"Quantum simulators can be potentially used for studying complex quantum systems which are otherwise difficult to realize in a laboratory [1]. Well controlled and high fidelity quantum operations make trapped ion systems most favorable for investigating many-body physics [2]. Scrambling of information in many-body quantum system can be studied using out-of-time ordered correlators (OTOC). Such tools have been routinely used in black hole physics in the past. We have recently used OTOC's to study the spread of quantum information in our many body system which is realized on a 10-qubit trapped ion quantum simulator. The many body dynamics are mimicked using a transverse Ising Hamiltonian which is realized with the help of bichromatic laser fields far detuned from the motional sidebands of a 10-ion chain. Here we measure statistical correlations between randomized initial states which are time evolved in the presence of the Ising Hamiltonian [3]. The parameters of the Ising Hamiltonian are further varied in order to demonstrate fast and slow scrambling for long and short range interactions.

[1] Kokail, C., et al. ""Self-verifying variational quantum simulation of lattice models."" Nature 569.7756 (2019): 355.

[2] Maier, Christine, et al. ""Environment-assisted quantum transport in a 10-qubit network."" Physical review letters 122.5 (2019): 050501.

[3] Vermersch, Benoît, et al. ""Probing scrambling using statistical correlations between randomized measurements."" arXiv preprint arXiv:1807.09087 (2018)"