Related papers: Using non-convex optimization in quantum process t…
Existing quantum state tomography methods are limited in scalability due to their high computation and memory demands, making them impractical for recovery of large quantum states. In this work, we address these limitations by reformulating…
This work proposes a rapid algorithm, BM-Global, for nuclear-norm-regularized convex and low-rank matrix optimization problems. BM-Global efficiently decreases the objective value via low-cost steps leveraging the nonconvex but smooth…
Rank minimization is of interest in machine learning applications such as recommender systems and robust principal component analysis. Minimizing the convex relaxation to the rank minimization problem, the nuclear norm, is an effective…
A fundamental model of quantum computation is the programmable quantum gate array. This is a quantum processor that is fed by a program state that induces a corresponding quantum operation on input states. While being programmable, any…
Constrained optimization plays a crucial role in the fields of quantum physics and quantum information science and becomes especially challenging for high-dimensional complex structure problems. One specific issue is that of quantum process…
Parametrized quantum optical circuits are a class of quantum circuits in which the carriers of quantum information are photons and the gates are optical transformations. Classically optimizing these circuits is challenging due to the…
In this paper, we are interested in finding the global minimizer of a nonsmooth nonconvex unconstrained optimization problem. By combining the discrete consensus-based optimization (CBO) algorithm and the gradient descent method, we develop…
This work considers two popular minimization problems: (i) the minimization of a general convex function $f(\mathbf{X})$ with the domain being positive semi-definite matrices; (ii) the minimization of a general convex function…
The majorization-minimization (MM) principle is an extremely general framework for deriving optimization algorithms. It includes the expectation-maximization (EM) algorithm, proximal gradient algorithm, concave-convex procedure, quadratic…
We propose a new quantum state reconstruction method that combines ideas from compressed sensing, non-convex optimization, and acceleration methods. The algorithm, called Momentum-Inspired Factored Gradient Descent (\texttt{MiFGD}), extends…
We present a technique for performing quantum detector tomography (QDT) of phase insensitive quantum detectors, a category under which many detectors of interest fall under, using gradient descent-based optimization to learn the positive…
We present theoretical results on the convergence of \emph{non-convex} accelerated gradient descent in matrix factorization models with $\ell_2$-norm loss. The purpose of this work is to study the effects of acceleration in non-convex…
We propose a simple, scalable, and fast gradient descent algorithm to optimize a nonconvex objective for the rank minimization problem and a closely related family of semidefinite programs. With $O(r^3 \kappa^2 n \log n)$ random…
We study a family of (potentially non-convex) constrained optimization problems with convex composite structure. Through a novel analysis of non-smooth geometry, we show that proximal-type algorithms applied to exact penalty formulations of…
We present a quantum process-tomography protocol based on a low-degree ansatz for the quantum channel, i.e. when it can be expressed as a fixed-degree polynomial in terms of Pauli operators. We demonstrate how to perform tomography of such…
Semidefinite programming (SDP) with diagonal constraints arise in many optimization problems, such as Max-Cut, community detection and group synchronization. Although SDPs can be solved to arbitrary precision in polynomial time, generic…
We consider the rank minimization problem from quadratic measurements, i.e., recovering a rank $r$ matrix $X \in \mathbb{R}^{n \times r}$ from $m$ scalar measurements $y_i=a_i^{\top} XX^{\top} a_i,\;a_i\in \mathbb{R}^n,\;i=1,\ldots,m$. Such…
Optimization over low rank matrices has broad applications in machine learning. For large scale problems, an attractive heuristic is to factorize the low rank matrix to a product of two much smaller matrices. In this paper, we study the…
We introduce two quantum algorithms for solving structured prediction problems. We first show that a stochastic gradient descent that uses the quantum minimum finding algorithm and takes its probabilistic failure into account solves the…
Precise reconstruction of unknown quantum states from measurement data, a process commonly called quantum state tomography, is a crucial component in the development of quantum information processing technologies. Many different tomography…