SONAR: a quantum harmonic balance technique for identifying nonlinear resonances in systems of many coupled modes

Spurious nonlinear processes often limit both the readout and gate operations of superconducting qubits. Recent work has shown that these processes can be analyzed and identified by solving numerically for the Floquet modes of a given system. While this technique has shown excellent agreement with experiments for systems with one to two quantum modes, it is not scalable when considering systems of many coupled linear and nonlinear modes. In this talk, we introduce a simple technique, which we name SONAR, for identifying and tracking nonlinear processes in systems of many coupled modes. This technique is based on quantum harmonic balance and careful tracking of ac-Stark shift effects, and is easily extended to multiple (not necessarily commensurate) drives. We present numerical results for systems of up to 15 coupled modes obtained on a laptop and demonstrate close agreement between theory and experimental data.