Super Quantum Search Algorithm with Weak Value Amplification and Postselection

Abstract: We propose a new model of quantum computation which aims to speed up quantum algorithms assisted by the weak value amplification and ancillay quantum register with the pre- and postelection. Within this model, we show that a quantum computer can solve a data base search of N entries in one step with probability close to one for large N, provided the post-selection on the ancillary quantum register is successful. In this model, to search a data base of N entries, the number of qubits grows from n to 2n, but there is a huge reduction in time complexity. Physically, this can be understood as the effect of weak value amplification that arises due to the pre- and postselection of the ancillary register which interacts with the n qubit register where quantum search is performed. This effectively accelerates the computation and takes the state of quantum computer much ahead in time, compared to what one would obtain without weak value amplification and post-selection.