Mon 10/30, 4pm in 26-214 (QIP seminar)
Rolando Somma (LANL)
Quantum Simulations of Quantum and Classical Systems
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-complete and therefore hard to solve, it is worth investigating
if a QC is a better device to find the corresponding solutions.
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