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In recent years, the use of information principles to understand quantum correlations has been very successful. Unfortunately, all principles considered so far have a bipartite formulation, but intrinsically multipartite principles, yet to…

Quantum spatial search has been widely studied with most of the study focusing on quantum walk algorithms. We show that quantum walk algorithms are extremely sensitive to systematic errors. We present a recursive algorithm which offers…

We study approximation properties of weighted $\mathrm{L}^2$-orthogonal projectors onto spaces of polynomials of bounded degree in the Euclidean unit ball, where the weight is of the reflection-invariant form $(1-\lVert x \rVert^2)^\alpha…

Stochastic gradient descent (SGD) is a popular stochastic optimization method in machine learning. Traditional parallel SGD algorithms, e.g., SimuParallel SGD, often require all nodes to have the same performance or to consume equal…

Non-orthogonal quantum states pose a fundamental challenge in quantum information processing, as they cannot be distinguished with absolute certainty. Conventionally, the focus has been on minimizing error probability in quantum state…

We analyze a new random algorithm for numerical integration of $d$-variate functions over $[0,1]^d$ from a weighted Sobolev space with dominating mixed smoothness $\alpha\ge 0$ and product weights $1\ge\gamma_1\ge\gamma_2\ge\cdots>0$, where…

We consider the problem of pricing discretely monitored Asian options over $T$ monitoring points where the underlying asset is modeled by a geometric Brownian motion. We provide two quantum algorithms with complexity poly-logarithmic in $T$…

We review the superspace technique to determine supersymmetric spacetimes in the framework of off-shell formulations for supergravity in diverse dimensions using the case of 3D N=2 supergravity theories as an illustrative example. This…

We consider the problem of approximating an unknown function $u\in L^2(D,\rho)$ from its evaluations at given sampling points $x^1,\dots,x^n\in D$, where $D\subset \mathbb{R}^d$ is a general domain and $\rho$ is a probability measure. The…

Self-testing is a phenomenon where the use of specific quantum states or measurements can be inferred solely from the correlations they generate. We introduce a universal method for conducting robustness analysis in the self-testing of…

Recently, the precise performance of the Generalized LASSO algorithm for recovering structured signals from compressed noisy measurements, obtained via i.i.d. Gaussian matrices, has been characterized. The analysis is based on a framework…

The resource theory of quantum superposition is an extension of the quantum coherent theory, in which linear independence relaxes the requirement of orthogonality. It can be used to quantify the nonclassical in superposition of finite…

Slater determinants have underpinned quantum chemistry for nearly a century, yet their full potential has remained challenging to exploit. In this work, we show that a variational wavefunction composed of a few hundred optimized…

We propose a new variational model in weighted Sobolev spaces with non-standard weights and applications to image processing. We show that these weights are, in general, not of Muckenhoupt type and therefore the classical analysis tools may…

The onset of quantum ergodicity is often quantified by the average ratio of consecutive level spacings. The reference values for ergodic quantum systems have been obtained numerically from the spectra of large but finite-dimensional random…

Quantum coherence is a critical resource for many operational tasks. Understanding how to quantify and manipulate it also promises to have applications for a diverse set of problems in theoretical physics. For certain applications, however,…

The ordered weighted $\ell_1$ norm (OWL) was recently proposed, with two different motivations: its good statistical properties as a sparsity promoting regularizer; the fact that it generalizes the so-called {\it octagonal shrinkage and…

We study the Gaussian sequence model, i.e. $X \sim N(\mathbf{\theta}, I_\infty)$, where $\mathbf{\theta} \in \Gamma \subset \ell_2$ is assumed to be convex and compact. We show that goodness-of-fit testing sample complexity is lower bounded…

We show a relation between quantum learning theory and algorithmic hardness. We use the existence of efficient, local learning algorithms for energy estimation -- such as the classical shadows algorithm -- to prove that finding near-ground…

This paper presents a pioneering exploration of the mechanisms underlying large foundation models' (LFMs) weights, aiming to simplify AI research. Through extensive observation and analysis on prevailing LFMs, we find that regardless of…