Quantum feedback error correction of a monitored system evolving adiabatically

We devise a quantum feedback error correction method to reverse the effect of thermal excitations in quantum annealing. Conditioned on the output signal I(t) from continuous measurement records, feedback is applied to an adiabatically evolving system in the hopes of increasing the ground state population at the end of the anneal. We propose an experimental setting for such continuous measurement and feedback in the case of superconducting flux qubits. We simulate the error correction performance of a system weakly coupled to a thermal bath based on methods like quantum trajectories and quantum bayesian updates. We also derive a feedback master equation for markovian feedback (feedback delay $\tau\rightarrow 0$) and further give the timescale condition for feedback Markovianity. Realistic feedbacks are also subjected to non-negligible feedback delay, detector efficiency, and restrictions on the form of the feedback Hamiltonian due to experimental challenges. We therefore study the effectiveness of feedback correction under such limitations and explore how the optimized feedback delay time depends on the annealing schedule and limitations in other experimental parameters.