Quantum Simulations of Quantum and Classical Systems

          @misc{ scivideos_PIRSA:07010006,
            doi = {10.48660/07010006},
            url = {https://pirsa.org/07010006},
            author = {Somma, Rolando},
            keywords = {Quantum Information},
            language = {en},
            title = {Quantum Simulations of Quantum and Classical Systems},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2007},
            month = {jan},
            note = {PIRSA:07010006 see, \url{https://scivideos.org/index.php/pirsa/07010006}}
          }
          

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 two-level physical systems or qubits. The existence of one-to-one 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 spin-1/2 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 d-dimensional classical system can be obtained by studying the zero-temperature properties of an associated d-dimensional quantum system. This classical-quantum correspondence allows us to understand classical annealing procedures as slow (adiabatic) evolutions of the lowest-energy state of the corresponding quantum system. Since many of these problems are NP-hard and therefore difficult to solve, is worth investigating if a QC would be a better device to find the corresponding solutions.