Implementing Grover'S Algorithm In Quantum Computing

Introduction

Quantum computing is an evolving field that leverages the principles of quantum physics to process information. Among the variety of quantum algorithms available, Grover's algorithm deserves particular attention. It provides a quantum solution for searching an unsorted database, offering a significantly faster approach compared to classical algorithms.

In this blog, we will delve into implementing Grover's Algorithm utilizing IBM's quantum computing SDK, Qiskit.

Understanding Grover's Algorithm

Grover's algorithm is quintessential for unstructured search problems, where we have an unsorted database, and the challenge is to find a specific element. Instead of going through each element as we do in classical computing, Grover's algorithm allows us to find the required element in fewer steps, executing in √N time as against N needed in a classical system.

Implementing Grover's Algorithm using Qiskit

To start with, be sure to install Qiskit on your local system. The following code snippet installs Qiskit:

pip install qiskit

Now let's move onto the implementation itself:

from qiskit import *
from qiskit.visualization import plot_histogram
from qiskit.aqua.algorithms import Grover
from qiskit.aqua.components.oracles import LogicalExpressionOracle

# Defining the problem
logical_expression = '((A & B) & ¬C)'

oracle = LogicalExpressionOracle(logical_expression)
grover = Grover(oracle)

result = grover.run(BasicAer.get_backend('qasm_simulator'), shots=1024)
plot_histogram(result.measurement)

In the above python code snippet, we start by importing the necessary classes from Qiskit. We define the problem statement using a LogicalExpressionOracle. Here, 'A', 'B', and 'C' represents our unsorted database, and the logical expression ((A & B) & ¬C) phases the state we are looking for.

Grover's Algorithm is run on a quantum simulator with a defined number of shots. The end result is visualized using the plot_histogram module, which will display the amplitudes of our quantum states on completion.

Conclusion

Grover's algorithm is a testament to the potential capabilities quantum computing holds over classical computing. Utilizing IBM's Qiskit SDK, the journey into quantum algorithms becomes much more accessible and decipherable. This simple yet powerful quantum procedure shapes the path of computational search problems towards a more efficient route.