Optimal Crossing of a Quantum Critical Point with a Noisy Control Field

Quantum evolution is widely used for state transformation, e.g., through adiabatic annealing. Crossing quantum phase transitions is of particular interest as it allows for the preparation of nontrivial correlated states. However, this scheme is challenging due to the closure of the energy gap and unavoidable Kibble-Zurek excitations. In the presence of noise, the problem is even more severe due to the recently discovered anti-Kibble-Zurek behavior, where slower driving results in the accumulation of more noise-induced excitations. Focusing on the canonical example of the transverse-filed Ising model, we show that optimal control provides fast shortcuts to the adiabatic evolution, which, in the absence of noise, can exactly prepare many-body ground states on the other side of a quantum critical point in a finite time. It also provides remarkable advantages in the presence of a noisy control field. We demonstrate that the optimal protocols contain both bang-bang and singular oscillatory segments in agreement with Pontryagin's minimum principle.