Trotter errors from dynamical structural instabilities of Floquet maps in quantum simulation

Understand

We study the behavior of errors in the quantum simulation of spin systems with long-range multi-body interactions resulting from the Trotter-Suzuki decomposition of the time-evolution operator.

• We identify a regime where the Floquet operator underlying the Trotter decomposition undergoes sharp changes even for small variations in the simulation step size.
• This results in a time evolution operator that is very different from the dynamics generated by the targeted Hamiltonian, which leads to a proliferation of errors in the quantum simulation.
• These regions of sharp change in the Floquet operator, referred to as structural instability regions, appear typically at intermediate Trotter step sizes and in the weakly-interacting regime, and are thus complementary to recently revealed quantum chaotic regimes of the Trotterized evolution (Sieberer et al., npj Quantum Information 5, 1 (2019)).