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)