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.
Sketch Tomography improves quantum state estimation accuracy.
Study online learning of quantum processes, showing feasibility for certain types.
A new method speeds up quantum state estimation.
The thesis optimizes quantum state exploration using bandit algorithms.
New quantum state reconstruction method accelerates convergence.
Quantum states can be learned efficiently using gentle measurements.
Protocol learns pure quantum states with minimal disturbance.
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…
Method learns topological states from randomized measurements.
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…
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…
This paper compares classical shadows and direct quantum measurement for efficient information extraction.
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.
Unified approach for learning quantum operations from measurements.
New quantum states capture more information, enabling advanced processing tasks.
Study on learning quantum dynamics without direct interaction.
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…
New method uses single quantum state for machine learning tasks, improving accuracy.
Most learning methods with rank or sparsity constraints use convex relaxations, which lead to optimization with the nuclear norm or the -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 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…
Paper generalizes VB-FTRL for online learning of quantum states with logarithmic loss.
Study travel time tomography for transversely isotropic media using modified pseudodifferential calculus.
Summary of tensor tomography proofs on manifolds with boundaries.
Paper addresses travel time tomography stability and statistical inversion.
Improved Bandit PCA with optimal regret bound.
Study uses machine learning to solve photoacoustic tomography's inverse problem.
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 network improves electrical tomography across multiple frequencies.
Over the past few years, trace regression models have received considerable attention in the context of matrix completion, quantum state tomography, and compressed sensing. Estimation of the underlying matrix from regularization-based approaches promoting low-rankedness, notably nuclear norm regularization, have enjoye…
Improved computed tomography reconstruction with deep learning and deep image prior.
Density matrices are positively semi-definite Hermitian matrices with unit trace that describe the states of quantum systems. Many quantum systems of physical interest can be represented as high-dimensional low rank density matrices. A popular problem in {\it quantum state tomography} (QST) is to estimate the unknown l…
We develop a 2D travel time tomography method which regularizes the inversion by modeling groups of slowness pixels from discrete slowness maps, called patches, as sparse linear combinations of atoms from a dictionary. We propose to use dictionary learning during the inversion to adapt dictionaries to specific slowness…
New method uses MRI data to improve PET tomography uncertainty quantification.
We present theoretical results on the convergence of \emph{non-convex} accelerated gradient descent in matrix factorization models with -norm loss. The purpose of this work is to study the effects of acceleration in non-convex settings, where provable convergence with acceleration should not be considered a \em…
Study inverse problems for twisted geodesic flows on manifolds.
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…
We propose a globally convergent alternating minimization (AM) algorithm for image reconstruction in transmission tomography, which extends automatic relevance determination (ARD) to Poisson noise models with Beer's law. The algorithm promotes solutions that are sparse in the pixel/voxel-differences domain by introduci…
TomOpt optimizes muon detector designs using differentiable programming.
Dissertation tackles geodesic ray transform on Riemannian manifolds.
The distribution of absorbed dose in radionuclide therapy with Lu can be approximated by convolving an image of the time-integrated activity distribution with a dose voxel kernel representing different tissue types. This fast but inaccurate approximation is unsuitable for personalised dosimetry because it negle…
Extends magnetic flow theory results to higher dimensions.
CRC method provides tighter uncertainty intervals for CT images.
Paper develops a new method for solving IBVPs on star-shaped domains.
We consider the problem of recovering low-rank matrices from random rank-one measurements, which spans numerous applications including covariance sketching, phase retrieval, quantum state tomography, and learning shallow polynomial neural networks, among others. Our approach is to directly estimate the low-rank factor …