New Quantum Algorithms Finally Crack Nonlinear Equations | Code it | Scoop.it
From www.quantamagazine.org - January 8, 2021 4:17 AM

Simple phenomena, such as how sap flows down a tree trunk, are straightforward and can be captured in a few lines of code using what mathematicians call linear differential equations.

 

But in nonlinear systems, interactions can affect themselves: When air streams past a jet’s wings, the air flow alters molecular interactions, which alter the air flow, and so on. This feedback loop breeds chaos, where small changes in initial conditions lead to wildly different behavior later, making predictions nearly impossible — no matter how powerful the computer.

 

“This is part of why it’s difficult to predict the weather or understand complicated fluid flow,” said Andrew Childs, a quantum information researcher at the University of Maryland. “There are hard computational problems that you could solve, if you could [figure out] these nonlinear dynamics.”

 

That may soon be possible. In separate studies posted in November, two teams — one led by Childs, the other based at the Massachusetts Institute of Technology — described powerful tools that would allow quantum computers to better model nonlinear dynamics.

 
Quantum computers take advantage of quantum phenomena to perform certain calculations more efficiently than their classical counterparts. Thanks to these abilities, they can already topple complex linear differential equations exponentially faster than classical machines. Researchers have long hoped they could similarly tame nonlinear problems with clever quantum algorithms.