Find Ground State Energy with Qiskit

Learn how to find the ground state energy of quantum systems using Qiskit. This tutorial covers quantum circuits, variational methods, and practical examples for quantum chemistry applications.

Introduction

In this article, we’ll explore how to find the ground state energy of a quantum system using Qiskit. Let’s start with a simple example.

Basic Example

Here’s a simple Python example you can run in your browser:

import numpy as np

# Simple quantum state representation
# Bell state: (|00⟩ + |11⟩) / √2
bell_state = np.array([1/np.sqrt(2), 0, 0, 1/np.sqrt(2)])
print("Bell State amplitudes:")
print(bell_state)
print(f"\nState probabilities: {np.abs(bell_state)**2}")
print(f"Sum of probabilities: {np.sum(np.abs(bell_state)**2)}")

Bell State amplitudes:
[0.70710678 0.         0.         0.70710678]

State probabilities: [0.5 0.  0.  0.5]
Sum of probabilities: 0.9999999999999998

Try running this code cell! Click the play button or use the code tools above.

This represents a Bell state, which is a fundamental entangled state in quantum computing.

Qiskit Example

For the full Qiskit example, you’ll need to install Qiskit locally. Here’s the code:

# Note: This requires Qiskit installation
# Run: pip install qiskit numpy

import numpy as np
from qiskit import QuantumCircuit
from qiskit.quantum_info import Statevector

# Create a simple quantum circuit
qc = QuantumCircuit(2)
qc.h(0)  # Apply Hadamard gate
qc.cx(0, 1)  # Apply CNOT gate

# Get the statevector
state = Statevector.from_instruction(qc)
print("Quantum State:")
print(state)
print(f"\nState probabilities: {np.abs(state.data)**2}")

To run this code: 1. Install Qiskit: pip install qiskit numpy 2. Copy the code above 3. Run it in your Python environment or Jupyter notebook

Next Steps

We can extend this to find ground state energies using variational quantum eigensolvers (VQE) or other quantum algorithms.