Abstract
Topologically ordered materials may serve as a platform for new quantum technologies, such as fault-tolerant quantum computers. To fulfil this promise, efficient and general methods are needed to discover and classify new topological phases of matter. We demonstrate that deep neural networks augmented with external memory can use the density profiles formed in quantum walks to efficiently identify properties of a topological phase as well as phase transitions. On a trial topological ordered model, our method’s accuracy of topological phase identification reaches 97.4%, and is shown to be robust to noise on the data. Furthermore, we demonstrate that our trained DNN is able to identify topological phases of a perturbed model, and predict the corresponding shift of topological phase transitions without learning any information about the perturbations in advance. These results demonstrate that our approach is generally applicable and may be used to identify a variety of quantum topological materials.
Highlights
The properties of topological quantum materials have been the subject of intense interest in recent years, due to their paradigmchanging implications for condensed matter physics[1,2,3,4] and potential applications to new technologies
For bulk systems of topological insulators, these can often be inferred from the existence of edge states,[2,10] or particle dynamics, such as the anomalous velocities obtained by wave packets under applied forces,[11,12] and quantum walks.[13,14,15,16,17,18,19]
Using the particle density profiles formed during a particle’s evolution driven by the system’s Hamiltonian, we demonstrate that a novel deep neural network (DNN) with external memory is able to identify the topological phases and phase transitions for a two-dimensional lattice model with spin–orbit coupling
Summary
The properties of topological quantum materials have been the subject of intense interest in recent years, due to their paradigmchanging implications for condensed matter physics[1,2,3,4] and potential applications to new technologies. The electric conductivity of topological materials such as topological insulators has potential applications for magnetoelectric devices with higher efficiency and lower energy consumption.[5,6,7] In addition, topological materials can support anyonic quasiparticle excitations, with exotic statistics under braiding transformations that may enable fault-tolerant quantum computing.[8,9] The topological ordering of quantum materials can be characterised with quantised, nonlocal topological invariants, such as the Chern number of the quantum Hall effect These invariants determine all of the key topological properties of quantum systems, such as the number of topological edge states and the types of anyonic excitations in topological materials. Our results demonstrate that quantum walks and DNN are a powerful and generic tool for the efficient discovery and analysis of novel topological quantum systems, and the design of robust quantum technologies
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