Measurement-based quantum feedback controls for quantum computation
Song Zhang · eScholarship (California Digital Library) · 2020
The advance of experimental techniques in circuit quantum electrodynamics over last decadehas made it possible to monitor the evolution of qubits under continuous measurements in real time . This kind of measurements, as compared to the discrete ones, provides a stream of information for feedback to alter the system's quantum dynamics continuously in a desired manner, thus allowing broader possibilities. We obtain the information at a cost, the backaction on the states. However, the back-action turns out not to be just something disturbing and harmful to the control but instead can be harnessed, together with the control, to steer the system to our targets. This thesis discusses one such application, namely to use measurements to create entanglement from remote qubits under locally optimal control. It is illustrated that by carefully designing symmetric measurement and feedback operators, we can construct efficient Markovian or non-Markovian protocols which generate N-qubit W, general Dicke and Greenberger-Horne-Zeilinger states with high fidelity above 94% up to N = 100. In some cases, the fidelity even approaches unity. Following that, we describe how to take advantages of the continuous stream of information to protect the unitary dynamics of a quantum system subject to noises. We develop a practical protocol for continuous operation of a quantum error correcting code for protection of coherent evolution due to an encoded Hamiltonian against environmental errors, using the three qubit bit-flip code and bit-flip errors as a canonical example. We demonstrate, for both quantum memory and adiabatic Hamiltonians, that the protocol, once optimized, can significantly reduce logical errors with a performance which is close to the theoretical limit of the bit-flip code's capability. In the adiabatic Hamiltonian case, we also propose some novel correction operators instead of the conventional ones to further reduce the logical errors.