Grover Search Inspired Alternating Operator Ansatz of Quantum Approximate Optimization Algorithm for Search Problems

TL;DR

This paper translates Grover's search algorithm into the Quantum Approximate Optimization Algorithm framework using adiabatic and Trotterization techniques, aiming to replicate Grover's optimal search behavior without iterative learning.

Contribution

It introduces a novel approach to embed Grover's search into QAOA by leveraging adiabatic quantum computing and Trotterization, bypassing traditional iterative methods.

Findings

Successful translation of Grover search into QAOA framework

Derivation of variational parameters matching Grover's optimal performance

Potential for more efficient quantum search algorithms

Abstract

We use the mapping between two computation frameworks , Adiabatic Grover Search (AGS) and Adiabatic Quantum Computing (AQC), to translate the Grover search algorithm into the AQC regime. We then apply Trotterization on the schedule-dependent Hamiltonian of AGS to obtain the values of variational parameters in the Quantum Approximate Optimization Algorithm (QAOA) framework. The goal is to carry the optimal behavior of Grover search algorithm into the QAOA framework without the iterative machine learning processes.