Related papers: Discovering Factorization Surface of Quantum Spin …
I first give an overview of the thesis and Matrix Product States (MPS) representation of quantum spin chains with an improvement on the conventional notation. The rest of this thesis is divided into two parts. The first part is devoted to…
We theoretically investigate parameter quantum estimation in quantum chaotic systems. Our analysis is based on an effective description of non-integrable quantum systems in terms of a random matrix Hamiltonian. Based on this approach we…
Factorization Machines (FMs) are a supervised learning approach that enhances the linear regression model by incorporating the second-order feature interactions. Despite effectiveness, FM can be hindered by its modelling of all feature…
Quantum state tomography (QST) is essential for validating quantum devices but suffers from exponential scaling in system size. Neural-network quantum states, such as Restricted Boltzmann Machines (RBMs), can efficiently parameterize…
As perhaps the most studied paradigm for a quantum phase transition, the periodic quantum Ising chain is exactly solvable via the Jordan-Wigner transformation followed by a Fourier transform that diagonalizes the model in the momentum space…
This paper further develops the Method of Matched Sections (MMS), a robust numerical framework for the solution of boundary value problems governed by partial differential equations. It demonstrates its unique applicability to the…
Machine-learning-based variational Monte Carlo simulations are a promising approach for targeting quantum many-body ground states, especially in two dimensions and in cases where the ground state is known to have a non-trivial sign…
We detect the quantum phase transition of a quantum many-body system by mapping the observed results of the quantum state onto a neural network. In the present study, we utilized the simplest case of a quantum many-body system, namely a…
High-order parametric models that include terms for feature interactions are applied to various data mining tasks, where ground truth depends on interactions of features. However, with sparse data, the high- dimensional parameters for…
Learning the structure of the entanglement Hamiltonian (EH) is central to characterizing quantum many-body states in analog quantum simulation. We describe a protocol where spatial deformations of the many-body Hamiltonian, physically…
Quantum phase transitions in many-body systems are fundamentally characterized by complex correlation structures, which pose computational challenges for conventional methods in large systems. To address this, we propose a hybrid…
We study the approximability of computing the partition functions of two-state spin systems. The problem is parameterized by a $2\times 2$ symmetric matrix. Previous results on this problem were restricted either to the case where the…
Inspired by the close relationship between Kolmogorov complexity and unsupervised machine learning, we explore quantum circuit complexity, an important concept in quantum computation and quantum information science, as a pivot to understand…
We apply the generalized Wigner function formalism to detect and characterize a range of quantum phase transitions in several cyclic, finite-length, spin-$\frac{1}{2}$ one-dimensional spin-chain models, viz., the Ising and anisotropic $XY$…
Phase transition in quantum many-body systems inevitably causes changes in certain physical properties which then serve as potential indicators of critical phenomena. Besides the traditional order parameters, characterization of quantum…
Systematic use of the infinite-dimensional spin representation simplifies and rigorizes several questions in Quantum Field Theory. This representation permutes ``Gaussian'' elements in the fermion Fock space, and is necessarily projective:…
Field-aware Factorization Machines (FFMs) have emerged as a powerful model for click-through rate prediction, particularly excelling in capturing complex feature interactions. In this work, we present an in-depth analysis of our in-house,…
Data representation in quantum state space offers an alternative function space for machine learning tasks. However, benchmarking these algorithms at a practical scale has been limited by ineffective simulation methods. We develop a quantum…
We present an efficient machine learning framework for detection and classification of nanoparticles on surfaces that are detected in the far-field with Coherent Fourier Scatterometry (CFS). We study silicon wafers contaminated with…
Ground-state fidelity (GSF) and quantum renormalization group theory (QRG) have proven useful tools in the study of quantum critical systems. Here we lay out a general, unified formalism of GSF and QRG; specifically, we propose a method to…