Grover's Algorithm

Introduction

Imagine a massive collection of unsorted and unfiltered data, and from that, we need to find something useful. For example, if there are a thousand boxes in front of you, but only one of them contains a surprise gift, it would be extremely tedious and time-consuming to open each box one by one to find the right one.

A classical computer would solve this problem sequentially, checking each item one at a time. However, quantum computing offers a more efficient solution.

Grover’s Algorithm is a powerful quantum computing method that leverages the property of superposition to significantly speed up search and extraction processes. It can search through an unsorted database of N items and identify the correct item in approximately √N steps, drastically reducing computational effort and time.

Though Grover’s Algorithm has a simple function, its applications in quantum computing outperform classical methods in large-scale searches with massive datasets, making it a promising approach for the future of quantum computing.

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How It Works

My implementation of Grover’s Algorithm demonstrates its working with two qubits, meaning there are four possible states: |00⟩, |01⟩, |10⟩, and |11⟩. The goal is to search for the |11⟩ state efficiently.

Steps in Grover’s Algorithm:

1. Superposition:

   • Initially, we ensure that all four possible states are in equal quantum superposition, allowing the system to explore all possibilities simultaneously.
   • This is achieved using Hadamard gates, which transform qubits into a superposition state.

2. Oracle:

   • A special quantum function called an Oracle is applied, marking the correct answer by flipping its phase using quantum logic gates whenever the required state is found.

3. Amplification:

   • The algorithm amplifies the probability of measuring the correct answer while reducing the probabilities of incorrect ones.
   • This is done using the Grover Diffusion Operator (inversion about the mean), increasing the likelihood of selecting the correct state upon measurement.

4. Measurement:

   • Finally, when the system is measured, it collapses into its most probable state.
   • Due to the amplification step, the correct state is observed with a high probability.
   • Running the algorithm multiple times further increases the confidence in the correct result.

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Expected Results

On running this code, the state |11⟩ should have the highest probability measurement since that is our required state. If the algorithm works correctly, |11⟩ should be observed with maximum overall probability as shown in the results.

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Applications

• Database search: Efficiently searching through large datasets.
• Cryptanalysis: Used in breaking cryptographic hash functions.
• Optimization problems: Finding optimal solutions in large solution spaces.
• Pattern recognition: Identifying patterns in machine learning and AI.

Grover’s Algorithm showcases the true potential of quantum computing, making it a revolutionary approach to solving complex problems more efficiently than classical methods.

Steps to run the file (WINDOWS)

• Clone the repo:

git clone https://github.com/kaavs1696/ACM-Task.git
cd ACM-Task

• Install the required libraries to run the file

pip install -r requirements.txt

• Run the python file

python acm_task.py