Quantum Monte Carlo methods use random sampling to analyze many-body quantum problems where the equations involved cannot be solved directly. Ringel and Kovrizhi showed that attempts to use quantum Monte Carlo to model systems exhibiting anomalies, such as the quantum Hall effect, will always become unworkable. They discovered that the complexity of the simulation increased exponentially with the number of particles being simulated.
They use the finding of an unworkable quantum problem to come to the conclusion that the universe could not be a simulation.
It is more accurate to say that any simulation of the universe could not be using any algorithms or computers imaginable by these physicists.
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.