Related papers: Rank penalized estimation of a quantum system
Matrices with low-rank structure are ubiquitous in scientific computing. Choosing an appropriate rank is a key step in many computational algorithms that exploit low-rank structure. However, estimating the rank has been done largely in an…
The reduced density matrix (RDM) is crucial in quantum many-body systems for understanding physical properties, including all local physical quantity information. This study aims to minimize various error constraints that causes challenges…
In this paper, we introduce a novel and robust approach to Quantized Matrix Completion (QMC). First, we propose a rank minimization problem with constraints induced by quantization bounds. Next, we form an unconstrained optimization problem…
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…
The optimal estimation of a quantum mechanical 2-state system (qubit) - with N identically prepared qubits available - is obtained by measuring all qubits simultaneously in an entangled basis. We report the experimental estimation of qubits…
Many results have been proved for various nuclear norm penalized estimators of the uniform sampling matrix completion problem. However, most of these estimators are not robust: in most of the cases the quadratic loss function and its…
The paper proposes a method for constructing a sparse estimator for the inverse covariance (concentration) matrix in high-dimensional settings. The estimator uses a penalized normal likelihood approach and forces sparsity by using a…
In supervised learning using kernel methods, we often encounter a large-scale finite-sum minimization over a reproducing kernel Hilbert space (RKHS). Large-scale finite-sum problems can be solved using efficient variants of Newton method,…
In the present paper, we consider the problem of matrix completion with noise. Unlike previous works, we consider quite general sampling distribution and we do not need to know or to estimate the variance of the noise. Two new nuclear-norm…
We introduce a rank-based bent linear regression with an unknown change point. Using a linear reparameterization technique, we propose a rank-based estimate that can make simultaneous inference on all model parameters, including the…
We propose an efficient quantum state tomography method inspired by compressed sensing and threshold quantum state tomography that can drastically reduce the number of measurement settings to reconstruct the density matrix of an $N$-qudit…
This work introduces a post-training quantization (PTQ) method for dense neural networks via a novel ADAROUND-based QUBO formulation. Using the Frobenius distance between the theoretical output and the dequantized output (before the…
Computational efficient evaluation of penalized estimators of multivariate exponential family distributions is sought. These distributions encompass among others Markov random fields with variates of mixed type (e.g. binary and continuous)…
New algorithm for quantum state estimation based on the maximum likelihood estimation is proposed. Existing techniques for state reconstruction based on the inversion of measured data are shown to be overestimated since they do not…
A common data analysis task is the reduced-rank regression problem: $$\min_{\textrm{rank-}k \ X} \|AX-B\|,$$ where $A \in \mathbb{R}^{n \times c}$ and $B \in \mathbb{R}^{n \times d}$ are given large matrices and $\|\cdot\|$ is some norm.…
Bayesian inference is a widely used technique for real-time characterization of quantum systems. It excels in experimental characterization in the low data regime, and when the measurements have degrees of freedom. A decisive factor for its…
The problem of recovering a matrix of low rank from an incomplete and possibly noisy set of linear measurements arises in a number of areas. In order to derive rigorous recovery results, the measurement map is usually modeled…
In the framework of noisy quantum homodyne tomography with efficiency parameter $0 < \eta \leq 1$, we propose two estimators of a quantum state whose density matrix elements $\rho_{m,n}$ decrease like $e^{-B(m+n)^{r/ 2}}$, for fixed known…
We present an algebraic algorithm for quantum state tomography that leverages measurements of certain observables to estimate structured entries of the underlying density matrix. Under low-rank assumptions, the remaining entries can be…
Inference based on the penalized density ratio model is proposed and studied. The model under consideration is specified by assuming that the log--likelihood function of two unknown densities is of some parametric form. The model has been…