# Introduction

Completed

Quantum computing promises to enable algorithms that are much faster than their classical counterparts for certain types of problems. This is one of the main reasons the space fleet wants to implement quantum computing, as it offers a computational speedup in certain problems.

However, not all problems are suitable for quantum computers. Identifying the problems for which a quantum speedup is possible and coming up with algorithms that offer it is an area of ongoing research.

One such algorithm is Grover's search algorithm - one of the most famous in quantum computing. The problem it solves is often referred to as "searching a database", but it's more accurate to think of it as "search problem" or "inverting a function": that is, given a function $f(x)$ that returns 0 or 1, find any input $x_0$ for which the function returns 1: $f(x_0) = 1$. This formulation seems rather mathematical at first, but it's powerful enough to express a broad class of problems. The core idea of Grover's algorithm also turns out to be an important building block of other, more complex quantum algorithms.

Get ready! Your first real task is here! In this module, we'll introduce the necessary concepts and tools for implementing Grover's algorithm and applying it to solve a problem that has challenged our interstellar communications division - assign a bandwidth to each space station so communications don't interfere. Then you'll demonstrate the implementation in Q#.

Finally, we'll outline some practical aspects of using Grover's algorithm for solving problems.

## Learning objectives

After completing this module, you'll be able to:

• Build quantum oracles that implement classical functions on a quantum computer.
• Explain the roles superposition, interference, and entanglement play in building quantum algorithms.
• Write a Q# program that uses Grover's algorithm to solve a graph coloring problem.
• Recognize the kinds of problems for which Grover's algorithm can offer speedup compared to classical algorithms.

## Prerequisites

You'll need basic knowledge of the principles of quantum computing: superposition, interference, entanglement, and measurement. For more information, see Explore the key concepts of quantum computing by using Q#.

You'll also need some familiarity with Q# and the Quantum Development Kit. For more information, see Create your first Q# program by using the Quantum Development Kit.