Measuring Quantum Progress

In August the Google Quantum AI Team posted a blog post How to compare a noisy quantum processor to a classical computer to measure progress in building quantum computers. 

So far quantum advantage (a term that has thankfully seem to replace quantum supremacy) has focused on approximating quantum distributions like Boson Sampling or random quantum circuits as described in the blog post. These results are messy, it's hard to measure success, hard to know the classical complexity of these problems, hard to explain to the public and seem to have little to no practical value.

The poster child for quantum computing has always been integer factoring. Factoring has lots of great properties.

1. Factoring is theoretically easy to solve on a quantum computer via Shor's algorithm.
2. While we don't know the classical hardness of factoring, considerable efforts over decades have yet to produce any even subexponential-time algorithms.
3. It is classically easy to check the factors.
4. It is classically easy to generate hard to factor numbers.
5. You can explain factoring to anyone with even a moderate interest in mathematics.
6. Factoring is critical to a number of cryptographic protocols most notably RSA.