Machine Learning for Quantum Design
Differentiable programming makes the optimization of a tensor network much cheaper (in unit of brain energy consumption) than before [e.g. arXiv: 1903.09650]. This talk mainly focuses on the technical aspects of differentiable programming tensor networks and quantum circuits with Yao.jl (https://github.com/QuantumBFS/Yao.jl). I will also show how quantum circuits can help with contracting and differentiating tensor networks.
Modern Machine Learning (ML) relies on cost function optimization to train model parameters. The non-convexity of cost function landscapes results in the emergence of local minima in which state-of-the-art gradient descent optimizers get stuck. Similarly, in modern Quantum Control (QC), a key to understanding the difficulty of multiqubit state preparation holds the control landscape -- the mapping assigning to every control protocol its cost function value.
Belief-propagation (BP) decoders are responsible for the success of many modern coding schemes. While many classical coding schemes have been generalized to the quantum setting, the corresponding BP decoders are flawed by design in this setting. Inspired by an exact mapping between BP and deep neural networks, we train neural BP decoders for quantum low-density parity-check codes, with a loss function tailored for the quantum setting. Training substantially improves the performance of the original BP decoders.
As quantum processors become increasingly refined, benchmarking them in useful ways becomes a critical topic. Traditional approaches to quantum tomography, such as state tomography, suffer from self-consistency problems, requiring either perfectly pre-calibrated operations or measurements. This problem has recently been tackled by explicitly self-consistent protocols such as randomized benchmarking, robust phase estimation, and gate set tomography (GST).
Site resolution in quantum gas microscopes for ultracold atoms in optical lattices have transformed quantum simulations of many-body Hamiltonians. Statistical analysis of atomic snapshots can produce expectation values for various charge and spin correlation functions and have led to new discoveries for the Hubbard model in two dimensions. Conventional approaches, however, fail in general when the order parameter is not known or when an expected phase has no clear signatures in the density basis.
Inspired by the "third wave" of artificial intelligence (AI), machine learning has found rapid applications in various topics of physics research. Perhaps one of the most ambitious goals of machine learning physics is to develop novel approaches that ultimately allows AI to discover new concepts and governing equations of physics from experimental observations. In this talk, I will present our progress in applying machine learning technique to reveal the quantum wave function of Bose-Einstein condensate (BEC) and the holographic geometry of conformal field theories.
For the past decade, there has been a new major architectural fad in deep learning every year or two.
One such fad for the past two years has been the transformer model, an implementation of the attention method which has superseded RNNs in most sequence learning applications. I'll give an overview of the model, with some discussion of non-physics applications, and intimate some possibilities for physics.
Density functional theory is a widely used electronic structure method for simulating and designing nanoscale systems based on first principles. I will outline our recent efforts to improve density functionals using deep learning. Improvement would mean achieving higher accuracy, better scaling (with respect to system size), improved computational parallelizability, and achieving reliable performance transferability across different electronic environments.