Related papers: Structure learning of Hamiltonians from real-time …
Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in classical mechanics, where the dynamics is fully determined…
This paper investigates the problem of data-driven modeling of port-Hamiltonian systems while preserving their intrinsic Hamiltonian structure and stability properties. We propose a novel neural-network-based port-Hamiltonian modeling…
We present a numerical approach for approximating unknown Hamiltonian systems using observation data. A distinct feature of the proposed method is that it is structure-preserving, in the sense that it enforces conservation of the…
We develop a computational method to learn a molecular Hamiltonian matrix from matrix-valued time series of the electron density. As we demonstrate for three small molecules, the resulting Hamiltonians can be used for electron density…
We study the problem of certifying local Hamiltonians from real-time access to their dynamics. Given oracle access to $e^{-itH}$ for an unknown $k$-local Hamiltonian $H$ and a fully specified target Hamiltonian $H_0$, the goal is to decide…
We consider the problem of learning the Hamiltonian of a quantum system from estimates of Gibbs-state expectation values. Various methods for achieving this task were proposed recently, both from a practical and theoretical point of view.…
We formalize and study the Hamiltonian certification problem. Given access to $e^{-\mathrm{i} Ht}$ for an unknown Hamiltonian $H$, the goal of the problem is to determine whether $H$ is $\varepsilon_1$-close to or $\varepsilon_2$-far from a…
Many important physical systems can be described as the evolution of a Hamiltonian system, which has the important property of being conservative, that is, energy is conserved throughout the evolution. Physics Informed Neural Networks and…
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…
We introduce a generalizable framework for learning to identify effective Hamiltonians directly from experimental data in solid-state quantum systems. Our approach is based on a physics-informed neural network architecture that embeds…
We build upon recent work on using Machine Learning models to estimate Hamiltonian parameters using continuous weak measurement of qubits as input. We consider two settings for the training of our model: (1) supervised learning where the…
We investigate the problem of determining the Hamiltonian of a locally interacting open-quantum system. To do so, we construct model estimators based on inverting a set of stationary, or dynamical, Heisenberg-Langevin equations of motion…
Learning the unknown Hamiltonian governing the dynamics of a quantum many-body system is a challenging task. In this manuscript, we propose a possible strategy based on repeated measurements on a single time-dependent state. We prove that…
Quantum systems governed by time-dependent Hamiltonians pose significant challenges for the accurate computation of unitary time-evolution operators, which are essential for predicting quantum state dynamics. In this work, we introduce a…
Machine-Learned Interatomic Potentials (MLIPs) require vast amounts of atomic structure data to learn forces and energies, and their performance continues to improve with training set size. Meanwhile, the even greater quantities of…
Characterizing noisy quantum devices requires methods for learning the underlying quantum Hamiltonian which governs their dynamics. Often, such methods compare measurements to simulations of candidate Hamiltonians, a task which requires…
Local Hamiltonians arise naturally in physical systems. Despite its seemingly `simple' local structure, exotic features such as nonlocal correlations and topological orders exhibit in eigenstates of these systems. Previous studies for…
We study the problem of simulating the time evolution of a lattice Hamiltonian, where the qubits are laid out on a lattice and the Hamiltonian only includes geometrically local interactions (i.e., a qubit may only interact with qubits in…
The solution of problems in physics is often facilitated by a change of variables. In this work we present neural transformations to learn symmetries of Hamiltonian mechanical systems. Maintaining the Hamiltonian structure requires novel…
Accurately learning the temporal behavior of dynamical systems requires models with well-chosen learning biases. Recent innovations embed the Hamiltonian and Lagrangian formalisms into neural networks and demonstrate a significant…