Stable Toffoli Gate on Fixed-Frequency Superconducting Qutrits

Entangling gates in superconducting quantum computers suffer from imperfection of control and relaxation of qubits. The Toffoli gate, essential to various quantum algorithms and to certain fast error correction schemes, represents a particular challenge, as it is decomposed into at least six two-qubit gates, whose errors accrue on top of the increased probability of qubit relaxation due to the long gate time. While it is possible to significantly reduce the depth of the Toffoli gate by exploiting three-level, i.e., qutrit states internally, existing methods are susceptible to errors arising from frequency drifts due to charge fluctuation effects in the second excited state of the transmon. In this poster, we propose a novel qutrit-based implementation of the Toffoli gate that is inherently robust against such errors. The method is extensively validated through a pulse-level simulation and experiments performed on IBM Quantum machines. On one device, where the total Toffoli gate time is 2.510μs, we obtained average gate fidelity values of 0.928 ± 0.007 and 0.896 ± 0.036 from multiple measurements performed during the first one and twenty-four hours after calibrations, respectively, where the errors represent the standard deviations of the measurement results.