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 compilation of known QSOs for the Gaia mission

Quasars are essential for astrometric in the sense that they are spatial stationary because of their large distance from the Sun. The European Space Agency (ESA) space astrometric satellite Gaia is scanning the whole sky with unprecedented accuracy up to a few muas level. However, Gaia's two fields of view observations strategy may introduce a parallax bias in the Gaia catalog. Since it presents no significant parallax, quasar is perfect nature object to detect such bias. More importantly, quasars can be used to construct a Celestial Reference Frame in the optical wavelengths in Gaia mission. In this paper, we compile the most reliable quasars existing in literatures. The final compilation (designated as Known Quasars Catalog for Gaia mission, KQCG) contains 1843850 objects, among of them, 797632 objects are found in Gaia DR1 after cross-identifications. This catalog will be very useful in Gaia mission