Optimization using quantum generalization of Markov chains

Témavezető:	Gilyén András Pál
	Rényi Intézet
email:	gilyenandras@gmail.com

Projekt leírás

Markov Chains and the Metropolis algorithm are foundational techniques in stochastic processes and statistical physics. Their utility extends to various domains including search algorithms, optimization, and computational models in natural sciences. Understanding these algorithms provides key insights into the probabilistic underpinnings of complex systems and data structures.

Quantum channels can be viewed as a generalization of classical Markov chains to the realm of quantum mechanics. Whereas classical Markov chains describe stochastic transitions between discrete states with well-defined probabilities, quantum channels govern the evolution of quantum states, encompassing both deterministic (quantum) and probabilistic (classical) dynamics. This framework naturally extends the classical ideas to include phenomena like superposition and entanglement, offering a richer and more versatile model for complex systems. Understanding quantum channels thus provides a more comprehensive picture of state transitions in both classical and quantum contexts. It might be the case that quantum channels help optimizing over classical problems, but this question is little studied so far, and this topic is about exploring this question through numerical and theoretical study.

Előfeltételek

Familiarity with Markov chains. Some background on or willingness to learn about quantum information theory / computing.

Hivatkozások

Michael M. Wolf: Quantum Channels & Operations -- Guided Tour: https://mediatum.ub.tum.de/download/1701036/1701036.pdf