Digital Quantum Simulation, Trotter Errors, and Quantum Chaos of the Kicked Top
Dr. Lukas Sieberer (Institut für Quantenoptik und Quanteninformation, Universität Innsbruck, Österreich)

Quantum simulation enables studying the non-equilibrium dynamics of complex quantum many-body systems in regimes which are inaccessible to numerical methods. With universal digital quantum simulators, time evolution generated by a large class of Hamiltonians can be simulated by approximating the unitary time-evolution operator by a sequence of quantum gates. However, this “Trotterization" introduces an intrinsic source of errors. Our work gives Trotter errors in digital quantum simulation (DQS) of collective spin systems an interpretation in terms of a paradigmatic model system of quantum chaos, the kicked top. In particular, we show that Trotter errors in DQS of collective spin systems remain bounded up to arbitrarily long times in the regime of small Trotter steps, which corresponds to regular motion of the kicked top. Instead, quantum chaos in the top, which sets in above a sharp threshold value of the Trotter step size, leads to the proliferation of Trotter errors. Our results, which can be tested in various experimental platforms ranging from single atomic spins to trapped-ion quantum simulators, show, that DQS with comparatively large Trotter steps can retain controlled Trotter errors. It is thus possible to reduce the number of quantum gate operations required to represent the desired time evolution faithfully, thereby mitigating the effects of imperfect individual gate operations.