EAPSI: Quantum Techniques for the Efficient Modeling of Random Processes

Pollard Blake S, Riverside CA

Investigators

Abstract

Randomness plays an essential role in nature and in life. In some cases, the presence of noise or randomness simply adds small deviations to otherwise deterministic behavior. In other situations, randomness can drive a system to new places, much as mutation and gene drift drive evolution. Stochastic processes provide a framework for modeling such probabilistic systems. Classically, simulating a given stochastic process requires a minimum amount of memory or information storage. Professor Vlatko Vedral, and his collaborators at the Centre for Quantum Technologies (CQT) at the National University of Singapore (NUS) have shown how to use quantum mechanics to systematically construct models of stochastic processes which utilize less information than the optimal classical models. The amount of information required to accurately simulate a process can be taken as a measure of its complexity; thus stochastic processes appear simpler when viewed through the lens of quantum models. Working with Prof. Vedral and his group at the CQT, the project will analyze the complexity of classical and quantum models for certain 'memoryless' stochastic processes called Markov processes. A system consists of several interacting parts, possibly interacting with their environment. Using ideas from category theory, the PI has developed a compositional framework for building up complicated Markov processes from smaller interacting pieces called ?open Markov processes.' In this framework one can analyze the complexity of a composite system in relation to the complexity of its parts. This project will determine how this relationship changes when quantum models are utilized. Open Markov processes allow one to naturally incorporate interactions between a system and its environment. For many systems, especially in biology, feedback between a system and its environment plays an important role in determining the behavior of a system. This research will analyze the possible advantages of using quantum models to simulate stochastic processes corresponding to simple biochemical networks coupled to a stochastic environment. This NSF EAPSI award is funded in collaboration with the National Research Foundation of Singapore.