  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.
