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Principal Component Analysis (PCA) is a well-known technique used to decorrelate a set of vectors. It has been applied to explore the star formation history of galaxies or to determine distances of mass-lossing stars. Here we apply PCA to…

Quantum algorithms based on Quantum Signal Processing (QSP) offer the potential for speedups across a broad range of applications, with block encodings serving as the central input model. In this framework, non-unitary matrices are embedded…

Coupled partial differential equations (PDEs) are key tasks in modeling the complex dynamics of many physical processes. Recently, neural operators have shown the ability to solve PDEs by learning the integral kernel directly in…

Error correction allows a quantum computer to preserve states long beyond the decoherence time of its physical qubits. Key to any scheme of error correction is the decoding algorithm, which estimates the error state of qubits from the…

Quantum entanglement is a crucial resource for learning properties from nature, but a precise characterization of its advantage can be challenging. In this work, we consider learning algorithms without entanglement to be those that only…

Attention-based regression models are often trained by jointly optimizing Mean Squared Error (MSE) loss and Pearson correlation coefficient (PCC) loss, emphasizing the magnitude of errors and the order or shape of targets, respectively. A…

Protein-protein interactions (PPIs) are fundamental to numerous cellular processes, and their characterization is vital for understanding disease mechanisms and guiding drug discovery. While protein language models (PLMs) have demonstrated…

The first order behavior of multivariate heavy-tailed random vectors above large radial thresholds is ruled by a limit measure in a regular variation framework. For a high dimensional vector, a reasonable assumption is that the support of…

We provide an integration of the universal, perturbative explicitly correlated [2]$_\text{R12}$-correction in the context of the Variational Quantum Eigensolver (VQE). This approach is able to increase the accuracy of the underlying…

Searching for departures from general relativity (GR) in more than one post-Newtonian (PN) phasing coefficients, called a \emph{multi-parameter test}, is known to be ineffective given the sensitivity of the present generation of…

Codes based on sparse matrices have good performance and can be efficiently decoded by belief-propagation (BP). Decoding binary stabilizer codes needs a quaternary BP for (additive) codes over GF(4), which has a higher check-node complexity…

Quantum error correction is widely believed to be essential for large-scale quantum computation, but the required qubit overhead remains a central challenge. Quantum low-density parity-check codes can substantially reduce this overhead…

Quantum error correction/detection (QEC/QED) and dynamical decoupling (DD) are tools for protecting quantum information. A natural goal is to combine them to outperform either approach alone. Such a benefit is not automatic: physical DD can…

A large amount of recent research has the far-reaching goal of finding training methods for deep neural networks that can serve as alternatives to backpropagation (BP). A prominent example is predictive coding (PC), which is a…

The traditional limitations of neural networks in reliably generalizing beyond the convex hulls of their training data present a significant problem for computational physics, in which one often wishes to solve PDEs in regimes far beyond…

Decoders of quantum error correction (QEC) experiments make decisions based on detected errors and the expected rates of error events, which together comprise a detector error model. Here we show that the syndrome history of QEC experiments…

We take steps towards understanding the "posterior collapse (PC)" difficulty in variational autoencoders (VAEs),~i.e. a degenerate optimum in which the latent codes become independent of their corresponding inputs. We rely on calculus of…

Quantum error correction (QEC) is essential for operating quantum computers in the presence of noise. Here, we accurately decode arbitrary Calderbank-Shor-Steane (CSS) codes via the maximum satisfiability (MaxSAT) problem. We show how to…

Variational quantum eigensolvers (VQE) are among the most promising approaches for solving electronic structure problems on near-term quantum computers. A critical challenge for VQE in practice is that one needs to strike a balance between…

The robust PCA of covariance matrices plays an essential role when isolating key explanatory features. The currently available methods for performing such a low-rank plus sparse decomposition are matrix specific, meaning, those algorithms…