Training Coupled Phase Oscillators as a Neuromorphic Platform using Equilibrium Propagation

Given the rapidly growing scale and resource requirements of machine learning applications, the idea of building more efficient learning machines much closer to the laws of physics is an attractive proposition. One central question for identifying promising candidates for such neuromorphic platforms is whether not only inference but also training can exploit the physical dynamics. In this work, we show that it is possible to successfully train a system of coupled phase oscillators - one of the most widely investigated nonlinear dynamical systems with a multitude of physical implementations, comprising laser arrays, coupled mechanical limit cycles, superfluids, and exciton-polaritons. To this end, we apply the approach of equilibrium propagation, which permits to extract training gradients via a physical realization of backpropagation, based only on local interactions. The complex energy landscape of the XY/ Kuramoto model leads to multistability, and we show how to address this challenge. Our study identifies coupled phase oscillators as a new general-purpose neuromorphic platform and opens the door towards future experimental implementations.

Optimizing ZX-Diagrams with Deep Reinforcement Learning

ZX-diagrams are a powerful graphical language for the description of quantum processes with applications in fundamental quantum mechanics, quantum circuit optimization, tensor network simulation, and many more. The utility of ZX-diagrams relies on a set of local transformation rules that can be applied to them without changing the underlying quantum process they describe. These rules can be exploited to optimize the structure of ZX-diagrams for a range of applications. However, finding an optimal sequence of transformation rules is generally an open problem. In this work, we bring together ZX-diagrams with reinforcement learning, a machine learning technique designed to discover an optimal sequence of actions in a decision-making problem and show that a trained reinforcement learning agent can significantly outperform other optimization techniques like a greedy strategy or simulated annealing. The use of graph neural networks to encode the policy of the agent enables generalization to diagrams much bigger than seen during the training phase.

Deep Bayesian Experimental Design for Quantum Many-Body Systems

Bayesian experimental design is a technique that allows to efficiently select measurements to characterize a physical system by maximizing the expected information gain. Recent developments in deep neural networks and normalizing flows allow for a more efficient approximation of the posterior and thus the extension of this technique to complex high-dimensional situations. In this paper, we show how this approach holds promise for adaptive measurement strategies to characterize present-day quantum technology platforms. In particular, we focus on arrays of coupled cavities and qubit arrays. Both represent model systems of high relevance for modern applications, like quantum simulations and computing, and both have been realized in platforms where measurement and control can be exploited to characterize and counteract unavoidable disorder. Thus, they represent ideal targets for applications of Bayesian experimental design.

Investigation of inverse design of multilayer thin-films with conditional invertible Neural Networks

The task of designing optical multilayer thin-films regarding a given target is currently solved using gradient-based optimization in conjunction with methods that can introduce additional thin-film layers. Recently, Deep Learning and Reinforcement Learning have been been introduced to the task of designing thin-films with great success, however a trained network is usually only able to become proficient for a single target and must be retrained if the optical targets are varied. In this work, we apply conditional Invertible Neural Networks (cINN) to inversely designing multilayer thin-films given an optical target. Since the cINN learns the energy landscape of all thin-film configurations within the training dataset, we show that cINNs can generate a stochastic ensemble of proposals for thin-film configurations that that are reasonably close to the desired target depending only on random variables. By refining the proposed configurations further by a local optimization, we show that the generated thin-films reach the target with significantly greater precision than comparable state-of-the art approaches. Furthermore, we tested the generative capabilities on samples which are outside the training data distribution and found that the cINN was able to predict thin-films for out-of-distribution targets, too. The results suggest that in order to improve the generative design of thin-films, it is instructive to use established and new machine learning methods in conjunction in order to obtain the most favorable results.

Artificial Intelligence and Machine Learning for Quantum Technologies

In recent years, the dramatic progress in machine learning has begun to impact many areas of science and technology significantly. In the present perspective article, we explore how quantum technologies are benefiting from this revolution. We showcase in illustrative examples how scientists in the past few years have started to use machine learning and more broadly methods of artificial intelligence to analyze quantum measurements, estimate the parameters of quantum devices, discover new quantum experimental setups, protocols, and feedback strategies, and generally improve aspects of quantum computing, quantum communication, and quantum simulation. We highlight open challenges and future possibilities and conclude with some speculative visions for the next decade.

TMM-Fast: A Transfer Matrix Computation Package for Multilayer Thin-Film Optimization

Achieving the desired optical response from a multilayer thin-film structure over a broad range of wavelengths and angles of incidence can be challenging. An advanced thin-film structure can consist of multiple materials with different thicknesses and numerous layers. Design and optimization of complex thin-film structures with multiple variables is a computationally heavy problem that is still under active research. To enable fast and easy experimentation with new optimization techniques, we propose the Python package TMM-Fast which enables parallelized computation of reflection and transmission of light at different angles of incidence and wavelengths through the multilayer thin-film. By decreasing computational time, generating datasets for machine learning becomes feasible and evolutionary optimization can be used effectively. Additionally, the sub-package TMM-Torch allows to directly compute analytical gradients for local optimization by using PyTorch Autograd functionality. Finally, an OpenAi Gym environment is presented which allows the user to train reinforcement learning agents on the problem of finding multilayer thin-film configurations.

Self-learning Machines based on Hamiltonian Echo Backpropagation

A physical self-learning machine can be defined as a nonlinear dynamical system that can be trained on data (similar to artificial neural networks), but where the update of the internal degrees of freedom that serve as learnable parameters happens autonomously. In this way, neither external processing and feedback nor knowledge of (and control of) these internal degrees of freedom is required. We introduce a general scheme for self-learning in any time-reversible Hamiltonian system. We illustrate the training of such a self-learning machine numerically for the case of coupled nonlinear wave fields.

Renormalized Mutual Information for Artificial Scientific Discovery

We derive a well-defined renormalized version of mutual information that allows to estimate the dependence between continuous random variables in the important case when one is deterministically dependent on the other. This is the situation relevant for feature extraction, where the goal is to produce a low-dimensional effective description of a high-dimensional system. Our approach enables the discovery of collective variables in physical systems, thus adding to the toolbox of artificial scientific discovery, while also aiding the analysis of information flow in artificial neural networks.

Renormalized Mutual Information for Extraction of Continuous Features

We derive a well-defined renormalized version of mutual information that allows to estimate the dependence between continuous random variables in the important case when one is deterministically dependent on the other. This is the situation relevant for feature extraction and for information processing in artificial neural networks. We illustrate in basic examples how the renormalized mutual information can be used not only to compare the usefulness of different ansatz features, but also to automatically extract optimal features of a system in an unsupervised dimensionality reduction scenario.