Physicists find we’re not living in a computer simulation

Physicists find we’re not living in a computer simulation

Summary:

https://cosmosmagazine.com/physics/physicists-find-we-re-not-living-in-a-computer-simulation

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.

If the complexity grew linearly with the number of particles being simulated, then doubling the number of partices would mean doubling the computing power required. If, however, the complexity grows on an exponential scale – where the amount of computing power has to double every time a single particle is added – then the task quickly becomes impossible.

The researchers calculated that just storing information about a couple of hundred electrons would require a computer memory that would physically require more atoms than exist in the universe.



Paper:

Quantized gravitational responses, the sign problem, and quantum complexity. Zohar Ringel and Dmitry L. Kovrizhin. Science Advances, Sep 27 2017, Vol. 3, no. 9, e1701758, DOI: 10.1126/sciadv.1701758

Abstract: 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.