Article Source - "Quantized gravitational responses, the sign problem, and quantum complexity"
by ZOHAR RINGEL, DMITRY L. KOVRIZHIN
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 answer to the question—whether there is a fundamental obstruction to such a sign-free representation in generic quantum systems—remains unclear. Focusing on systems with bosonic degrees of freedom, we show that quantized gravitational responses appear as obstructions to local sign-free QMC. In condensed matter physics settings, these responses, such as thermal Hall conductance, are associated with fractional quantum Hall effects. We show that similar arguments also hold in the case of spontaneously broken time-reversal (TR) symmetry such as in the chiral phase of a perturbed quantum Kagome antiferromagnet. The connection between quantized gravitational responses and the sign problem is also manifested in certain vertex models, where TR symmetry is preserved.
Whether we live in a simulation or not is not a question that physics can answer. Unless it's a question of "are we living in a simulation that's running on a computer in a universe with exactly identical laws of physics to our own" which is much more boring. The paper's pretty cool, though.
All that said, the idea that we're living in a simulation is silly. It's on the same level as solipsism, saying that I'm the only one that's real, and that everyone else and the whole external world are just figments of my imagination. Both ideas are functionally useless, philosophically boring, and impossible to prove. And believing in either solipsism or simulation theory requires you to set such impossibly high standards of what it means to "know" something that it isn't actually possible to know with certainty that anything is true.