Various ensembles of quantum dots embedded onto a superconducting surface have been addressed within the recently derived generalized atomic limit model. We study how the model is able to capture the emerging phenomena such as Andreev bound states and quantum phase transitions. This is done through the methods of exact diagonaliza- tion with the Lanczos algorithm and variational Monte Carlo, where the wavefunction is approximated by the machine learning based approach of restricted Boltzmann machines, known as neural network quantum states. We demonstrate that these systems exhibit complex phase diagrams and a rich spectrum of bound states within the superconduct- ing gap. The advantages and limitations of both methods are analyzed providing an important foundation for future research.
Various ensembles of quantum dots embedded onto a superconducting surface have been addressed within the recently derived generalized atomic limit model. We study how the model is able to capture the emerging phenomena such as Andreev bound states and quantum phase transitions. This is done through the methods of exact diagonaliza- tion with the Lanczos algorithm and variational Monte Carlo, where the wavefunction is approximated by the machine learning based approach of restricted Boltzmann machines, known as neural network quantum states. We demonstrate that these systems exhibit complex phase diagrams and a rich spectrum of bound states within the superconduct- ing gap. The advantages and limitations of both methods are analyzed providing an important foundation for future research.
The Neural-Network Quantum States (NNQS) method is rapidly emerging as a powerful tool for investigating quantum many-body physics.By combining variational Monte Carlo techniques with neural network-based variational functions, this approach leverages the remarkable advancements in deep learning achieved in recent years.While substantial progress has been made in simulating magnetic systems on lattices, simple molecules, and even continuous systems, the ab initio simulation of complex strongly correlated electron systems continues to pose significant challenges.With the help of the generalized atomic limit (GAL) -a recently developed model describing a system of quantum dots coupled to a superconducting lead -we attempt to show the efficiency and accuracy of NNQS, mainly the Restricted Boltzmann Machine, by comparing the acquired results to other available methods such as exact diagonalization.The simultaneous study of the system's properties such as the energy spectrum and quantum phase transitions could bring advancements in electronics, sensors or the design of high-quality qubits used in quantum computers.
The Neural-Network Quantum States (NNQS) method is rapidly emerging as a powerful tool for investigating \nquantum many-body physics. By combining variational Monte Carlo techniques with neural network-based \nvariational functions, this approach leverages the remarkable advancements in deep learning achieved in \nrecent years. While substantial progress has been made in simulating magnetic systems on lattices, simple \nmolecules, and even continuous systems, the ab initio simulation of complex strongly correlated electron \nsystems continues to pose significant challenges. With the help of the generalized atomic limit (GAL) – a \nrecently developed model describing a system of quantum dots coupled to a superconducting lead – we \nattempt to show the efficiency and accuracy of NNQS, mainly the Restricted Boltzmann Machine, by comparing \nthe acquired results to other available methods such as exact diagonalization. The simultaneous study of the \nsystem’s properties such as the energy spectrum and quantum phase transitions could bring advancements \nin electronics, sensors or the design of high-quality qubits used in quantum computers.
Systems of quantum dots coupled to superconducting (SC) leads designed for practical applications are becoming increasingly complicated, ren- dering traditional analytical and numerical methods insufficient. Therefore, we tested new Neural Network Quantum States (NNQS) methods based on various network architectures and on variational Monte Carlo. To simplify their appli- cation, a new Chain Expansion method developed in our research group, which constructs effective models, was used. We applied these methods to systems of one to three quantum dots coupled to one to three SC leads, benchmarking them against conventional techniques and analyzing their phase diagrams. While at least one NNQS variant typically yielded correct predictions, no single method performed consistently well across all studied configurations. Thus, we conclude that current NNQS methods still face significant limitations when systematically studying complex hybrid su- perconducting nanostructures. This thesis also introduces a focused analytical study of effective models for fundamental quantum dot configurations. 1
We utilize neural network quantum states (NQS) to investigate the ground state properties of the Heisenberg model on a Shastry-Sutherland lattice using the variational Monte Carlo method. We show that already relatively simple NQSs can be used to approximate the ground state of this model in its different phases and regimes. We first compare several types of NQSs with each other on small lattices and benchmark their variational energies against the exact diagonalization results. We argue that when precision, generality, and computational costs are taken into account, a good choice for addressing larger systems is a shallow restricted Boltzmann machine NQS. We then show that such NQS can describe the main phases of the model in zero magnetic field. Moreover, NQS based on a restricted Boltzmann machine correctly describes the intriguing plateaus forming in magnetization of the model as a function of increasing magnetic field.
Over the past years, machine learning has emerged as a powerful computational tool to tackle complex problems over a broad range of scientific disciplines. In particular, artificial neural networks have been successfully deployed to mitigate the exponential complexity often encountered in quantum many-body physics, the study of properties of quantum systems built out of a large number of interacting particles. In this Article, we overview some applications of machine learning in condensed matter physics and quantum information, with particular emphasis on hands-on tutorials serving as a quick-start for a newcomer to the field. We present supervised machine learning with convolutional neural networks to learn a phase transition, unsupervised learning with restricted Boltzmann machines to perform quantum tomography, and variational Monte Carlo with recurrent neural-networks for approximating the ground state of a many-body Hamiltonian. We briefly review the key ingredients of each algorithm and their corresponding neural-network implementation, and show numerical experiments for a system of interacting Rydberg atoms in two dimensions.
Over the past few years, machine learning has emerged as a powerful computational tool to tackle complex problems in a broad range of scientific disciplines.In particular, artificial neural networks have been successfully used to mitigate the exponential complexity often encountered in quantum many-body physics, the study of properties of quantum systems built from a large number of interacting particles.In this article, we review some applications of neural networks in condensed matter physics and quantum information, with particular emphasis on hands-on tutorials serving as a quick start for a newcomer to the field.The prerequisites of this tutorial are basic probability theory and calculus, linear algebra, basic notions of neural networks, statistical physics, and quantum mechanics.The reader is introduced to supervised machine learning with convolutional neural networks to learn a phase transition, unsupervised learning with restricted Boltzmann machines to perform quantum tomography, and the variational Monte Carlo method with recurrent neural networks for approximating the ground state of a many-body Hamiltonian.For each algorithm, we briefly review the key ingredients and their corresponding neuralnetwork implementation, and show numerical experiments for a system of interacting Rydberg atoms in two dimensions.