A Fast fixed-point Quantum Search Algorithm by using Disentanglement and Measurement

TL;DR

This paper introduces a novel quantum search method that uses disentanglement and measurement to efficiently locate targets in an unsorted database, overcoming the limitations of unknown target counts with improved success probability.

Contribution

It proposes a new stopping scheme for quantum search that is simpler and more efficient than existing fixed-point methods, requiring minimal additional resources.

Findings

Ensures success probability > 50% for practical target ratios

Simpler than quantum counting and more efficient than fixed-point schemes

Maintains the same order of complexity as Grover's algorithm, with slight slowdown

Abstract

Generic quantum search algorithm searches for target entity in an unsorted database by repeatedly applying canonical Grover's quantum rotation transform to reach near the vicinity of the target entity. Thus, upon measurement, there is a high probability of finding the target entity. However, the number of times quantum rotation transform is to be applied for reaching near the vicinity of the target is a function of the number of target entities present in an unsorted database, which is generally unknown. A wrong estimate of the number of target entities can lead to overshooting or undershooting the targets, thus reducing the success probability. Some proposals have been made to overcome this limitation. These proposals either employ quantum counting to estimate the number of solutions or fixed-point schemes. This paper proposes a new scheme for stopping the application of quantum rotation transformation on reaching near the targets by disentanglement, measurement and subsequent processing to estimate the distance of the state vector from the target states. It ensures a success probability, which is greater than half for all practically significant ratios of the number of target entities to the total number of entities in a database. The search problem is trivial for remaining possible ratios. The proposed scheme is simpler than quantum counting and more efficient than the known fixed-point schemes. It has same order of computational complexity as canonical Grover`s search algorithm but is slow by a factor of two and requires two additional ancilla qubits.