A multilevel tensor network compression technique for simulating Lindblad dynamics in superconducting circuits

Designing superconducting quantum hardware requires simulation tools that can account for various deviations from ideal scenarios. This, in turn, requires approaches that automatically detect certain structures and leverage them to make the computation affordable. Here, we develop a tensor network based technique to simulate the Lindblad dynamics of a few interacting bosonic modes with a focus on superconducting quantum circuits. The technique detects and takes advantage of two very common situations: (i) the density matrix being pure or not far from pure and (ii) the entanglement between different modes being moderate (typically qubit-like). However, (iii) the occupation of the modes can be arbitrarily high (making naïve truncations inefficient). To leverage these features, we use three different nested levels of tensor network compression: (i) we work with a global purification of the density matrix, (ii) we compress the connection between different modes to account for the moderate entanglement and (iii) we use a quantics representation of the Fock occupation number. We showcase the technique for the simulation of large cat qubits as well as for the ionization of transmon qubits, demonstrating orders-of-magnitude speed-up with respect to brute force approaches. In the latter example, it brings the simulation, previously reported on a large supercomputing infrastructure, to laptop level. The favorable scaling with system size should bring genuine computer assisted design of these systems within scope.