Tomography, topology, and more

Some preprints that caught my attention over the last few weeks:

Attention-based transformer networks for quantum state tomography. The tremendous surge in popularity of transformer-based large language models means that there is a lot of effort towards developing efficient hardware and algorithms for implementing transformer-based neural networks. It is thus timely to understand how this architecture may be useful for solving problems in physics. This preprint proposes a transformer-based model for density matrix reconstruction.

A discrete formulation of the Kane-Mele Z2 invariant. Newcomers to topological materials are often stumped on how to efficiently implement gauge-invariant formulas for topological invariants in numerical calculations; analytical formulas assume a smooth choice of gauge for the eigenfunctions, whereas numerical calculations will return a non-smooth random gauge. The method reported here for calculating Chern numbers without requiring any gauge-fixing greatly simplifies numerical calculations. The present preprint concisely presents a numerical-friendly formulation of the Z2 invariant describing quantum spin Hall phases.

Valley photonic crystal waveguides fabricated with CMOS-compatible process. This work presents valley Hall photonic crystals based on an improved mask design that yields more triangular-shaped holes, improving their performance as valley Hall waveguides. It will be interesting to see measurements of the absolute propagation loss and how it compares to the strong backscattering reported earlier this year.

Photonic Landau Levels. Two groups (from the Netherlands and from the USA) report experiments with strained photonic crystals that emulate Landau levels formed by electrons subjected to uniform magnetic fields. These works show how previous theory and experiments based on weakly-coupled waveguide arrays can be generalized beyond the tight-binding approximation and may serve as a novel platform for achieving high quality factor modes and enhanced light-matter interactions. 

Questions and concerns about Google's quantum supremacy claim. The lead author Gil Kalai is one of the most prominent skeptics of quantum computing. This preprint summarizes efforts to rigorously analyze the raw data behind Google's 2019 quantum supremacy experiments. Since there now exist efficient classical algorithms for reproducing the output of the quantum supremacy circuits, the most important outstanding result from the 2019 paper is that the errors in large scale quantum circuits are uncorrelated to a good approximation, suggesting that quantum error correction can work in principle. This preprint argues that the data underlying this claim is flawed and that more effort should be devoted to understanding noise sources present in NISQ devices.