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Sampling from quantum Gibbs states has proven to be a task of major importance in quantum computation. This problem is not trivial even for quantum computers since the exponential of a quantum many-body Hamiltonian requires too much computational power. On the one hand, different methods to prepare quantum Gibbs states have already been proposed. On the other hand, as far as we know, no certification protocol has been proposed so far. Here, we propose methods to certify one-dimensional Gibbs state preparations. The main idea behind the methods is to build a fidelity witness for the purification of the target Gibbs state, which is known as the thermofield double state. The procedure to build the parent Hamiltonian relies on a useful locality bound for imaginary-time evolutions, in the same way Lieb-Robinson bounds are used for real-time ones. The method allows a highly efficient estimation of the fidelity lower-bound through block quantum tomography.

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Eric G. Arrais, Federal University of Rio de Janeiro/University of Cologne
Seminar Room 0.02, ETP
Contact: David Gross