Digital quantum simulation of bosonic systems and quantum complementarity

Abstract: Digital quantum simulation has emerged as a powerful approach to investigate complex quantum systems using digital quantum computers. Many-particle bosonic systems and intricate optical experimental setups pose significant challenges for classical simulation methods. Utilizing a recently developed formalism that maps bosonic operators to Pauli operators via the Gray code, we digitally simulate interferometric variants of Afshar's experiment on IBM's quantum computers. We investigate the analogous experiments of Unruh and Pessoa J\'unior, exploring discussions on the apparent violation of Bohr's complementarity principle when considering the entire experimental setup. Furthermore, we analyze these experiments within the framework of an updated quantum complementarity principle, which applies to specific quantum state preparations and remains consistent with the foundational principles of quantum mechanics. Our quantum computer demonstration results are in good agreement with the theoretical predictions and underscore the potential of quantum computers as effective simulators for bosonic systems.