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Q: Fachverband Quantenoptik und Photonik

Q 30: Quantum Information: Concepts and Methods V

Q 30.8: Vortrag

Mittwoch, 2. März 2016, 12:45–13:00, e214

Certified efficient simulation of local unitary dynamics by ground state preparations — •Dominik Hangleiter, Martin Kliesch, Martin Schwarz, and Jens Eisert — Freie Universität Berlin

Typically, one cannot expect to find efficient classical simulation schemes for quantum systems. Hence, the usual scientific method to ``predict-and-test'' in order to falsify a theory is not guaranteed to work in the context of quantum many-body systems. So, is there at all a way to certify such systems? Recent experimental advances allowing for precise engineering of, and high-resolution measurements on large-scale quantum systems have brought this question from the theorist's desk into the lab. In this work, we explore alternative strategies to certify that a system engineered in the lab -- a quantum simulator -- is indeed well described by some target model. We find that there are conceivable physical systems that can be certified and which are, indeed, expected to be classically intractable. For example, this is the case for frustration-free and gapped Hamiltonians: their ground states can be certified by local energy measurements and encode the full complexity of quantum computers. This example shows: we do not need to merely trust quantum simulators but can also certify their outcome. To show our results, we bring together methods from quantum tomography and Hamiltonian complexity, in particular, constructions based on the Feynman-Kitaev Hamiltonian used to prove the QMA-hardness of the Local Hamiltonian Problem.