Depth-First Grover Search Algorithm on Hybrid Quantum-Classical Computer

TL;DR

This paper introduces a hybrid quantum-classical approach called Depth-First Grover Search (DFGS) that efficiently handles multi-solution search problems on unstructured databases, demonstrating comparable or improved complexity and robustness.

Contribution

The paper presents a novel hybrid quantum-classical algorithm, DFGS, integrating depth-first search with Grover's algorithm for multi-solution problems, with detailed architecture and complexity analysis.

Findings

Achieves average complexity of O(m√N), comparable to standard Grover search.

Attains complexity of O(√p N) when all elements are solutions.

Demonstrates increased robustness and stability over traditional methods.

Abstract

We demonstrated the detailed construction of the hybrid quantum-classical computer. Based on this architecture, the useful concept of amplitude interception is illustrated. It is then embedded into a combination of Depth-First Search and Grover's algorithm to generate a novel approach, the Depth-First Grover Search(DFGS), to handle multi-solution searching problems on unstructured databases with an unknown number of solutions. Our new algorithm attains an average complexity of $\mathcal{O}(m\sqrt{N})$ which performs as efficient as a normal Grover Search, and a $\mathcal{O}(\sqrt{p}N)$ complexity with a manually determined constant $p$ for the case with all elements are solutions, where a normal Grover Search will degenerate to $\mathcal{O}(N\sqrt{N})$. The DFGS algorithm is more robust and stable in comparison.