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.

Preparing talks with the help of large language models

It seems every day there's another news article about how large language models (LLMs) are going to replace hundreds of thousands of jobs.

At least in science, we are safe (for now) because the model outputs cannot be trusted and must be carefully vetted for factual accuracy. Thus, we should be thinking about applying LLMs to tasks in research where accuracy is not essential.

Next week I will be giving a talk on reviewing the scientific literature to the graduate students at CQT. Whenever I have to present a somewhat dry-sounding topic it is nice to begin the talk with a semi-humorous ice-breaker to grab the audience's attention. For example, one might try to relate the topic to a popular movie or book.

This is an area where LLMs can really shine! I quickly obtained some good ideas using the 7B and 13B parameter versions of LLaMA (running locally using llama.cpp). The prompt used is highlighted in red:

• Reviewing scientific literature can be challenging. It's like the movie Groundhog Day, you have to keep going through all the old material before finally getting past it and reading something new. And then having to do it all over again.
• Reviewing the scientific literature can be challenging. It's like the movie Inception; you have to wade through layers of reality before you find what's really going on.
• Reviewing the scientific literature can be challenging. It's like the movie Speed - if you slow down, you die! Rather than read every paper in a specific area of interest, scientists typically search through several papers to find those that relate to their research. But finding the right information requires patience and skill.
  
• Reviewing the scientific literature can be challenging. It's like the movie The Matrix where you have to plug into a computer to find out what is real and what is not.
• Reviewing the physics literature can be challenging. It's like the movie 300, "this is madness." If you read an academic paper or scientific article and you don't understand what it's about, chances are very good that the author didn't either.
• Reviewing the scientific literature can be challenging. It's like the movie 300, where 300 Spartans tried to hold off the Persian army. The odds were bad and the Spartans knew it, but they held off the vastly larger enemy force until they were completely annihilated. That was a glorious defeat and I hope this is one as well. The scientific literature is also vastly larger than your typical researcher can read and understand. One paper I am reviewing has over 600 references, so that's not a very promising start for the scientifically challenged like myself.

For further engagement, the next step can be to take the idea you like the most and use an image generation model (such as AUTOMATIC1111 - now easy to install and run locally!) to make a mash up of the movie and the talk topic. More on this another time!

Physics models that are wrong but useful

 "All models are wrong, but some are useful" is a saying usually attributed to statistician George Box. In physics we are often tempted to create a model that might be correct, but ends up being hopelessly useless. 

For example, the multi-particle Schrodinger equation in principle can give us an exact description of the energy levels of any molecule we would like to study, underlying the field of ab-initio quantum chemistry. But it cannot be solved except for the simplest of molecules. Heuristic approximation schemes which may not rigorously justified are essential to obtain useful predictions for large problems of practical interest. String theory is another example, with some arguing it is not even wrong.

There are many neat examples of models that, while wrong, lead to useful predictions and progress in our understanding:

• The Drude model of electrical conductivity. In the original paper there was a fortuitous cancellation of two big errors yielding agreement with experimental data for the specific heat. Nevertheless, the model remains a very good approximation for the frequency-dependent conductivity of metals.
• Conductivity at low temperatures: Before 1911 there were various predictions for the resistivity of metals cooled to zero temperature: zero, a finite value, and even infinite (argued by Lord Kelvin). Efforts to determine which prediction was correct led to the unexpected discovery of superconductivity.
• The Quantum Hall effect: quantization of the Hall conductivity was originally predicted in the absence of scattering, and thus the quantization was expected to only hold to a finite precision. Effects to measure a finite accuracy of the quantization led to the Nobel Prize-winning experiments.

A good model doesn't need to be 100% correct. A good model needs to give an actionable prediction.

Scaling up quantum processors

 Last November IBM announced with much fanfare their new 433-qubit superconducting quantum processor, named Osprey. Skeptics wanted to see the technical specifications before deciding whether this represented an important breakthrough or not. A few weeks ago the device (with 413 working qubits) finally became available for cloud users. Some technical specifications can be found here. 

Disappointingly, the quantum volume proposed by IBM themselves as a better measure of quantum processor performance than the raw qubit count is not yet available for this device. Presumably the slightly lower gate fidelities reported mean that the quantum volume does not exceed that achieved on their smaller devices with higher gate fidelity.

Meanwhile, Quantinuum announced their new trapped ion quantum processor with 32 fully-connected qubits and a whopping quantum volume of 65,536 (for reference, the best reported quantum volume from a cloud-accessible IBM device is 128). The announcement coincided with the upload of preprints to arXiv using the device to study quantum states with topological order and benchmarking its performance using various metrics.

metriq is a great resource for keeping track of all the different quantum processor platforms and devices and comparing their reported fidelities. Raw qubit counts are not meaningful without knowing the gate fidelities and device connectivity!

Suppression of modulational instability in valley-Hall waveguides

Posting has become infrequent due to some urgent deadlines and talk preparations over the last few weeks. Lots of great stuff has appeared on arXiv in May which I'm hoping to read and perhaps post about later. 

In the meantime, we also have a preprint out:

Self-steepening-induced stabilization of nonlinear edge waves at photonic valley-Hall interfaces

Several previous works demonstrated instabilities of topological edge states in the presence of weak nonlinearities, both numerically and analytically, often via reduction to a 1D nonlinear Schrodinger equation (NSE). We show here that if you go to stronger intensities, higher-order nonlinear effects (essentially arising from an intensity dependence of the effective Kerr nonlinearity strength) described by a modified nonlinear Schrodinger equation (MNSE) can stabilize the edge states! The phase diagram below nicely summarizes our central result:

I prepared some slides on this and our earlier analyses of nonlinear Dirac models describing topological edge states. The slides including some background material on photonic crystals and topological photonics are available here!