Characterization and tomography of a hidden qubit*

In circuit-based quantum computing it is typically assumed that the available gate set consists of single qubit gates acting on each individual qubit as well as an entangling gate between pairs of qubits. In some physical architectures, not all qubits may be addressable, but some may be hidden and only connected to another control qubit. In this case, no single qubit operations can be applied to the hidden qubit and its state cannot be measured directly, but entangling gates with the control qubit can be carried out. Tomography of the combined two-qubit system is still possible on the combined two-qubit system whenever an iSWAP-type interaction in combination with a controlled-phase gate and single qubit operations on the control qubit is available. In our experiment we use transmon-type superconducting qubits along with parametric tunable-coupler gates to realize both types of two-qubit interactions. We further discuss the tune-up process required to completely characterize the gate set used for tomography and we evaluate the resulting fidelities.