Super Quantum Search Algorithm with Weak Value Amplification and Postselection

TL;DR

This paper introduces a quantum search algorithm leveraging weak value amplification and postselection, enabling the solution of database searches in a single step with high probability, significantly reducing time complexity.

Contribution

The paper presents a novel quantum computation model that uses weak value amplification and postselection to drastically speed up database search algorithms.

Findings

Achieves database search in one step with high probability for large N.

Increases qubit count from n to 2n but greatly reduces time complexity.

Demonstrates the physical mechanism of weak value amplification accelerating quantum computation.

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.