacy of a candidate without experimentally synthesizing and characterizing it. This study explores the feasibility of using fault-tolerant quantum computers to accelerate the discovery of homogeneous catalysts for nitrogen fixation, an industrially important chemical process. It introduces a set of ground-state energy estimation problems representative of calculations needed for the discovery of homogeneous catalysts and analyzes them on three dimensions: economic utility, classical hardness, and quantum resource requirements. For the highest utility problem considered, two steps of a catalytic cycle for the generation of cyanate anion from dinitrogen, the economic utility of running these computations is estimated to be $200,000, and the required runtime for double-factorized phase estimation on a fault-tolerant superconducting device is estimated under conservative assumptions to be 139,000 QPU-hours. The computational cost of an equivalent DMRG calculation is estimated to be about 400,000 CPU-hours. These results suggest that, with continued development, it will be feasible for fault-tolerant quantum computers to accelerate the discovery of homogeneous catalysts., Comment: 27 pages, 11 tables, 8 figures plus appendix

We study the new $Z'$ boson as a portal for the production of Higgs bosons $h_0$ and $H_0$ predicted by the Bestest Little Higgs Model through the Higgs-strahlung processes $\mu^+\mu^- \to (Z, Z') \to Zh_0, ZH_0$. We focus on the resonance and non-resonance effects of the $Zh_0, ZH_0$ signals. In our analysis, we consider the center-of-mass energies of $\sqrt{s}=3, 4, 5, 6, 7, 10, 30$ TeV and integrated luminosities of ${\cal L}=2, 4, 6, 10, 30$ ${\rm ab^{-1}}$ projected for a future muon collider. The possibility of performing precision measurements for the Higgs bosons $h_0$ and $H_0$ is very promising at the future muon collider. Furthermore, our results may be helpful to the High Energy Physics community. Complementarily, we generate and provide the Feynman rules necessary for studying the processes $\mu^+\mu^- \to (Z, Z') \to Zh_0, ZH_0$., Comment: 35 pages, 11 figures

This study shows the feasibility of an eHealth solution for tackling eating habits and physical activity in the adolescent population. The participants were children from 11 to 15 years old. An intervention was carried out on 139 students in the intervention group and 91 students in the control group, in two schools during 14 weeks. The intervention group had access to the web through a user account and a password. They were able to create friendship relationships, post comments, give likes and interact with other users, as well as receive notifications and information about nutrition and physical activity on a daily basis and get (virtual) rewards for improving their habits. The control group did not have access to any of these features. The homogeneity of the samples in terms of gender, age, body mass index and initial health-related habits was demonstrated. Pre- and post-measurements were collected through self-reports on the application website. After applying multivariate analysis of variance, a significant alteration in the age-adjusted body mass index percentile was observed in the intervention group versus the control group, as well as in the PAQ-A score and the KIDMED score. It can be concluded that eHealth interventions can help to obtain healthy habits. More research is needed to examine the effectiveness in achieving adherence to these new habits.

BLDC motor applications require precise position and speed measurements, traditionally obtained with sensors. This article presents a method for estimating those measurements without position sensors using terminal phase voltages with attenuated spurious, acquired with a FPGA that also operates a PWM-controlled inverter. Voltages are labelled with electrical and virtual rotor states using an encoder that provides training and testing data for two three-layer ANNs with perceptron-based cascade topology. The first ANN estimates the position from features of voltages with incremental timestamps, and the second ANN estimates the speed from features of position differentials considering timestamps in an acquisition window. Sensor-based training and sensorless testing at 125 to 1,500 rpm with a loaded 8-pole-pair motor obtained absolute errors of 0.8 electrical degrees and 22 rpm. Results conclude that the overall position estimation significantly improved conventional and advanced methods, and the speed estimation slightly improved conventional methods, but was worse than in advanced ones.

One of the ways to encode many-body Hamiltonians on a quantum computer to obtain their eigen-energies through Quantum Phase Estimation is by means of the Trotter approximation. There were several ways proposed to assess the quality of this approximation based on estimating the norm of the difference between the exact and approximate evolution operators. Here, we would like to explore how these different error estimates are correlated with each other and whether they can be good predictors for the true Trotter approximation error in finding eigenvalues. For a set of small molecular systems we calculated the exact Trotter approximation errors of the first order Trotter formulas for the ground state electronic energies. Comparison of these errors with previously used upper bounds show almost no correlation over the systems and various Hamiltonian partitionings. On the other hand, building the Trotter approximation error estimation based on perturbation theory up to a second order in the time-step for eigenvalues provides estimates with very good correlations with the Trotter approximation errors. The developed perturbative estimates can be used for practical time-step and Hamiltonian partitioning selection protocols, which are paramount for an accurate assessment of resources needed for the estimation of energy eigenvalues under a target accuracy., Comment: 3 figures

We investigate some topological and spectral properties of Erd\H{o}s-R\'{e}nyi (ER) random digraphs $D(n,p)$. In terms of topological properties, our primary focus lies in analyzing the number of non-isolated vertices $V_x(D)$ as well as two vertex-degree-based topological indices: the Randi\'c index $R(D)$ and sum-connectivity index $\chi(D)$. First, by performing a scaling analysis we show that the average degree $\langle k \rangle$ serves as scaling parameter for the average values of $V_x(D)$, $R(D)$ and $\chi(D)$. Then, we also state expressions relating the number of arcs, spectral radius, and closed walks of length 2 to $(n,p)$, the parameters of ER random digraphs. Concerning spectral properties, we compute six different graph energies on $D(n,p)$. We start by validating $\langle k \rangle$ as the scaling parameter of the graph energies. Additionally, we reformulate a set of bounds previously reported in the literature for these energies as a function $(n,p)$. Finally, we phenomenologically state relations between energies that allow us to extend previously known bounds.

We consider the question of how correlated the system hardness is between classical algorithms of electronic structure theory in ground state estimation and quantum algorithms. To define the system hardness for classical algorithms we employ empirical criterion based on the deviation of electronic energies produced by coupled cluster and configuration interaction methods from the exact ones along multiple bonds dissociation in a set of molecular systems. For quantum algorithms, we have selected the Variational Quantum Eigensolver (VQE) and Quantum Phase Estimation (QPE) methods. As characteristics of the system hardness for quantum methods, we analyzed circuit depths for the state preparation, the number of quantum measurements needed for the energy expectation value, and various cost characteristics for the Hamiltonian encodings via Trotter approximation and linear combination of unitaries (LCU). Our results show that the quantum resource requirements are mostly unaffected by classical hardness, with the only exception being the state preparation part, which contributes to both VQE and QPE algorithm costs. However, there are clear indications that constructing the initial state with a significant overlap with the true ground state (>10%) is easier than obtaining the state with an energy expectation value within chemical precision. These results support optimism regarding the identification of a molecular system where a quantum algorithm excels over its classical counterpart, as quantum methods can maintain efficiency in classically challenging systems., Comment: 11 pages

In the current industry, the development of optimized mechanical components able to satisfy the customer requirements evolves quickly. Therefore, companies are asked for efficient solutions to improve their products in terms of stiffness and strength. In this sense, Topology Optimization has been extensively used to determine the best topology of structural components from the mechanical point of view. Its main objective is to distribute a given amount of material into a predefined domain to reach the maximum overall stiffness of the component. Besides, high-resolution solutions are essential to define the final distribution of material. Standard Topological Optimization tools are able to propose an optimal topology for the whole component, but when small topological details are required (i.e. trabecular-type structures) the computational cost is prohibitive. In order to mitigate this issue, the present work proposes a two-level topology optimization method to solve high-resolution problems by using density-based methods. The proposed methodology includes three steps: The first one subdivides the whole component in cells and generates a coarse optimized low-definition material distribution assigning one different density to each cell. The second one uses an equilibrating technique that provides tractions continuity between adjacent cells, thus ensuring the material inter-cell continuity after the cells optimization process. Finally, each cell is optimized at fine scale taking as input data the densities and the equilibrated tractions obtained from the macro problem. The main goal of this work is to efficiently solve high-resolution topology optimization problems using density-based methods, which would be unaffordable with standard computing facilities and the current methodologies., Comment: 23 pages