Related papers: Rank penalized estimation of a quantum system
Graded posets frequently arise throughout combinatorics, where it is natural to try to count the number of elements of a fixed rank. These counting problems are often $\#\textbf{P}$-complete, so we consider approximation algorithms for…
This paper concerns the problem of matrix completion, which is to estimate a matrix from observations in a small subset of indices. We propose a calibrated spectrum elastic net method with a sum of the nuclear and Frobenius penalties and…
When an informationally complete measurement is not available, the reconstruction of the density operator that describes the state of a quantum system can be accomplish, in a reliable way, by adopting the maximum entropy principle (MaxEnt…
We develop a penalized likelihood estimation framework to estimate the structure of Gaussian Bayesian networks from observational data. In contrast to recent methods which accelerate the learning problem by restricting the search space, our…
We present a method to reduce the variance of stochastic trace estimators used in quantum typicality (QT) methods via a randomized low-rank approximation of the finite-temperature density matrix $e^{-\beta H}$. The trace can be evaluated…
Reduced-rank regression recognises the possibility of a rank-deficient matrix of coefficients. We propose a novel Bayesian model for estimating the rank of the coefficient matrix, which obviates the need for post-processing steps and allows…
We present a general method to compute canonical averages for physical models sampled via quantum or classical quadratic unconstrained binary optimization (QUBO). First, we introduce a histogram reweighting scheme applicable to QUBO-based…
We present in this paper a novel approach for training deterministic auto-encoders. We show that by adding a well chosen penalty term to the classical reconstruction cost function, we can achieve results that equal or surpass those attained…
Quantum state tomography (QST) allows for the reconstruction of quantum states through measurements and some inference technique under the assumption of repeated state preparations. Bayesian inference provides a promising platform to…
This investigation continues a program aiming at obtaining effective quantum models to describe measurement statistics. In [Stark, arXiv:1209.5737 (2012)], we have described how the Gram matrix associated to the prepared states and the…
This paper presents a hybrid classical-quantum program for density estimation and supervised classification. The program is implemented as a quantum circuit in a high-dimensional quantum computer simulator. We show that the proposed quantum…
This article proposes a novel density estimation based algorithm for carrying out supervised machine learning. The proposed algorithm features O(n) time complexity for generating a classifier, where n is the number of sampling instances in…
We propose a general error analysis related to the low-rank approximation of a given real matrix in both the spectral and Frobenius norms. First, we derive deterministic error bounds that hold with some minimal assumptions. Second, we…
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…
Ranking, and inferences based on ranking of a set of entities, are important problems in numerous contexts. This is especially true in small area statistics where there may be only a limited amount of directly observed data from each entity…
Impressive progress has been made in the past decade in the study of technological applications of varied types of quantum systems. With industry giants like IBM laying down their roadmap for scalable quantum devices with more than…
We consider the problem of estimating a rank-one matrix in Gaussian noise under a probabilistic model for the left and right factors of the matrix. The probabilistic model can impose constraints on the factors including sparsity and…
We consider the multivariate response regression problem with a regression coefficient matrix of low, unknown rank. In this setting, we analyze a new criterion for selecting the optimal reduced rank. This criterion differs notably from the…
We propose a versatile and efficient algorithmic framework for optimizing fermion-to-qubit mappings by generalizing the idea of randomized block coordinate descent. Our greedy approach, termed Randomized Subsystem Descent, iteratively…
Affine rank minimization algorithms typically rely on calculating the gradient of a data error followed by a singular value decomposition at every iteration. Because these two steps are expensive, heuristic approximations are often used to…