### A quantum approach to population dynamics

Publication by Wout Merbis can be found here.

In recent years the field of quantum information has been the focus of great interest both from academia and from industry. The evolving development of the quantum computer has led to claims of ‘quantum supremacy’, but it also underlines the relevance of the question: *what kind of problems are quantum computers good at? *And, particularly fitting the broad remit of the NWA: *is it possible to look outside the domains of computer science or quantum chemistry and physics for interesting problems? *

A surprising new direction here could come from population dynamics, which can be highlighted with an example from epidemiological models of the spread of infectious disease. To model the spread of a disease through a population, one could take each individual to be in a specific state and assign rules for their interactions, creating a deterministic, agent-based model.

In the real world, there is always an uncertainty about the status of an outbreak. This uncertainty is active at the level of each individual. One does not know if they are infected until a test has been performed or clear symptoms appear. Is it possible to hardwire this uncertainty into the model? One way to do this is to use a concept familiar from quantum mechanics: the superposition of states. By presenting individuals as being in a superposition, we can also create entanglement between individuals. In this way we can start using the well-developed mathematical tools from quantum mechanics to create what could be called non-deterministic agent-based models, which yield *probabilities *for individuals to be infected.

The purpose of this research is to explore the application of mathematical tools from many-body quantum systems and quantum field theory to problems in population dynamics. The ultimate goal is to develop a mathematical framework for the understanding of dynamical interacting populations as many-body quantum systems. Examples of tools which can be applied in this context are: the path integral formulation of quantum mechanics, tensor networks techniques to represent large tensors as products of matrices, and renormalization group methods.

Within the timeframe of 8 months that fits this funding instrument, an understanding of the SIR (**S**usceptible, **I**nfectious **R**ecovered) model of epidemiology as a quantum many-body system will be developed. Specifically, the spread of an infectious disease through a population will be modeled using the growth of operator size in a quantum chaotic system. There are already indications that this is possible for simpler models of epidemiology in relation to a well-known model in quantum many-body physics (see “Quantum Epidemiology: Operator Growth, Thermal Effects, and SYK”, Xiao-Liang Qi, Alexandre Streicher, *JHEP *08 (2019) 012) in which dualities between gravitational physics and SYK-type models of condensed matter physics are explored).

The proposed research direction would open up new avenues in both the fields of population dynamics and quantum information. It could lay the groundwork for developing a better understanding of the spread of quantum information through complex systems, such as the interaction networks within populations.

This project fits perfectly within the goals of NWA route 2 as it aims at establishing a dialogue between physics, mathematics and computer science in an area where aspects of emergence are investigated, as part of the Dutch Institute for Emergent Phenomena, DIEP.