Related papers: Deep Quantum Geometry of Matrices
Supersymmetric quantum gauge theories are important mathematical tools in high energy physics. As an example, supersymmetric matrix models can be used as a holographic description of quantum black holes. The wave function of such…
We apply the variational Monte Carlo method based on neural network quantum states, using a neural autoregressive flow architecture as our ansatz, to determine the ground state wave function of the bosonic SU($N$) Yang-Mills-type two-matrix…
Variational Monte Carlo calculations have recently reached state-of-the-art accuracy in the approximation of ground state properties of quantum many-body systems. Making use of flexible neural quantum states and automatic differentiation…
Matrix quantum mechanics plays various important roles in theoretical physics, such as a holographic description of quantum black holes. Understanding quantum black holes and the role of entanglement in a holographic setup is of paramount…
We propose an efficient numerical method, which combines the advantages of recently developed tensor-network based methods and standard trial wave functions, to study the ground state properties of quantum many-body systems. In this…
Variational quantum calculations have borrowed many tools and algorithms from the machine learning community in the recent years. Leveraging great expressive power and efficient gradient-based optimization, researchers have shown that trial…
Recently, the use of neural quantum states for describing the ground state of many- and few-body problems has been gaining popularity because of their high expressivity and ability to handle intractably large Hilbert spaces. In particular,…
We develop a systematic approach to determine and measure numerically the geometry of generic quantum or "fuzzy" geometries realized by a set of finite-dimensional hermitian matrices. The method is designed to recover the semi-classical…
This Dissertation presents results of a thorough study of ultracold bosonic and fermionic gases in three-dimensional and quasi-one-dimensional systems. Although the analyses are carried out within various theoretical frameworks…
These lecture notes introduce quantum spin systems and several computational methods for studying their ground-state and finite-temperature properties. Symmetry-breaking and critical phenomena are first discussed in the simpler setting of…
Quantum Monte Carlo (QMC) methods can very accurately compute ground state properties of quantum systems. We applied these methods to a system of boson hard spheres to get exact, infinite system size results for the ground state at several…
We propose a new quantum Monte Carlo algorithm to compute fermion ground-state properties. The ground state is projected from an initial wavefunction by a branching random walk in an over-complete basis space of Slater determinants. By…
In this study we present an optimization method based on the quantum Monte Carlo diagonalization for many-fermion systems. Using the Hubbard-Stratonovich transformation, employed to decompose the interactions in terms of auxiliary fields,…
Recent years have witnessed a surge of experimental and theoretical interest in controlling the properties of matter, such as its chemical reactivity, by confining it in optical cavities, where the enhancement of the light-matter coupling…
Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. We present an extension to the variational quantum eigensolver that approximates the…
Neural-network quantum states (NQS) offer a versatile and expressive alternative to traditional variational ans\"atze for simulating physical systems. Energy-based frameworks, like Hopfield networks and Restricted Boltzmann Machines,…
The conventional tensor-network states employ real-space product states as reference wave functions. Here, we propose a many-variable variational Monte Carlo (mVMC) method combined with tensor networks by taking advantages of both to study…
Artificial neural networks have been successfully incorporated into variational Monte Carlo method (VMC) to study quantum many-body systems. However, there have been few systematic studies of exploring quantum many-body physics using deep…
We develop a Monte Carlo wave function algorithm for the quantum linear Boltzmann equation, a Markovian master equation describing the quantum motion of a test particle interacting with the particles of an environmental background gas. The…
Artificial neural networks have been recently introduced as a general ansatz to compactly represent many- body wave functions. In conjunction with Variational Monte Carlo, this ansatz has been applied to find Hamil- tonian ground states and…