Direct Calculation of the ZZ-interaction Rates in the Multi-Mode circuit-QED

Superconducting quantum processors might suffer from unwanted ZZ-interactions which naturally arise as a result of the finite and small anharmonicities of the Transmon qubits. Non-zero ZZ-terms in the qubit Hamiltonians can lead to the accumulation of the spurious phases during the execution of certain two-qubit gates. Recently novel qubit-qubit couplers have been proposed to suppress the ZZ-interactions while keeping a finite exchange coupling strength necessary to run the two-qubit gates. These new couplers typically involve multiple modes and their engineering requires diagonalization of the multi-mode Hamiltonians which can very quickly become computationally demanding as the number of modes of the coupler increases. Here we describe a new method for the accurate calculation of the ZZ-rates in the multi-mode circuit-QED by capturing their frequency dependence with simple relations of the entries of the multiport impedance matrix defined between the qubit ports. We observe very good agreement between the predictions of our method and the measurement data collected from the multi-qubit devices. Our method being an extension of the framework developed in (**) makes the quantum microwave engineering of the superconducting qubits more streamlined.

(*) Firat Solgun, Srikanth Srinivasan, “Direct calculation of the ZZ-interaction rates in the multi-mode circuit-QED”, arXiv:2111.05765.

(**) Firat Solgun, David P. DiVincenzo and Jay M. Gambetta, “Simple Impedance Response Formulas for the Dispersive Interaction Rates in the Effective Hamiltonians of Low Anharmonicity Superconducting Qubits”, IEEE Transactions on Microwave Theory and Techniques, Volume: 67, Issue: 3, March 2019.

*F. S. acknowledges support from Intelligence Advanced Research Projects Activity (IARPA) under contract W911NF-16-1-0114-FE.