Feedback control of a monitored system evolving adiabatically

Time evolution of a system evolving adiabatically while coupled weakly to a thermal bath can be described by a quantum adiabatic master equation in Lindblad form. In quantum annealing it is desirable is to maintain the state as the ground state of the time-dependent Hamiltonian. This is difficult due to diabatic or thermal transitions. We devised a quantum feedback control method to reverse the effect of thermal excitation. Under specific continuous measurement schemes, quantum trajectories of the measurement records can be obtained and feedbacks conditioned on these records can be applied to increase the ground state population. We derived the feedback master equation for markovian feedback (feedback delay $\tau \rightarrow 0$) and further gave the timescale condition for feedback Markovianity. However, realistic feedbacks are non-markovian and subjected to non-negligible feedback delay, detector efficiency and restrictions of the form of the feedback Hamiltonian. We studied the effectiveness of feedback control under such limitations and explored how the optimized feedback delay time depends on the annealing schedule.