Free Mode Removal and Mode Decoupling for General Superconducting Quantum Circuits

Superconducting quantum circuits is one of the leading candidates for a universal quantum computer. Designing these circuits requires the ability simulate and analyze the properties of a general superconducting circuit. In particular, going outside the transmon approach, we cannot make assumptions on anharmonicity, thus precluding blackbox quantization approaches. We consider a few issues involved in simulating general superconducting circuits. One of the issues often faced is the handling of free modes in the circuit, that is, circuit modes with vanishing frequency. Another issue is circuit size, namely the challenge of simulating large circuits. The main mathematical tool we use to address these issues is linear canonical transformations in the setting of quantum mechanics. We address the first issue by giving a provably correct algorithm for removing free modes by performing a linear canonical transformation to completely decouple the free modes from other circuit modes. We address the second by giving a series of different linear canonical transformations to reduce inter-mode couplings, thereby reducing the overhead for classical simulation.