Entanglement stabilization by synchronous and asynchronous feedback

Quantum feedback for error correction is now an important component of superconducting quantum information processing. We have implemented two feedback schemes, autonomous (AT) and measurement-based (MB), to stabilize entanglement between two transmon qubits coupled to a cavity. The two qubits are coupled with nearly equal dispersive shifts to the cavity, such that a cavity drive maps the qubits' parity onto the cavity state. Entanglement is autonomously stabilized by applying continuous photon-number-selective Rabi drives on qubit transitions with phases conditioned on the cavity state. Alternatively, entanglement can be stabilized in a measurement-based scheme by directing the cavity output via a high-fidelity measurement chain to an FPGA (Field Programmable Gate Array) which applies pi/2 pulses to the qubits with phases conditioned on the measured signal. A synchronous protocol stabilizes entanglement for a fixed duration using either scheme resulting in a target Bell state with an unconditioned fidelity in excess of 55 {\%} for MB and 77 {\%} for AT. Furthermore, we have enhanced the fidelity of the entanglement by implementing an asynchronous ``wait until success'' protocol conditioning the tomography on a parity measurement in real time.