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Superconducting quantum circuits is one of the leading candidates for auniversal quantum computer. Designing novel qubit and multiqubitsuperconducting circuits requires the ability to simulate and analyze theproperties of a general circuit. In particular, going outside the transmonapproach, we cannot make assumptions on anharmonicity, thus precluding blackboxquantization approaches and necessitating the formal circuit quantizationapproach. We consider and solve two issues involved in simulating generalsuperconducting circuits. One of the issues is the handling of free modes inthe circuit, that is, circuit modes with no potential term in the Hamiltonian.Another issue is circuit size, namely the challenge of simulating stronglycoupled multimode circuits. The main mathematical tool we use to address theseissues is the linear canonical transformation in the setting of quantummechanics. We address the first issue by giving a provably correct algorithmfor removing free modes by performing a linear canonical transformation tocompletely decouple the free modes from other circuit modes. We address thesecond by giving a series of different linear canonical transformations toreduce intermode couplings, thereby reducing the problem to the weakly coupledcase and greatly mitigating the overhead for classical simulation. We benchmarkour decoupling methods by applying them to the circuit of two inductivelycoupled fluxonium qubits, obtaining several orders of magnitude reduction inthe size of the Hilbert space that needs to be simulated.

Free Mode Removal and Mode Decoupling for Simulating General Superconducting Quantum Circuits