Related papers: Agnostic Product Mixed State Tomography via Robust…

Matrix product operators allow efficient descriptions (or realizations) of states on a 1D lattice. We consider the task of learning a realization of minimal dimension from copies of an unknown state, such that the resulting operator is…

We study high-dimensional distribution learning in an agnostic setting where an adversary is allowed to arbitrarily corrupt an $\varepsilon$-fraction of the samples. Such questions have a rich history spanning statistics, machine learning…

Quantum tomography is a process of quantum state reconstruction using data from multiple measurements. An essential goal for a quantum tomography algorithm is to find measurements that will maximize the useful information about an unknown…

We discuss quantum state tomography via a stepwise reconstruction of the eigenstates of the mixed states produced in experiments. Our method is tailored to the experimentally relevant class of nearly pure states or simple mixed states,…

We study the task of agnostic tomography: given copies of an unknown $n$-qubit state $\rho$ which has fidelity $\tau$ with some state in a given class $C$, find a state which has fidelity $\ge \tau - \epsilon$ with $\rho$. We give a new…

Stochastic optimization is a widely used approach for optimization under uncertainty, where uncertain input parameters are modeled by random variables. Exact or approximation algorithms have been obtained for several fundamental problems in…

The theory of boosting provides a computational framework for aggregating approximate weak learning algorithms, which perform marginally better than a random predictor, into an accurate strong learner. In the realizable case, the success of…

Robust, accurate and efficient quantum tomography is key for future quantum technologies. Traditional methods are impractical for even medium sized systems and are not robust against noise and errors. Here we report on an experimental…

We use a meta-learning neural-network approach to analyse data from a measured quantum state. Once our neural network has been trained it can be used to efficiently sample measurements of the state in measurement bases not contained in the…

Shadow tomography for quantum states provides a sample efficient approach for predicting the properties of quantum systems when the properties are restricted to expectation values of $2$-outcome POVMs. However, these shadow tomography…

Machine learning techniques have led to broad adoption of a statistical model of computing. The statistical distributions natively available on quantum processors are a superset of those available classically. Harnessing this attribute has…

We study several questions in the reliable agnostic learning framework of Kalai et al. (2009), which captures learning tasks in which one type of error is costlier than others. A positive reliable classifier is one that makes no false…

This dissertation studies the statistics and modeling of a quantum system probed by a coherent laser field. We focus on an ensemble of qubits dispersively coupled to a traveling wave light field. The first research topic explores the…

We study distribution-free property testing and learning problems where the unknown probability distribution is a product distribution over $\mathbb{R}^d$. For many important classes of functions, such as intersections of halfspaces,…

Using quantum algorithms, we obtain, for accuracy $\epsilon>0$ and confidence $1-\delta,0<\delta<1,$ a new sample complexity upper bound of $O((\mbox{log}(\frac{1}{\delta}))/\epsilon)$ as $\epsilon,\delta\rightarrow 0$ for a general…

Quantum state tomography (QST) is plagued by the ``curse of dimensionality'' due to the exponentially-scaled complexity in measurement and data post-processing. Efficient QST schemes for large-scale mixed states are currently missing. In…

Quantum state preparation, a crucial subroutine in quantum computing, involves generating a target quantum state from initialized qubits. Arbitrary state preparation algorithms can be broadly categorized into arithmetic decomposition (AD)…

We consider a distributionally robust formulation of stochastic optimization problems arising in statistical learning, where robustness is with respect to uncertainty in the underlying data distribution. Our formulation builds on…

Quantum noise constitutes a fundamental obstacle to realizing practical quantum technologies. To address the pivotal challenge of identifying quantum systems least affected by noise, we introduce the purest quantum state identification,…

We investigate approximation guarantees provided by logistic regression for the fundamental problem of agnostic learning of homogeneous halfspaces. Previously, for a certain broad class of "well-behaved" distributions on the examples,…