A Long-Range Multi-Resonator Coupler

In the past decade, a variety of two-qubit couplers have been developed, with state-of-the-art gate fidelities exceeding 99.9% [1]. One drawback of many of these coupler architectures is their length limit. Longer two-qubit couplers naturally host distributed low-frequency modes with thermal population that increases exponentially with length, dephasing the coupled qubits. In practice, this restricts single-element coupler lengths to approximately 1 cm- limiting the connectivity of devices and, in-turn, the speed and efficacy of algorithms and error correction [2,3]. In this work, we investigate a coupler composed of a series of strongly coupled, nominally identical CPW resonators where the total length of the coupler is set by the number of resonators. The lowest coupler mode frequency is bounded by the inter-resonator coupling and largely independent of length, preventing exponential buildup of thermal population. In addition, the qubit-qubit ZZ is exponentially suppressed with length. This leads to a flexible design space where a wide range of coupler lengths exhibit low ZZ, low thermal population, and appreciable qubit-coupler dispersive interaction, useful for gates. We use this series-resonator coupler to implement a two-photon microwave-activated phase (MAP) gate between two transmon qubits. 

[1] L. Ding, M. Hays, Y. Sung, B. Kannan, J. An, A. Di Paolo, A. H. Karamlou, T. M. Hazard, K. Azar, D. K. Kim, B. M. Niedzielski, A. Melville, M. E. Schwartz, J. L. Yoder, T. P. Orlando, S. Gustavsson, J. A. Grover, K. Serniak, and W. D. Oliver Phys. Rev. X 13 031035 (2023) 

[2] B. Alexandre, A. L. Grimsmo, S. M. Girvin, A. Wallraff, Rev. Mod. Phys. 93 025005 (2021) 

[3] N. P. Breuckmann, J. N. Eberhardt, PRX Quantum 2 040101 (2021)