Quantum algorithm for unstructured search of ranked targets

TL;DR

This paper introduces a new phase-encoding method for Grover's quantum search algorithm that incorporates item priorities into phases, compares it with amplitude encoding, and analyzes robustness and effectiveness in finding highly prioritized items.

Contribution

It proposes a novel phase-based encoding for priorities in Grover's algorithm and compares its performance and noise robustness to amplitude-based encoding.

Findings

Phase encoding can effectively incorporate priorities.

Performance depends on priority parameters and phase error magnitude.

Phase encoding shows increased probability of finding top-priority items under certain conditions.

Abstract

Grover's quantum algorithm can find a marked item from an unstructured database faster than any classical algorithm, and hence it has been used for several applications such as cryptanalysis and optimization. When there exist multiple marked items, Grover's algorithm has the property of finding one of them uniformly at random. To further broaden the application range, it was generalized so that it finds marked items with probabilities according to their priority by encoding the priority into amplitudes applied by Grover's oracle operator. In this paper, to achieve a similar generalization, we examine a different encoding that incorporates the priority into phases applied by the oracle operator. We compare the previous and our oracle operators and observe that which one performs better depends on priority parameters. Since the priority parameters can be considered as the magnitude of the correlated phase error on Grover's oracle operator, the analysis of our oracle operator also reveals the robustness of the original Grover's algorithm against correlated noises. We further numerically show that the coherence between multiple marked items tends to increase the probability of finding the most prioritized one in Grover's algorithm with our oracle operator.