Tensor Network methods for the simulation of the dynamic of superconducting circuits.

Tensor Networks (TN) methods have been used extensively to study the properties of many body problems. Recently, new methods were created that have permitted to extend the TN toolbox to a larger class of problems. Those methods allow to build TN representation of large quantum-systems efficiently and to represent complex functions in TN form, that are seemingly unrelated to the many-body problem. At the same time, the development and scaling of quantum computing platforms based on bosonic systems requires the creation of more efficient simulation methods to accurately predict the dynamic of larger systems.

In this work, we apply those TN networks techniques to represent and evolve open bosonic systems in a reduced manifold. By exploiting the well-behaved properties of qubit systems to represent their density matrix, including low-entanglement and purity, we obtain a compressed representation. We show that this method allows Lindblad simulations of those systems with an exponential speed-up in the size of the system of study compared to other techniques. These results pave the way towards a potential path for efficient simulation of open many-body bosonic systems.