Experimental Realization of Optimal Time-Reversal on an Atom Chip for Quantum Undo Operations

The authors report the use of the dressed chopped random basis optimal control algorithm to realize time-reversal procedures. The latter are aimed for the implementation of quantum undo operations in quantum technology contexts as quantum computing and quantum communications.. The last performed operation can be time-reversed via the undo command so as to perfectly restore a condition in which any new operation, chosen by the external user, can be applied. By generalizing this concept, the undo command can also allow for the reversing of a quantum operation in a generic time instant of the past. Here, thanks to optimal time-reversal routines, all these functionalities are experimentally implemented on the fivefold F=2$F=2$ Hilbert space of a Bose-Einstein condensate of non-interacting Rb-87 atoms in the ground state, realized with an atom chip. Each time-reversal transformation is attained by designing an optimal modulated radio frequency field, achieving on average an accuracy of around 92% in any performed test. The experimental results are accompanied by a thermodynamic interpretation based on the Loschmidt echo. These findings are expected to promote the implementation of time-reversal operations in a real scenario of gate-based quantum computing with a more complex structure than the five-level system considered here.