  We propose a hybrid quantum system consisting of a magnetic particle
inductively coupled to two superconducting transmon qubits, where qubit-qubit
interactions are mediated via magnons. We show that the system can be tuned
into three different regimes of effective qubit-qubit interactions, namely a
transverse ($XX + YY$), a longitudinal ($ZZ$) and a non-trivial $ZX$
interaction. In addition, we show that an enhanced coupling can be achieved by
employing an ellipsoidal magnet, carrying anisotropic magnetic fluctuations. We
propose a scheme for realizing two-qubit gates, and simulate their performance
under realistic experimental conditions. We find that iSWAP and CZ gates can be
performed in this setup with an average fidelity $\gtrsim 99 \% $ , while an
iCNOT gate can be applied with an average fidelity $\gtrsim 88 \%$. Our
proposed hybrid circuit architecture offers an alternative platform for
realizing two-qubit gates between superconducting qubits and could be employed
for constructing qubit networks using magnons as mediators.
