Prochain séminaire

Séminaire interne LPMMC

Anton Khvalyuk (LPMMC)
Influence of Trotterization error on single-particle tunneling
le mercredi 03 avril 2024 à 11:00
Lieu : G421

Personne à contacter : Denis Basko ()

Quantum simulation of the single-particle tunneling problem by means of the Suzuki-Trotter approximation (STA) is analyzed. The target system describes a particle hopping across a chain of sites with position-dependent potential profile. The latter is assumed to be smooth and to posses several local minima separated by a potential barrier, arranging a tunneling problem between the localized states in different minima. The conducted analysis confirms the naive criteria of applicability max{T,P} ≪ 1/δt (with T, P being the typical scales of kinetic and potential terms, respectively), while also revealing the structure of error and its actual behavior with system parameters. Notably, in certain cases we find an exponential acceleration of tunneling, while other configurations lead to a complete suppression of the latter. Analysis of the case of large Trotter step is also performed, with the main result being the reconstruction of the low-energy spectrum due to coupling between states with energy difference close to 2π/δt. The connection of the obtained results with the rigorous upper error bounds on the STA error is discussed, with particular emphasis on the reasons for the fact that these rigorous bounds are not always saturated. We also point out that the proposed problem can be directly implemented on existing quantum devices arXiv:2012.00921. The talk is based on the recent paper arXiv:2312.04735.