Drive-induced nonlinearities of cavity modes coupled to a transmon ancilla

Abstract

High-Q microwave cavity modes coupled to transmon ancillas provide a hardware-efficient platform for quantum computing. Due to their coupling, the cavity modes inherit finite nonlinearity from the transmons. In this paper, we theoretically and experimentally investigate how an off-resonant drive on the transmon ancilla modifies the nonlinearities of the cavity modes in qualitatively different ways, depending on the interrelation among cavity-transmon detuning, drive-transmon detuning, and transmon anharmonicity. For a cavity-transmon detuning that is smaller than or comparable to the drive-transmon detuning and transmon anharmonicity, the off-resonant transmon drive can induce multiphoton resonances among cavity and transmon excitations that strongly modify cavity nonlinearities as drive parameters vary. For a large cavity-transmon detuning, the drive induces cavity-photon-number-dependent ac Stark shifts of transmon levels that translate into effective cavity nonlinearities. In the regime of weak transmon-cavity coupling, the cavity Kerr nonlinearity relates to the third-order nonlinear susceptibility function χ(3) of the driven ancilla. This susceptibility function provides a numerically efficient way of computing the cavity Kerr, particularly for systems with many cavity modes controlled by a single transmon. It also serves as a diagnostic tool for identifying undesired drive-induced multiphoton resonance processes. Lastly, we show that by judiciously choosing the drive amplitude, a single off-resonant transmon drive can be used to cancel the cavity self-Kerr nonlinearity or the intercavity cross-Kerr. This provides a way of dynamically correcting the cavity Kerr nonlinearity during bosonic operations and quantum error correction protocols that rely on the cavity modes being linear.

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