That “we live in a simulation" trope being advanced by Elon Musk and some folk on the fringes of science? Fuggeddaboutit, because it's impossible to build a simulator that would reproduce what humans already know about quantum systems.
That's the confident conclusion drawn from a paper that revels in the title “Quantized gravitational responses, the sign problem, and quantum complexity”, by Zohar Ringel and Dmitry Kovrizhi of Oxford University, the Hebrew University of Jerusalem, and Russia's NRC Kurchatov Institute.
Ringel and Kovrizhi weren't setting out as antagonists to Elon Musk, Sam Altman, Oxford's Nick Bostrom or JPL scientist Rick Terrile. Rather, they want to try and understand the limits humans face trying to build simulations of quantum systems – as their abstract says:
“It is believed that not all quantum systems can be simulated efficiently using classical computational resources. This notion is supported by the fact that it is not known how to express the partition function in a sign-free manner in quantum Monte Carlo (QMC) simulations for a large number of important problems.”
The physics is dense, but the conclusion is straightforward: for some quantum interactions, complexity scales up so fast that the system quickly goes beyond the reach of either classical or quantum computers.
One such interaction Ringel and Kovrizhi examine is fractional quantum Hall effects, which the Oxford University press release describes as “thermal Hall conductance implies a generation of energy currents in the direction transverse to either temperature gradient, or a twist in the underlying geometry of space-time”.
El Reg can't help feeling that the explanation is missing something, but thankfully the most important point from the paper stands on its own, which comes straight from Ringel: “Our work provides an intriguing link between two seemingly unrelated topics: gravitational anomalies and computational complexity. It also shows that the thermal Hall conductance is a genuine quantum effect: one for which no local classical analogue exists”.
With no way to represent thermal Hall conductance in classical terms, there's also no way to make it scale linearly – that is, so that doubling the number of molecules merely doubles the size of the simulator. It scales exponentially, so adding just one particle to the system doubles the system need to model it, or as they put it in the paper, “such a transformation requires computational resources that scale exponentially with the system size”.
To model just a few hundred electrons needs a computer bigger than the universe, and that looks like a fundamental constraint, rather than merely a matter of finding a smarter way to model the system.
In other words: a simulation that goes all the way down to modelling things at a quantum level is only possible for tiny numbers of objects. It's just not possible to build anything big enough to model our universe. ®