When it comes to solving problems, even the most advanced quantum computers still use the same basic approach as your old desktop: do as many calculations as you need to to get the solution. But what if instead of working through the calculations, a computer could just “know” the solution outright? That far-fetched idea is the basis for a weird new breakthrough in computer science. How could such a thing be possible? With particles of “magic dust” they call polaritons.

## Just Crazy Enough To Work

The “optimal” solution to a mathematical problem — from modeling the way proteins fold to figuring out how the stock market behaves — is the simplest one possible. A computer’s task is to figure out a way to solve a problem with the absolute minimum number of steps. The way computers do this now is via the “brute-force” method, where they calculate and calculate and calculate until they finally happen on the optimal solution. To be fair, that can happen with wicked speed — at the time of this writing, the world’s fastest supercomputer can carry out 93 quadrillion calculations per second — but it’s not the most efficient approach.

A University of Cambridge press release compares that search for an optimal solution to a hiker trying to find the lowest point on a mountain range. “A hiker may go downhill and think that they have reached the lowest point of the entire landscape, but there may be a deeper drop just behind the next mountain. Such a search may seem daunting in natural terrain, but imagine its complexity in high-dimensional space.” To overcome that challenge, Cambridge professor Natalia Berloff and her colleagues came at it from a completely new angle: instead of using a hiker, what if you used a magical dust that settled into each valley, but only glowed at the deepest level?

“A few years ago our purely theoretical proposal on how to do this was rejected by three scientific journals,” said Berloff. “One referee said, ‘Who would be crazy enough to try to implement this?!’ So we had to do it ourselves, and now we’ve proved our proposal with experimental data.”

## Bibbidi Bobbidi Boo

This magical dust is made up of real quasiparticles called polaritons, which are created when a laser hits stacked layers of specific atoms to create a weird combination of matter and light. These super-lightweight particles easily crowd together and sync up to form a state of matter known as a Bose-Einstein condensate. In essence, that turns these ultra-tiny, hard-to-measure particles into one object that lights up in ways you can detect.

Once they had the magic dust, they just needed a mountain to try it out on. That’s where the metaphor turns weirdly literal. See, there are ways you can map pen-and-paper math formulas into quantum models that deal with actual particles in actual space. One of these is known as the XY model, a fundamental optimization problem that can be represented on a graph. In a paper published in 2017 in Nature Materials, Berloff and her colleagues demonstrated that they could make the condensing polaritons arrange themselves on the vertices of a graph in a configuration that corresponded to the “absolute minimum of the objective function” — i.e. the optimal solution.

This is the first step in many to come. “We are just at the beginning of exploring the potential of polariton graphs for solving complex problems,” said co-author Professor Pavlos Lagoudakis.