Differentiable Programming Tensor Networks

Differentiable programming is a fresh programming paradigm which composes parameterized algorithmic components and trains them using automatic differentiation (AD). The concept emerges from deep learning but is not only limited to training neural networks. We present theory and practice of programming tensor network algorithms in a fully differentiable way. By formulating the tensor network algorithm as a computation graph, one can compute higher order derivatives of the program accurately and efficiently using AD. We present essential techniques to differentiate through the tensor networks contractions, including stable AD for tensor decomposition and efficient backpropagation through fixed point iterations. As a demonstration, we compute the specific heat of the Ising model directly by taking the second order derivative of the free energy obtained in the tensor renormalization group calculation. Next, we perform gradient based variational optimization of infinite projected entangled pair states for quantum antiferromagnetic Heisenberg model and obtain start-of-the-art variational energy and magnetization with moderate efforts. Differentiable programming removes laborious human efforts in deriving and implementing analytical gradients for tensor network programs, which opens the door to more innovations in tensor network algorithms and applications.Comment: Typos corrected, discussion and refs added; revised version accepted for publication in PRX. Source code available at https://github.com/wangleiphy/tensorgra

A scalable hardware and software control apparatus for experiments with hybrid quantum systems

Modern experiments with fundamental quantum systems - like ultracold atoms, trapped ions, single photons - are managed by a control system formed by a number of input/output electronic channels governed by a computer. In hybrid quantum systems, where two or more quantum systems are combined and made to interact, establishing an efficient control system is particularly challenging due to the higher complexity, especially when each single quantum system is characterized by a different timescale. Here we present a new control apparatus specifically designed to efficiently manage hybrid quantum systems. The apparatus is formed by a network of fast communicating Field Programmable Gate Arrays (FPGAs), the action of which is administrated by a software. Both hardware and software share the same tree-like structure, which ensures a full scalability of the control apparatus. In the hardware, a master board acts on a number of slave boards, each of which is equipped with an FPGA that locally drives analog and digital input/output channels and radiofrequency (RF) outputs up to 400 MHz. The software is designed to be a general platform for managing both commercial and home-made instruments in a user-friendly and intuitive Graphical User Interface (GUI). The architecture ensures that complex control protocols can be carried out, such as performing of concurrent commands loops by acting on different channels, the generation of multi-variable error functions and the implementation of self-optimization procedures. Although designed for managing experiments with hybrid quantum systems, in particular with atom-ion mixtures, this control apparatus can in principle be used in any experiment in atomic, molecular, and optical physics.Comment: 10 pages, 12 figure

Electronics and control technology

Until recently, there was no requirement to learn electronics and control technology in the New Zealand school curriculum. Apart from isolated pockets of teaching based on the enthusiasm of individual teachers, there is very little direct learning of electronics in New Zealand primary or secondary schools. The learning of electronics is located in tertiary vocational training programmes. Thus, few school students learn about electronics and few school teachers have experience in teaching it. Lack of experience with electronics (other than using its products) has contributed to a commonly held view of electronics as out of the control and intellectual grasp of the average person; the domain of the engineer, programmer and enthusiast with his or her special aptitude. This need not be true, but teachers' and parents' lack of experience with electronics is in danger of denying young learners access to the mainstream of modern technology

Graph Networks as a Universal Machine Learning Framework for Molecules and Crystals

Graph networks are a new machine learning (ML) paradigm that supports both relational reasoning and combinatorial generalization. Here, we develop universal MatErials Graph Network (MEGNet) models for accurate property prediction in both molecules and crystals. We demonstrate that the MEGNet models outperform prior ML models such as the SchNet in 11 out of 13 properties of the QM9 molecule data set. Similarly, we show that MEGNet models trained on $\sim 60,000$ crystals in the Materials Project substantially outperform prior ML models in the prediction of the formation energies, band gaps and elastic moduli of crystals, achieving better than DFT accuracy over a much larger data set. We present two new strategies to address data limitations common in materials science and chemistry. First, we demonstrate a physically-intuitive approach to unify four separate molecular MEGNet models for the internal energy at 0 K and room temperature, enthalpy and Gibbs free energy into a single free energy MEGNet model by incorporating the temperature, pressure and entropy as global state inputs. Second, we show that the learned element embeddings in MEGNet models encode periodic chemical trends and can be transfer-learned from a property model trained on a larger data set (formation energies) to improve property models with smaller amounts of data (band gaps and elastic moduli)