An almost deterministic cooling by measurements

Nondeterministic measurement-based techniques are efficient in reshaping the population distribution of a quantum system but suffer from a limited success probability of holding the system in the target state. To reduce the experimental cost, we exploit the state-engineering mechanisms of both conditional and unconditional measurements and propose a two-step protocol assisted by a qubit to cool a resonator down to the ground state with a near-unit probability. In the first step, the unconditional measurements on the ancillary qubit are applied to reshape the target resonator from a thermal state to a reserved Fock state. The measurement sequence is optimized by reinforcement learning for a maximum fidelity. In the second step, the population on the reserved state can be faithfully transferred in a stepwise way to the resonator's ground state with a near-unit fidelity by the conditional measurements on the qubit. Intrinsic nondeterminacy of the projection-based conditional measurement is effectively inhibited by properly spacing the measurement sequence, which makes the Kraus operator act as a lowering operator for neighboring Fock states. Through dozens of measurements, the initial thermal average occupation of the resonator can be reduced by five orders in magnitude with a success probability over $95\%$.