This paper explores the quantum complexity of bosonic oscillator systems using a geometric approach. It addresses limitations of previous methods by focusing on the Lie algebra rather than the group, providing a more computable definition, particularly for high-dimensional Hilbert spaces. The authors investigate the complexity of unitary operators associated with harmonic, inverted harmonic, and coupled harmonic oscillators, as well as an anharmonic oscillator with a cubic term, demonstrating the generality of their approach.

Satyaki Chowdhury, Martin Bojowald, Jakub Mielczarek