Quantization of Large Superconducting Circuits with Tensor Networks*

We report on efficient quantum simulation of large superconducting circuits using matrix product states (MPS) and the density matrix renormalization group (DMRG) technique. We analyze a circuit containing a chain of Josephson junctions, forming a superinductor, with a flux-tunable compound center junction. Kuzmin et al. explored similar circuits experimentally, achieving super strong coupling in circuit electrodynamics [1]. We obtain the lowest-lying eigenstates and energies for a chain length of 40 Josephson junctions with derived error bounds. Using these tensor network techniques we investigate the offset charge sensitivity of the circuit as a function of compound junction flux, which is not amenable to classical analysis and is intractable via exact diagonalization.

[1] R. Kuzmin et al., npj Quantum Information 5, 20 (2019)