# Function Maximization with Dynamic Quantum Search

## TL;DR

This paper introduces an iterative quantum algorithm for dynamic function maximization, updating search results with a quantum search approach and verifying its effectiveness through simulations on the Knapsack problem.

## Contribution

It presents a novel quantum algorithm that adapts to dynamic search results for function maximization, verified through extensive numerical simulations.

## Key findings

- Successful simulation of the quantum algorithm up to 30 qubits
- Effective implementation of the dynamic oracle function
- Potential for improved optimization in quantum computing

## Abstract

Finding the maximum value of a function in a dynamic model plays an important role in many application settings, including discrete optimization in the presence of hard constraints. We present an iterative quantum algorithm for finding the maximum value of a function in which prior search results update the acceptable response. Our approach is based on quantum search and utilizes a dynamic oracle function to mark items in a specified input set. As a realization of function optimization, we verify the correctness of the algorithm using numerical simulations of quantum circuits for the Knapsack problem. Our simulations make use of an explicit oracle function based on arithmetic operations and a comparator subroutine, and we verify these implementations using numerical simulations up to 30 qubits.