Grover’s Algorithm: A Step by Step Implementation in Qiskit

In the world of quantum computing, Grover’s algorithm stands out as a groundbreaking quantum search algorithm. It significantly speeds up the process of searching unsorted databases, making it a key player in the quest for quantum supremacy. This article will guide you through the steps of implementing Grover’s Algorithm in Qiskit, an open source quantum computing framework developed by IBM. Whether you’re a quantum computing novice or a seasoned professional, this guide will help you understand the intricacies of this powerful algorithm.

An Introduction to Grover’s Algorithm

Lov Grover, a researcher at Bell Labs, introduced Grover’s algorithm in 1996. It’s designed to search through an unsorted database with a quantum speedup, making it quadratically faster than any classical algorithm. This quantum advantage makes Grover’s algorithm a cornerstone of quantum computing.

The algorithm works by repeatedly applying a specific quantum operation, known as the Grover iterate, which amplifies the amplitude of the desired state, making it more likely to be measured. The key challenge in implementing Grover’s algorithm is constructing this Grover iterate for your given problem.

Using Qiskit for Grover’s Algorithm

Qiskit is a comprehensive open-source SDK for quantum computing. It provides tools for creating and manipulating quantum programs and running them on prototype quantum devices and simulators. It also provides a platform to write quantum computing programs in Python.

Installation of Qiskit

To use Qiskit, you must first install it. Here are the steps:

• Ensure that you have Python 3.5 or later installed on your system.
• Install Qiskit using pip by running the command “pip install qiskit”.
• Verify the installation by importing Qiskit in a Python shell and checking the version with “qiskit.__version__”.

Implementing Grover’s Algorithm in Qiskit

Now that you’ve installed Qiskit, let’s dive into the implementation of Grover’s Algorithm. We’ll start by importing the necessary modules:

from qiskit import QuantumCircuit, execute, Aer
from qiskit.visualization import plot_histogram

Next, we’ll create a function called phase_oracle to mark the specific elements in our database. This is done by flipping the sign of the state we’re searching for. In this example, we’ll be searching for the state |11>, so our oracle will be a controlled-Z gate:

def phase_oracle(circuit):
circuit.cz(0, 1)

Then, we’ll create a function for the Grover diffusion operator. This operator amplifies the marked states by inverting about the average amplitude:

def diffusion_operator(circuit):
circuit.h([0,1])
circuit.z([0,1])
circuit.cz(0,1)
circuit.h([0,1])

Lastly, we’ll construct the Grover iterate, which is the oracle followed by the diffusion operator. We’ll apply this iterate sqrt(N) times, where N is the number of elements in the database. Then, we’ll run and visualize the circuit:

grover_circuit = QuantumCircuit(2)
grover_circuit.h([0,1])
phase_oracle(grover_circuit)
diffusion_operator(grover_circuit)
grover_circuit.measure_all()

backend = Aer.get_backend(‘qasm_simulator’)
results = execute(grover_circuit, backend=backend, shots=1024).result()
counts = results.get_counts()
plot_histogram(counts)

Conclusion

There you have it, a step-by-step guide on how to implement Grover’s Algorithm in Qiskit. By understanding and implementing this quantum search algorithm, you’ll be well on your way to mastering the exciting field of quantum computing. Remember, the key to understanding quantum computing lies in continual learning and hands-on practice.