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Response theory has a successful history of connecting experimental observations with theoretical predictions. Of particular interest is the optical response of matter, from which spectroscopy experiments can be modelled. However, the…
Nonlinear function estimation is core to modern machine learning applications. In this paper, to perform nonlinear function estimation, we reduce a nonlinear inverse problem to a linear one using a polynomial kernel expansion. These kernels…
Iterative multiscale methods for electronic structure calculations offer several advantages for large-scale problems. Here we examine a nonlinear full approximation scheme (FAS) multigrid method for solving fixed potential and…
Randomized measurements are increasingly appreciated as powerful tools to estimate properties of quantum systems, e.g., in the characterization of hybrid classical-quantum computation. On many platforms they constitute natively accessible…
Classical shadows are an efficient method for constructing an approximate classical description of a quantum state using very few measurements. In the paper we propose to enhance classical shadow methods using bootstrap resampling methods.…
Advances in quantum technologies are accelerating the demand for optical quantum state sensors that combine high precision, versatility, and scalability within a unified hardware platform. Quantum reservoir computing offers a powerful route…
This paper contributes improvements on both the effectiveness and efficiency of Matrix Factorization (MF) methods for implicit feedback. We highlight two critical issues of existing works. First, due to the large space of unobserved…
Nonlinear quantum photonics serves as a cornerstone in photonic quantum technologies, such as universal quantum computing and quantum communications. The emergence of integrated photonics platform not only offers the advantage of…
We extend correlated sampling from classical auxiliary-field quantum Monte Carlo to the quantum-classical (QC-AFQMC) framework, enabling accurate nuclear force computations crucial for geometry optimization and reaction dynamics. Stochastic…
Quantum computing is a promising technology that accelerates the partial differential equations solver for practical problems. The reconstruction of solutions (i.e., the readout of quantum states) remains a crucial problem, although…
We describe an exact, flexible, and computationally efficient algorithm for a joint estimation of the large-scale structure and its power-spectrum, building on a Gibbs sampling framework and present its implementation ARES (Algorithm for…
Conventional LIDAR systems require hundreds or thousands of photon detections to form accurate depth and reflectivity images. Recent photon-efficient computational imaging methods are remarkably effective with only 1.0 to 3.0 detected…
Incorporating nonlinearity into quantum machine learning is essential for learning a complicated input-output mapping. We here propose quantum algorithms for nonlinear regression, where nonlinearity is introduced with feature maps when…
Full quantum tomography of high-dimensional quantum systems is experimentally infeasible due to the exponential scaling of the number of required measurements on the number of qubits in the system. However, several ideas were proposed…
Auxiliary particle filters (APFs) are a class of sequential Monte Carlo (SMC) methods for Bayesian inference in state-space models. In their original derivation, APFs operate in an extended state space using an auxiliary variable to improve…
Feature selection is a critical task in machine learning and statistics. However, existing feature selection methods either (i) rely on parametric methods such as linear or generalized linear models, (ii) lack theoretical false discovery…
A scalable Bayesian machine learning framework is introduced for estimating scalar properties of an unknown quantum state from measurement data, which bypasses full density matrix reconstruction. This work is the first to integrate the…
Deep neural networks have achieved remarkable performance in various applications but are extremely vulnerable to adversarial perturbation. The most representative and promising methods that can enhance model robustness, such as adversarial…
Interfacing quantum and classical processors is an important subroutine in full-stack quantum algorithms. The so-called "classical shadow" method efficiently extracts essential classical information from quantum states, enabling the…
Quantum state tomography is a fundamental task in quantum information science, enabling detailed characterization of correlations, entanglement, and electronic structure in quantum systems. However, its exponential measurement and…