Nielsen complexity of coherent spin state operators

We calculate Nielsen???s circuit complexity of coherent spin state operators. An expression for the complexity is obtained by using the small angle approximation of the Euler angle parametrization of a general SO(3) rotation. This is then extended to arbitrary times for systems whose time evolutions are generated by couplings to an external field, as well as nonlinearly interacting Hamiltonians. In particular, we show how the Nielsen complexity relates to squeezing parameters of the one-axis twisted Hamiltonians in a transverse field, thus indicating its relation with pairwise entanglement. We further point out the difficulty with this approach for the Lipkin-Meshkov-Glick model and resolve the problem by computing the complexity in the Tait-Bryan parametrization.

Automated summary

In this study, the Nielsen circuit complexity of coherent spin state operators is calculated. The complexity expression is derived using the small angle approximation of the Euler angle parametrization. The results are extended to systems with time evolutions generated by external field couplings and nonlinearly interacting Hamiltonians. The relationship between Nielsen complexity and squeezing parameters, as well as pairwise entanglement, is investigated. The difficulty with this approach for the Lipkin-Meshkov-Glick model is identified and resolved by computing the complexity using the Tait-Bryan parametrization.