Effective Hamiltonian and parametric tuning for the cross-cross-resonance gate in the transmon model

Abstract

The two-qubit entangler is one of the most important components of quantum computers. The cross-cross resonance (CCR) gate has recently been proposed and shown to operate faster than the cross-resonance (CR) gate as an iSWAP gate. However, unlike the CR gate, the CCR gate requires frequency modifications of the input microwave pulses induced by a Stark shift. We present a theoretical study on the CCR gate in the two-transmon system. Using the Schrieffer-Wolff transformation and the rotating-wave approximation, we obtain both the effective Hamiltonian and the input microwave pulse frequencies of the CCR gate. It is well known that the static ZZ term degrades the performance of the CR gate in the transmon system. For the CCR gate, an additional dynamic ZZ term arises from the combined coupling to the qubits by the input microwave pulses, whose strength increases as the product of the two pulse amplitudes Ω0Ω1. We perform numerical simulations using the set of parameters for the IBM Hanoi quantum processor. We show that the CCR gate has a phase tunability and that varying the relative phase of the input microwave pulses can significantly improve the gate performance. This demonstrates that the static ZZ term in the CCR gate can be effectively reduced by optimizing the relative phase of the input microwave pulses.

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