Quantum Simulations of Quantum and Classical Systems Speaker(s): Rolando Somma
Abstract: If a large quantum computer (QC) existed today, what type of physical problems could we efficiently simulate on it that we could not simulate on a conventional computer? In this talk, I argue that a QC could solve some relevant physical "questions" more efficiently. First, I will focus on the quantum simulation of quantum systems satisfying different particle statistics (e.g., anyons), using a QC made of twolevel physical systems or qubits. The existence of onetoone mappings between different algebras of observables or between different Hilbert spaces allow us to represent and imitate any physical system by any other one (e.g., a bosonic system by a spin1/2 system). We explain how these mappings can be performed showing quantum networks useful for the efficient evaluation of some physical properties, such as correlation functions and energy spectra. Second, I will focus on the quantum simulation of classical systems. Interestingly, the thermodynamic properties of any ddimensional classical system can be obtained by studying the zerotemperature properties of an associated ddimensional quantum system. This classicalquantum correspondence allows us to understand classical annealing procedures as slow (adiabatic) evolutions of the lowestenergy state of the corresponding quantum system. Since many of these problems are NPhard and therefore difficult to solve, is worth investigating if a QC would be a better device to find the corresponding solutions.
Date: 22/01/2007  4:00 pm
