Astute followers of this blog know that quantum computing was the brain child of Richard Feynman whose contribution to the quantum field theory of electrodynamics earned him a Nobel prize. Feynman was the first to remark on the fact that classical computers cannot efficiently simulate quantum systems. Since then the field has come a long way and it has been shown theoretically and experimentally that quantum computers can efficiently simulate quantum mechanical multi-body systems. And recent experimental setups like NIST's 300 qbit quantum simulator are destined to surpass anything that could be modeled on a classical computer.
Yet, for the longest time it was not clear if quantum computers could also efficiently simulate quantum field theories.
Fields are a bit more tricky. Just recall the classic experiment to illustrate a magnetic field as shown in the picture.
The typical way to get around this problem is to perform the calculations on a grid. And the algorithm introduced by Jordan et. al. in this, just three pages long, paper does that as well.
Unfortunately, Feynman is no longer around to appreciate the work that now made it official: Quantum Field theories can be efficiently simulated i.e. with polynomial time scaling.
It is quite clever how they spread their simulation over the qbits, represent scattering particles and manage to derive an error estimate. The fact that they actually do this within the Schrödinger picture makes this paper especially accessible.
If you don't know the first thing about quantum mechanics, this paper will still give you a good sense that the constriction of quantum algorithms does not look anything like conventional coding - even, as is the case here, one using the gate based quantum computing model.
This goes to the heart of the challenge to bring quantum computing to the masses. Steven Job's quip about the iPhone is just as true for any quantum computer: “What would it be without the software? It would make a nice paperweight!” (h/t R. Tucci) Only difference is that a quantum computer will make a really big paperweight, but otherwise it'll be just as dead.
This somewhat resembles the days of yore when computer programs had to be hand compiled for a specific machine architecture. Hence, the race is one to find a suitable abstraction layer on top of this underlying quantum weirdness, in order to make this power accessible to non-physicists.
Just in case you wondered: It is still not clear if String theories can be efficiently simulated on a quantum computer. But it has been suggested that those that cannot should be considered unphysical.