Quantum Feedback Control of Multiple Superconducting Qubit

In this thesis I will present the results of my effort to implement quantum feedback control of superconducting qubits. The first goal of the thesis work was to build a control system capable of running feedback experiments. There has been tremendous progress in both coherence and high fidelity single shot readout of superconducting qubits. Latency in measurement can now be reduced to just a small percentage of a qubit coherence time. All these improvements in system parameters were very welcoming to measurement-based feedback control of quantum systems and error correction protocols. But feedback control experiments were still challenging to perform because we were still missing a capable controller to complete the feedback loop. The operations of the controller need to be fast, deterministic in terms of timing and flexible. To meet those demands, we implemented an all-in-one system that contains a digitizer, a demodulator, a state estimator and an AWG on a commercial field-programmable-gate-array (FPGA) board. The FPGA system shows superior performance in terms of throughput, timing stability and on-the-fly programmability compared to traditional technology.;The FPGA controller development has been a continuing effort. As the controller's capabilities became more sophisticated, the second goal of the thesis came into action: to use the control system to implement feedback experiments. As a proof of principle, we first successfully demonstrated reset of a single qubit in high entropy state to ground state of very high purity using active feedback protocol implemented on the FPGA system. We then tested our feedback platform on a system consisting of two superconducting qubits coupled to a cavity. Using the same experimental setup, we stabilized entanglement of the two qubits by two nominally distinct schemes: a "passive" reservoir engineering method and an "active" correction based on conditional parity measurements. Furthermore, the flexibility of our feedback controller enabled us to implement a "nested" feedback protocol that combined both schemes to get the best of both worlds.