A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Quantum Process Tomography (QPT) methods aim at identifying, i.e. estimating, a given quantum process. QPT is a major quantum information processing tool, since it especially allows one to characterize the actual behavior of quantum gates, which are the building blocks of quantum computers. However, usual QPT procedure…
The problem of using observed correlations to infer causal relations is relevant to a wide variety of scientific disciplines. Yet given correlations between just two classical variables, it is impossible to determine whether they arose from a causal influence of one on the other or a common cause influencing both, unle…
We study the projected gradient descent method on low-rank matrix problems with a strongly convex objective. We use the Burer-Monteiro factorization approach to implicitly enforce low-rankness; such factorization introduces non-convexity in the objective. We focus on constraint sets that include both positive semi-defi…
Adversarial learning is one of the most successful approaches to modelling high-dimensional probability distributions from data. The quantum computing community has recently begun to generalize this idea and to look for potential applications. In this work, we derive an adversarial algorithm for the problem of approxim…
We consider 1-qubit mixed quantum state estimation by adaptively updating measurements according to previously obtained outcomes and measurement settings. Updates are determined by the average-variance-optimality (A-optimality) criterion, known in the classical theory of experimental design and applied here to quantum …
Global stability bounds for matrix frames in phase retrieval problems.
problem Phase retrieval for matrix frames in various applications.
method Computable global stability bounds for the quasi-linear analysis map β, using Whitney stratification of positive semidefinite matrices of low rank.
result Novel conditions for a frame to be generalized phase retrievable.
The density matrices are positively semi-definite Hermitian matrices of unit trace that describe the state of a quantum system. The goal of the paper is to develop minimax lower bounds on error rates of estimation of low rank density matrices in trace regression models used in quantum state tomography (in particular, i…
Quantum machine learning has received significant attention in recent years, and promising progress has been made in the development of quantum algorithms to speed up traditional machine learning tasks. In this work, however, we focus on investigating the information-theoretic upper bounds of sample complexity - how ma…
We study the problem of reconstructing an unknown matrix M of rank r and dimension d using O(rd poly log d) Pauli measurements. This has applications in quantum state tomography, and is a non-commutative analogue of a well-known problem in compressed sensing: recovering a sparse vector from a few of its Fourier coeffic…
Most learning methods with rank or sparsity constraints use convex relaxations, which lead to optimization with the nuclear norm or the ℓ1-norm. However, several important learning applications cannot benefit from this approach as they feature these convex norms as constraints in addition to the non-convex rank a…
Studying general quantum many-body systems is one of the major challenges in modern physics because it requires an amount of computational resources that scales exponentially with the size of the system.Simulating the evolution of a state, or even storing its description, rapidly becomes intractable for exact classical…
Consider a compact Riemannian manifold of dimension ≥3 with strictly convex boundary, such that the manifold admits a strictly convex function. We show that the attenuated ray transform in the presence of an arbitrary connection and Higgs field is injective modulo the natural obstruction for functions and one-for…
Deep learning is having a profound impact in many fields, especially those that involve some form of image processing. Deep neural networks excel in turning an input image into a set of high-level features. On the other hand, tomography deals with the inverse problem of recreating an image from a number of projections.…
These are lecture notes for the course "Analysis and X-ray tomography". The course is a broad overview of various tools in analysis that can be used to study X-ray tomography. The focus is on tools and ideas, not so much on technical details and minimal assumptions. Only very basic functional analysis is assumed as bac…
Deep kernel learning refers to a Gaussian process that incorporates neural networks to improve the modelling of complex functions. We present a method that makes this approach feasible for problems where the data consists of line integral measurements of the target function. The performance is illustrated on computed t…
Deep network improves electrical tomography across multiple frequencies.
problem Nonlinear multi-frequency electrical impedance tomography (mfEIT) for tissue conductivity estimation.
method Integrates graph neural networks (GNNs) into the iterative Proximal Regularized Gauss Newton (PRGN) framework to reconstruct tissue concentrations accurately.
result Accurate reconstruction of overlapping tissue fraction concentrations across multiple frequencies.
This paper proposes a brain-inspired approach to quantum machine learning with the goal of circumventing many of the complications of other approaches. The fact that quantum processes are unitary presents both opportunities and challenges. A principal opportunity is that a large number of computations can be carried ou…
Quantum systems with scrambling improve temporal information processing, but scaling requires exponential overhead.
problem Scalability and memory retention of quantum reservoirs in temporal information processing.
method Examined a quantum reservoir processing framework with scrambling reservoirs modeled by high-order unitary designs, analyzed in noiseless and noisy settings.
result Memory retention improves exponentially with reservoir size but worsens with reservoir iterations, requiring exponential shot overhead for scaling.