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JQTM, Sebastian Gonzalez, Hao Jia, Ian Lu, Deniz Sogutlu, Abhishek Abhishek, Colin Gay, Eric Paquet, Roger Melko, Geoffrey C Fox, Maximilian Swiatlowski, Wojciech Fedorko (2024)

Particle collisions at accelerators such as the Large Hadron Collider, recorded and analyzed by experiments such as ATLAS and CMS, enable exquisite measurements of the Standard Model and searches for new phenomena. Simulations of collision events at these detectors have played a pivotal role in shaping the design of future experiments and analyzing ongoing ones. However, the quest for accuracy in Large Hadron Collider (LHC) collisions comes at an imposing computational cost, with projections estimating the need for millions of CPU-years annually during the High Luminosity LHC (HL-LHC) run. Simulating a single LHC event with Geant4 currently devours around 1000 CPU seconds, with simulations of the calorimeter subdetectors in particular imposing substantial computational demands. To address this challenge, we propose a conditioned quantum-assisted deep generative model. Our model integrates a conditioned variational autoencoder (VAE) on the exterior with a conditioned Restricted Boltzmann Machine (RBM) in the latent space, providing enhanced expressiveness compared to conventional VAEs. The RBM nodes and connections are meticulously engineered to enable the use of qubits and couplers on D-Wave's Pegasus-structured \textit{Advantage} quantum annealer (QA) for sampling. We introduce a novel method for conditioning the quantum-assisted RBM using flux biases. We further propose a novel adaptive mapping to estimate the effective inverse temperature in quantum annealers. The effectiveness of our framework is illustrated using Dataset 2 of the CaloChallenge.

JQTM, James A. Glazier (2023)

Generative models rely on the idea that data can be represented in terms of latent variables which are uncorrelated by definition. Lack of correlation among the latent variable support is important because it suggests that the latent-space manifold is simpler to understand and manipulate than the real-space representation. Many types of generative model are used in deep learning, e.g., variational autoencoders (VAEs) and generative adversarial networks (GANs). Based on the idea that the latent space behaves like a vector space Radford et al. (2015), we ask whether we can expand the latent space representation of our data elements in terms of an orthonormal basis set. Here we propose a method to build a set of linearly independent vectors in the latent space of a trained GAN, which we call quasi-eigenvectors. These quasi-eigenvectors have two key properties: i) They span the latent space, ii) A set of these quasi-eigenvectors map to each of the labeled features one-to-one. We show that in the case of the MNIST image data set, while the number of dimensions in latent space is large by design, 98% of the data in real space map to a sub-domain of latent space of dimensionality equal to the number of labels. We then show how the quasi-eigenvectors can be used for Latent Spectral Decomposition (LSD). We apply LSD to denoise MNIST images. Finally, using the quasi-eigenvectors, we construct rotation matrices in latent space which map to feature transformations in real space. Overall, from quasi-eigenvectors we gain insight regarding the latent space topology.

JQTM, Denis Boyer (2023)

We explore the effects of stochastic resetting to random positions of a Brownian particle on first passage times and Shannon’s entropy. We explore the different entropy regimes, namely, the externally-driven, the zero-entropy and the Maxwell demon regimes. We show that the mean first passage time (MPFT) minimum can be found in any of these regimes. We provide a novel analytical method to compute the MFPT and the mean first passage number of resets (MFPNR) in the case where the Brownian particle resets to random positions sampled from a set of distributions known a priori. We also calculate the mean first passage resetting entropy (MFPRE), defined as the mean entropy change due to resetting events until the first passage process. We show the interplay between the resetting position distribution’s second moment and the reset rate, and the effect it has on the MFPT and MFPRE. We further propose a mechanism whereby the entropy per reset can be either in the Maxwell demon or the externally driven regime, yet the overall mean first passage resetting entropy corresponds to the zero-entropy regime. Additionally, we find an overlap between the dynamic phase space and the entropy phase space. We use this method in a generalized version of the Evans–Majumdar model by assuming the reset position is random and sampled from a Gaussian distribution. We then consider the toggling reset whereby the Brownian particle resets to a random position sampled from a distribution dependent on the reset parity. All our results are compared to and in agreement with numerical simulations.

JQTM, Carlos Rodriguez, Yosdel Plasencia Montesinos, Gerardo G Naumis (2020)

Spin-crossover has a wide range of applications from memory devices to sensors. This has to do mainly with the nature of the transition, which may be abrupt, gradual or incomplete and may also present hysteresis. This transition alters the properties of a given sample, such as magnetic moment, color and electric resistance to name some. Yet, a thorough understanding of the phenomenon is still lacking. In this work a simple model is provided to mimic some of the properties known to occur in spin-crossover. A detailed study of the model parameters is presented using a mean field approach and exhaustive Monte Carlo simulations. A good agreement is found between the analytical results and the simulations for certain regions in the parameter-space. This mean field approach breaks down in parameter regions where the correlations and cooperativity may no longer be averaged over.