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Steering Quantum Dynamics via Bang-Bang Control: Implementing optimal fixed point quantum search algorithm

A robust control over quantum dynamics is of paramount importance for quantum technologies. Many of the existing control techniques are based on smooth Hamiltonian modulations involving repeated calculations of basic unitaries resulting in time complexities scaling rapidly with the length of the control sequence. On the other hand, the bang-bang controls need one-time calculation of basic unitaries and hence scale much more efficiently. By employing a global optimization routine such as the genetic algorithm, it is possible to synthesize not only highly intricate unitaries, but also certain nonunitary operations. Here we demonstrate the unitary control through the first implementation of the optimal fixed-point quantum search algorithm in a three-qubit NMR system. More over, by combining the bang-bang pulses with the twirling process, we also demonstrate a nonunitary transformation of the thermal equilibrium state into an effective pure state in a five-qubit NMR system.