Related papers: Hamiltonian-based neural networks for systems unde…
Accurate models of the world are built upon notions of its underlying symmetries. In physics, these symmetries correspond to conservation laws, such as for energy and momentum. Yet even though neural network models see increasing use in the…
The Lie-Hamilton approach for $t$-dependent Hamiltonians is extended to cover the so-called nonlinear Lie-Hamilton systems, which are no longer related to a linear $t$-dependent combination of a basis of a finite-dimensional Lie algebra of…
Variational approaches are among the most powerful modern techniques to approximately solve quantum many-body problems. These encompass both variational states based on tensor or neural networks, and parameterized quantum circuits in…
HNets is a class of neural networks on grounds of physical prior for learning Hamiltonian systems. This paper explains the influences of different integrators as hyper-parameters on the HNets through error analysis. If we define the network…
Neural networks are discrete entities: subdivided into discrete layers and parametrized by weights which are iteratively optimized via difference equations. Recent work proposes networks with layer outputs which are no longer quantized but…
Virtual constraints are invariant relations imposed on a control system via feedback as opposed to real physical constraints acting on the system. Nonholonomic systems are mechanical systems with non-integrable constraints on the…
This paper proposes a novel approach to Hamiltonian simulation using Decision Diagrams (DDs), which are an exact representation based on exploiting redundancies in representations of quantum states and operations. While the simulation of…
Modified Hamiltonians are used in the field of geometric numerical integration to show that symplectic schemes for Hamiltonian systems are accurate over long times. For nonlinear systems the series defining the modified Hamiltonian usually…
The combinations of machine learning with ab initio methods have attracted much attention for their potential to resolve the accuracy-efficiency dilemma and facilitate calculations for large-scale systems. Recently, equivariant message…
We present novel Hamiltonian descriptions of some three-dimensional systems including two well-known systems describing the three-wave-interaction problem and some well-known chaotic systems, namely, the Chen, L\"u, and Qi systems. We show…
Deep learning for predicting the electronic-structure Hamiltonian of quantum systems necessitates satisfying the covariance laws, among which achieving SO(3)-equivariance without sacrificing the non-linear expressive capability of networks…
We develop Hamilton-Jacobi theory for Chaplygin systems, a certain class of nonholonomic mechanical systems with symmetries, using a technique called Hamiltonization, which transforms nonholonomic systems into Hamiltonian systems. We give a…
We propose dynamical control schemes for Hamiltonian simulation in many-body quantum systems that avoid instantaneous control operations and rely solely on realistic bounded-strength control Hamiltonians. Each simulation protocol consists…
We propose a \emph{hybrid} real- and complex-valued \emph{neural network} (HNN) architecture, designed to combine the computational efficiency of real-valued processing with the ability to effectively handle complex-valued data. We…
The extended Hamilton's Principle and other methods proposed to handle non-holonomic constraints are considered. They dont agree with each other. By looking at its consistency with D'Alembert's principle for linear non-holonomic…
Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore high-dimensional parameter spaces guided by simulated Hamiltonian flows. However, 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…
In order to describe the impact of different geometric structures and constraints for the dynamics of a regular controlled Hamiltonian system, in this paper, we first define a kind of controlled magnetic Hamiltonian (CMH) system, and give a…
Sampling from an unnormalized probability distribution is a fundamental problem in machine learning with applications including Bayesian modeling, latent factor inference, and energy-based model training. After decades of research,…
The time-dependent pseudo-Hermitian formulation of quantum mechanics allows to study open system dynamics in analogy to Hermitian quantum systems. In this setting, we show that the notion of holonomic quantum computation can equally be…