MTA-HUN-REN RI Lendület "Momentum" Quantum Computing Research Group

Markov Chain Monte Carlo (MCMC) methods are essential for simulating the behavior of complex systems and have become indispensable in certain areas of computational physics, biology, and finance, for example. 

The essence of the method is a simple iterative process that explores the system state space through a series of small changes and converges to the desired result. The power of the MCMC method lies in its ability to simulate the effect of an exponentially large stochastic matrix in a probabilistic manner by selecting appropriate probability transitions between states.

Quantum generalizations of MCMC methods further enhance the method by exploiting quantum effects such as superposition and entanglement. These algorithms have the potential to revolutionize various fields, from materials science to financial modeling, enabling simulations that are impossible for classical computers and offering unprecedented computational power.