experimental measurement of out-of-time-order correlators at finite temperature on a trapped ion quantum computer*

Out-of-time-order correlators (OTOCs) are a key observable in the study of quantum scrambling dynamics and, by extension, for exploring the physics of black holes and many-body systems using quantum simulators [1]. Here we report the first experimental measurements of an OTOC at finite temperatures using a digital simulation of the transverse-field Ising model on a trapped-ion quantum computer. We efficiently measure the OTOC through local observables only, following separate Trotterized time evolution of each half of a variationally-prepared thermofield double state [2]. We use this technique to quantify the dependence of OTOC decay on the temperature using 6-qubit quantum circuits.

[1] Landsman et al. Nature 567, 61–65 (2019).

[2] Sundar, Bhuvanesh. arXiv:2006.15093.