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!