Mitigating quasiparticle tunneling of the transmon qudit with charge parity measurements

As a promising platform for quantum computing, superconducting transmon circuits are widely used as qubits, with the lowest two energy levels as the computational basis. By design, the 0-1 transition is insensitive to the offset charge fluctuation in the standard transmon regime. As a natural extension, accessing the upper energy levels can be an attractive direction to efficiently encode quantum information in the transmon circuit. However, the upper energy levels are more vulnerable to offset charge fluctuation, which limits their application as a coherent quantum resource. We study one of the dominant mechanisms of offset charge fluctuations, the tunneling event of a quasiparticle across the Josephson junction, which switches the charge parity, shifts the frequencies of the energy levels, and alters the coupling strength. We take advantage of this effect by utilizing the third excited energy level for the direct dispersive readout of the charge parity state. Additionally, we mitigate the effects of quasiparticle tunneling by using the charge parity measurement result to pre-select the quantum evolution. This method gives us effectively deterministic quantum evolution unaffected by the charge parity switching. We demonstrate this method with a high-quality tantalum transmon in the standard charge insensitive regime (E_J / E_C = 50) with a common cavity-QED readout setup, available through remotely accessing the LLNL quantum design and integration testbed (QuDIT facility). This method enables us to access the lowest four energy levels of the transmon qudit encoding two qubits of quantum information. Our work improves the performance of a transmon circuit as a qudit system.