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Bulletin of the American Physical Society

Longitudinal qubit-resonator interaction in circuit QED

Philip Krantz, Simon Gustavsson, Fei Yan, Daniel L. Campbell, David K. Kim, Jonilyn Yoder, Arne L. Grimsmo, Jérôme Bourassa, Alexandre Blais, Andrew J. Kerman, Terry P. Orlando, William D. Oliver

Published Mar 15, 2017• 0 citations
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We present a circuit construction for a fixed-frequency superconducting qubit and show how it can be scaled up to a grid with strictly local interactions. The circuit QED realization we propose implements ${\ensuremath{\sigma}}_{z}$ type coupling between a superconducting qubit and any number of LCLCLC resonators. The resulting longitudinal coupling is inherently different from the usual ${\ensuremath{\sigma}}_{x}$ type transverse coupling, which is the one that has been most commonly used for superconducting qubits. In a grid of fixed-frequency qubits and resonators with a particular pattern of always-on interactions, coupling is strictly confined to nearest and next-nearest neighbor resonators; there is never any direct qubit-qubit coupling. We note that just a single unique qubit frequency suffices for the scalability of this scheme. The same is true for the resonators, if the resonator-resonator coupling constants are varied instead. A controlled phase gate between two neighboring qubits can be realized with microwave drives on the qubits, without affecting the other qubits. This fact is a significant advantage for the scalability of this scheme.
Multiphoton processes deteriorate the quantum nondemolition (QND) character of the dispersive readout in circuit QED, causing the readout to lag behind single- and two-qubit gates in both speed and fidelity. Alternative methods such as longitudinal readout have been proposed; however, it is unknown to what extent multiphoton processes hinder this approach. Here, we investigate the QND character of the longitudinal readout of the transmon qubit. We show that the deleterious effects that arise due to multiphoton transitions can be heavily suppressed with detuning because the longitudinal interaction strength is independent of the transmon-resonator detuning. We consider the effect of circuit disorder, the selection rules that act on the transmon, and the description of longitudinal readout in the classical limit of the transmon to qualitatively demonstrate that longitudinal readout is robust. We show that fast, high-fidelity QND readout of transmon qubits is possible with longitudinal coupling.