相关论文: Projected Least-Squares Quantum Process Tomography

We propose a randomized first order optimization algorithm Gradient Projection Iterative Sketch (GPIS) and an accelerated variant for efficiently solving large scale constrained Least Squares (LS). We provide theoretical convergence…

Despite rapidly growing interest in harnessing machine learning in the study of quantum many-body systems, training neural networks to identify quantum phases is a nontrivial challenge. The key challenge is in efficiently extracting…

Linear regression is a widely used technique to fit linear models and finds widespread applications across different areas such as machine learning and statistics. In most real-world scenarios, however, linear regression problems are often…

Quantum state tomography (QST) is one of the fundamental problems in quantum information. Among various metrics, sample complexity is widely used to evaluate QST algorithms. While multi-copy measurements are known to achieve optimal sample…

We introduce maximum likelihood fragment tomography (MLFT) as an improved circuit cutting technique for running clustered quantum circuits on quantum devices with a limited number of qubits. In addition to minimizing the classical computing…

We study the functional linear regression model with a scalar response and a Hilbert space-valued predictor, a canonical example of an ill-posed inverse problem. We show that the functional partial least squares (PLS) estimator attains…

The partial least squares procedure was originally developed to estimate the slope parameter in multivariate parametric models. More recently it has gained popularity in the functional data literature. There, the partial least squares…

Quantum phase estimation (QPE) is one of the most important subroutines in quantum computing. In general applications, current QPE algorithms either suffer an exponential time overload or require a set of - notoriously quite fragile - GHZ…

A novel square equal-area map projection is proposed. The projection combines closed-form forward and inverse solutions with relatively low angular distortion and minimal cusps, a combination of properties not manifested by any previously…

In this paper, the problem of robust estimation and validation of location-scale families is revisited. The proposed methods exploit the joint asymptotic normality of sample quantiles (of i.i.d random variables) to construct the ordinary…

In this paper, we introduce principal asymmetric least squares (PALS) as a unified framework for linear and nonlinear sufficient dimension reduction. Classical methods such as sliced inverse regression (Li, 1991) and principal support…

Unlike the classical smoothing theory, it is well known that quantum smoothers are, in general, not well--defined by the quantum conditional expectation. The purpose of this paper is to propose a new quantum smoothing theory based on the…

This paper presents a new method for estimating high dimensional covariance matrices. The method, permuted rank-penalized least-squares (PRLS), is based on a Kronecker product series expansion of the true covariance matrix. Assuming an…

We develop a unified geometric framework for quantum circuit compilation based on quantized orbifold phases and their diagrammatic semantics. Physical qubit platforms impose heterogeneous phase resolutions, anisotropic Bloch-ball…

This work investigates measurement strategies for link parameter estimation in Quantum Network Tomography (QNT), where network links are modeled as depolarizing quantum channels distributing Werner states. Three distinct measurement schemes…

Presented is a new algorithm for estimating the frequency of a single-tone noisy signal using linear least squares (LLS). Frequency estimation is a nonlinear problem, and typically, methods such as Nonlinear Least Squares (NLS) (batch) or a…

Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required…

Constrained least-squares regression problems, such as the Nonnegative Least Squares (NNLS) problem, where the variables are restricted to take only nonnegative values, often arise in applications. Motivated by the recent development of the…

Bayesian optimisation is an adaptive sampling strategy for constructing a Gaussian process surrogate to efficiently search for the global minimum of a black-box computational model. Gaussian processes have limited applicability in…

This work presents a differentiable geometric parameterization of quantum channels in Kraus representation, which can be efficiently probed to find an unknown quantum channel. We explore its feasibility in finding the quasi inverse…