Scalable Hamiltonian learning for large-scale out-of-equilibrium quantum dynamics

Abstract

Large-scale quantum devices provide insights beyond the reach of classical simulations. However, for a reliable and verifiable quantum simulation, the building blocks of the quantum device require exquisite benchmarking. This benchmarking of large-scale dynamical quantum systems represents a major challenge due to lack of efficient tools for their simulation. Here, we present a scalable algorithm based on neural networks for Hamiltonian tomography in out-of-equilibrium quantum systems. We illustrate our approach using a model for a forefront quantum simulation platform: ultracold atoms in optical lattices. Specifically, we show that our algorithm is able to reconstruct the Hamiltonian of an arbitrary sized bosonic ladder system using an accessible amount of experimental measurements. We are able to significantly increase the previously known parameter precision.

One-to-one correspondence between thermal structure factors and coupling constants of general bilinear Hamiltonians

“…This approach may be used to accurately determine the spin Hamiltonian of Kitaev materials, such as RuCl 3 [30,31]. Likewise, it may assist in the characterization of state-of-the-art quantum technologies [19,[32][33][34][35].…”

Hamiltonian learning with real-space impurity tomography in topological moiré superconductors

“…In certain instances, obtaining the Hamiltonian parameters of the model can be done by fitting specific features of the data [9,10]. Many-body Hamiltonians with local interactions can be extracted local observables by exploiting time evolution and quantum Hamiltonian tomography, a strategy demonstrated theoretically and experimentally [11][12][13][14][15][16]. However, in some instances, no simple fitting procedure nor time-dependent measurements can be performed to extract Hamiltonian parameters.…”

Adversarial Hamiltonian learning of quantum dots in a minimal Kitaev chain

“…Inferring the description of a quantum system from available data, a problem known as Hamiltonian learning, is a central problem in quantum systems [16][17][18][19][20][21]. Neural network-based algorithms have recently risen to prominence as a tool for Hamiltonian learning and parameter estimation from experimental data [22][23][24][25][26][27][28][29][30]. While machine-learning algorithms are by far not a universal answer to parameter determination challenges in noisy quantum systems, their generalization properties and fast evaluation make them suitable candidates to address technical questions connected to quantum control and parameter estimation.…”