Influence of Trotterization error on single-particle tunneling

Abstract

Existing superconducting quantum devices struggle to simulate spatial quantum tunneling as it is exponentially slow and inherently nonlocal. The Suzuki-Trotter algorithm (STA) offers a practical solution for existing quantum hardware by approximating nonlocal evolution with a local two-qubit gate sequence that requires no ancilla qubits and preserves physical interpretability. However, estimating the required gate count from naive fidelity-based error bounds yields values exceeding the constraints imposed by noise and decoherence in real devices. Here, we fully characterize STA for a semiclassical tunneling model by adapting the Wentzel-Kramers-Brillouin approximation. We find that, in the general case, tunneling is suppressed by resonance detuning. In contrast, if STA preserves the target resonance, tunneling rates are exponentially enhanced via non-perturbative renormalization, dramatically reducing the gate count required to observe tunneling and thus benefiting from large Trotter steps$\unicode{x2013}$equally natural for existing quantum hardware. However, for the latter regime, we further find that Floquet mixing of quasi-energy levels reconstructs the low-energy spectrum and strongly deforms tunneling dynamics by introducing additional allowed regions. Based on the semiclassical picture, we conjecture interplay of tunneling and large-step STA in the presence of topology-altering modifications, such as staggered potential modulation$\unicode{x2013}$a subject of future work. Our findings enable direct tunneling simulations on existing superconducting platforms, providing a controlled platform for studying the nontrivial interplay of tunneling and STA, with the possibility of addressing the effects of noise, disorder, and interaction.