Microwave-Activated Control-Z Gate for Fixed-Frequency Fluxonium Qubits.

A unique feature of a fluxonium superconducting circuit at half flux quantum is the hierarchy of its low energy transitions: the transition frequency between the states 1 and 2 can be an order of magnitude higher than between states 0 and 1. This feature allows combination of long information storage with fast information processing in a single circuit. We propose a microwave activated control-z (CZ) gate for two fixed-frequency (i.e., parked at flux sweet spot) fluxonium qubits coupled via a common capacitance or inductance. The hybridization of noncomputational states 21 and 12 by capacitive coupling or hybridization of computational states 10 and 01 by inductive coupling lifts the degeneracy between 10-20 and 11-21 transitions. As a result, resonant driving of 11-21 transition can lead to an extra π-phase accumulation for the state 11, which is equivalent to the CZ gate. Furthermore, for the case of 10-01 inductive coupling, the gate can be implemented by driving 10-02 transition, which reduces undesired effects on the remaining computational states since the transition is well separated in frequency. Our simulations show that these CZ gates have fidelity well above 99% with gate time below 100 ns. We discuss the application of the proposed gates to both 2D and 3D circuit QED.