Exploring parametric gate rate limits in transmons and other couplers (part 1)

Many superconducting quantum processors rely on strong parametric drives acting on qubits or an associated coupler to implement fast gates. However, these drives can induce unwanted excitations of the qubit or coupler, setting an upper limit on the rate, and hence fidelity, of operations. Here, we explore strong, low-frequency drives on transmon qubits as prototypical parametric couplers to determine how the drive strength threshold (η_max) depends on circuit parameters such as E_J, and E_C. We examine transmon designs with similar frequency and differing anharmonicities to evaluate the relative strength of four-wave parametric processes for single- and two-qubit parametric gates. We find that the lowest anharmonicity devices (α=-21 MHz) tolerate the highest effective photon number and have the highest figure of merit for processes which scale as αη³. The more typical transmon design (α=-136 MHz) tolerates a lower effective photon number, but the increased anharmoncity leads to the largest product αη² of the devices tested. The highest anharmonicity design (α=-290 MHz) has the lowest η_max measured, but the large anharmonicity makes for favorable scaling of processes involving the product αη. We also discuss extending these studies to arrayed nonlinear elements as well as other coupler elements such as SNAILs, and how these data affect the overall use of parametrically driven qubit processors.