Joint quantum state tomography of an entangled qubit–resonator hybrid

Abstract

The integration of superconducting qubits and resonators in one circuit offers a promising solution for quantum information processing (QIP), which also realizes the on-chip analogue of cavity quantum electrodynamics (QED), known as circuit QED. In most prototype circuit designs, qubits are active processing elements and resonators are peripherals. As resonators typically have better coherence performance and more accessible energy levels, it is proposed that the entangled qubit–resonator hybrid can be used as a processing element. To achieve such a goal, an accurate measurement of the hybrid is first necessary. Here we demonstrate a joint quantum state tomography (QST) technique to fully characterize an entangled qubit–resonator hybrid. We benchmarked our QST technique by generating and accurately characterizing multiple states, e.g. | gN 〉 + | e ( N − 1)〉 where (| g 〉 and | e 〉) are the ground and excited states of the qubit and (|0〉,…,| N 〉) are Fock states of the resonator. We further provided a numerical method to improve the QST efficiency and measured the decoherence dynamics of the bipartite hybrid, witnessing dissipation coming from both the qubit and the N -photon Fock state. As such, the joint QST presents an important step toward actively using the qubit–resonator element for QIP in hybrid quantum devices and for studying circuit QED.