US government takes $2 billion equity stake in nine quantum computing firms

Introduction

In this tutorial, we'll explore quantum computing using Qiskit, the open-source quantum computing framework. With the US government investing $2 billion in quantum computing firms, understanding this emerging technology is becoming increasingly important. We'll build a practical quantum circuit that demonstrates quantum superposition and entanglement - core concepts in quantum computing that make quantum computers potentially exponentially more powerful than classical computers.

Prerequisites

• Python 3.7 or higher installed on your system
• Basic understanding of quantum computing concepts (qubits, superposition, entanglement)
• Intermediate knowledge of Python programming
• Installed Qiskit library (can be installed via pip)

Step-by-step instructions

Step 1: Install and Import Required Libraries

First, we need to install the Qiskit library which provides the tools to work with quantum circuits. This is essential because quantum computing requires specialized software that can handle quantum operations.

Install Qiskit

pip install qiskit

Import Libraries

from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister
from qiskit import execute, Aer
from qiskit.visualization import plot_histogram
import matplotlib.pyplot as plt

Why this step? These imports give us access to the core quantum computing functionality, including circuit creation, execution, and visualization tools. The Aer simulator allows us to run quantum circuits on classical computers for testing.

Step 2: Create a Basic Quantum Circuit

Let's start by creating a simple quantum circuit with two qubits. This will demonstrate the fundamental concept of superposition, where qubits can exist in multiple states simultaneously.

Create Quantum and Classical Registers

# Create a quantum circuit with 2 qubits and 2 classical bits
qr = QuantumRegister(2, 'q')
cr = ClassicalRegister(2, 'c')
circuit = QuantumCircuit(qr, cr)

Add Quantum Gates

# Apply Hadamard gate to both qubits to create superposition
# This puts each qubit in equal probability of being 0 or 1
for i in range(2):
    circuit.h(qr[i])

# Add measurement to classical bits
circuit.measure(qr, cr)

Why this step? The Hadamard gate creates superposition - a qubit in superposition has equal probability of being measured as 0 or 1. This is the quantum equivalent of a coin spinning in the air.

Step 3: Simulate the Quantum Circuit

Now we'll run our circuit on the Qiskit simulator to see the quantum behavior in action.

Set Up the Simulator

# Get the Aer simulator backend
backend = Aer.get_backend('qasm_simulator')

# Execute the circuit
job = execute(circuit, backend, shots=1000)
result = job.result()
counts = result.get_counts(circuit)

Visualize Results

# Plot the histogram of results
plot_histogram(counts)
plt.show()

Why this step? Running simulations helps us understand quantum behavior without needing actual quantum hardware. The results should show roughly equal distribution between 00, 01, 10, and 11 states, demonstrating superposition.

Step 4: Create an Entangled Circuit

Next, we'll create a more advanced circuit that demonstrates quantum entanglement - a phenomenon where qubits become correlated in such a way that measuring one instantly affects the other, regardless of distance.

Build Entangled Circuit

# Create new circuit for entanglement demonstration
entangle_circuit = QuantumCircuit(2, 2)

# Apply Hadamard gate to first qubit
entangle_circuit.h(0)

# Apply CNOT gate (controlled-NOT) to entangle qubits
# This creates Bell state |Φ+⟩ = (|00⟩ + |11⟩)/√2
entangle_circuit.cx(0, 1)

# Measure both qubits
entangle_circuit.measure_all()

# Execute and visualize
backend = Aer.get_backend('qasm_simulator')
job = execute(entangle_circuit, backend, shots=1000)
result = job.result()
counts = result.get_counts(entangle_circuit)
plot_histogram(counts)
plt.show()

Why this step? Entanglement is one of the most important quantum phenomena that enables quantum algorithms to solve certain problems exponentially faster than classical computers. This is a core concept behind quantum computing's potential advantage.

Step 5: Analyze Quantum Results

Let's examine what we've learned from our quantum circuits and how they relate to the broader quantum computing landscape.

Interpret Results

# Print the counts for analysis
print("Superposition Circuit Results:")
print(counts)

# For entangled circuit, we expect to see correlation
# 00 and 11 should occur much more frequently than 01 or 10
print("\nEntangled Circuit Results:")
print(counts)

# Calculate probability of each outcome
total_shots = sum(counts.values())
for outcome, count in counts.items():
    probability = count / total_shots
    print(f"Outcome {outcome}: {probability:.2%}")

Why this step? Understanding the mathematical probabilities behind quantum results helps us appreciate why quantum computers can solve specific problems more efficiently. In entangled circuits, we should see near 100% correlation between measurement outcomes.

Step 6: Extend to Multi-Qubit Systems

Finally, let's create a more complex circuit with multiple qubits to demonstrate how quantum computing scales.

Multi-Qubit Circuit

# Create a 4-qubit circuit
multi_circuit = QuantumCircuit(4, 4)

# Apply Hadamard to all qubits for superposition
for i in range(4):
    multi_circuit.h(i)

# Add some entanglement
multi_circuit.cx(0, 1)
multi_circuit.cx(2, 3)

# Measure all qubits
multi_circuit.measure_all()

# Execute and analyze
backend = Aer.get_backend('qasm_simulator')
job = execute(multi_circuit, backend, shots=1000)
result = job.result()
counts = result.get_counts(multi_circuit)
print("4-Qubit Circuit Results:")
print(counts)

Why this step? As quantum computers scale to more qubits, they can process exponentially more information. This is the fundamental advantage that makes quantum computing potentially revolutionary for fields like cryptography, drug discovery, and optimization problems.

Summary

In this tutorial, we've explored fundamental quantum computing concepts using Qiskit. We created circuits that demonstrate superposition, where qubits exist in multiple states simultaneously, and entanglement, where qubits become correlated. These concepts are the foundation of quantum advantage - the ability of quantum computers to solve certain problems exponentially faster than classical computers.

As the US government invests heavily in quantum computing through initiatives like the $2 billion stake in quantum firms, understanding these technologies becomes increasingly important. While we've only scratched the surface of quantum computing in this tutorial, you've now learned the basic tools and concepts needed to build more complex quantum algorithms. The field is rapidly advancing, with companies and governments worldwide investing billions in quantum research and development, making this an exciting time to start learning quantum computing.