As a quantum theorist, my job is to study quantum systems and understand their inner workings. However, since I’m a theoretical physicist and not a experimental physicist, most of my “experiments” come in the form of simulations. My laboratory is my computer, and this means writing numerical experiments.

But wait a second, you tell me. Isn’t the whole point of quantum computers to do things that our regular computers can’t? And aren’t there issues with exponential memory?

These are both very good questions, and we’ll dive into them below. But in short: Yes, these are issues that limit the experiments I can do. And it’s a reason I’d like to get my hands on a good, error-correcting quantum computer!

If condensed matter theorists have the Ising model, gravitational physicists have the Schwarzschild solution, and quantum foundation theorists have the Bell inequalities, then theoretical computer scientists have satisfiability, or SAT. In the world of computer science (and particularly computational complexity), many discussions inevitably circle back to SAT. In fact, SAT isn’t just something that theoretical computer scientists study. Satisfiability has a rich history with statistical physics, a field which wields powerful tools to probe the properties of SAT. As such, SAT is a problem which touches several fields, which makes it a breeding ground for cross-disciplinary ideas.

To be a scientist means to explore. You need to start from what is known and jump out into the void, investigating new ideas. In this regard, the scientist is an explorer, a person searching for new truths in a world without a map. To be more precise, a scientist uncovers the new map as they learn.

If you want to learn a topic today, the resources are much more plentiful than even a few decades ago. The internet has given us wonderful resources to learn from, including some which leverage internet technologies to provide animations and teach topics in a much more interactive way. This is particularly true for mathematics and physics, which have been entrenched in dry textbooks that are a chore to read¹ for much too long.