Rapid optimization of working parameters of microwave-driven multi-level qubits for minimal gate leakage

We propose an effective method to optimize the working parameters (WPs) of microwave-driven quantum logical gates implemented with multi-level physical qubits. We show that by treating transitions between each pair of levels independently, intrinsic gate errors due primarily to population leakage to undesired states can be estimated accurately from spectroscopic properties of the qubits and minimized by choosing appropriate WPs. The validity and efficiency of the approach are demonstrated by applying it to optimize the WPs of two coupled rf SQUID flux qubits for controlled-NOT (CNOT) operation. The result of this independent transition approximation (ITA) is in good agreement with that of dynamic method (DM). Furthermore, the ratio of the speed of ITA to that of DM scales exponentially as 2^n when the number of qubits n increases.