From Bits to Qubits: Quantum Binary Classification

Classical Binary Classification is a fundamental problem in data analysis, which implies assigning two labels or categories to a given input dataset based on its features. Wait, what if the data has exponential complexity? Well, in that case, classical computers will struggle with identifying complex patterns in high-dimensional datasets, thus leading to suboptimal classification performance. That's where quantum computing comes into the picture!

Quantum Artificial Intelligence (QAI) - is a multidisciplinary field that combines principles from quantum computing and artificial intelligence to develop new algorithms/techniques for solving complex problems more efficiently than classical algorithms. Quantum Computing's unique properties - such as quantum annealing, Shor's algorithm, and superposition - can significantly benefit in solving computationally intractable problems, such as certain optimization and factorization tasks. Also, we can leverage the concept of quantum entanglement - to improve probabilistic modelling and optimization tasks relevant to binary classification, but hey! - what's the building block behind such concepts!?

Let's delve into the building blocks that form the bedrock of quantum computing -

• Quantum States - Quantum bit (qubit) is a basic unit of quantum information, just like the binary bit is a basic unit of information in classical systems.

• Quantum Logic Gates - Let's say you have a magic coin that can be both heads (H) and tails (T) at the same time (superposition principle), and you have a magic wand (Quantum Flippy Gate) which can twist your magic coin. If it's in a superposition of H and T, then your wand can twist it to a different superposition - H and H at the same time, or T and T. In a nutshell, quantum gates manipulate qubits in endless possibilities!

• Quantum Circuits - It's a kind of conductor orchestrating a complex symphony, which involves arranging qubits and gates to perform an intricate dance of computation!

Now, let's witness the convergence of classical wisdom and quantum magic via binary classification.

Let's say you want to harness the power of quantum states and quantum gates to perform binary classification tasks with high accuracy. In binary classification - you want to classify the data points into one of two categories. For this, we can use quantum programming frameworks like Qiskit (for IBM's quantum devices) or Cirq (for Google's quantum devices). I've used Qiskit at the minute since I have yet to get myself familiar with Cirq.

Step 1: Set up the quantum simulator backend and import necessary packages.

import numpy as np
from qiskit import QuantumCircuit, transpile, assemble, Aer, execute
from qiskit.visualization import plot_histogram
from qiskit.visualization import plot_histogram
from scipy.optimize import minimize
import matplotlib.pyplot as plt
from qiskit import Aer
backend = Aer.get_backend('qasm_simulator')

Step 2: Define the sample dataset. Here is the snippet of my tiny dataset.

data = {
    'class_0': [0.2, 0.1],
    'class_1': [0.7, 0.9]
}

Step 3: Define the quantum circuit, which will include two qubits and is responsible for performing quantum binary classification.

def qnn_circuit(params):
    circuit = QuantumCircuit(2, 2)
    circuit.ry(params[0], 0)
    circuit.ry(params[1], 1)
    circuit.measure([0, 1], [0, 1])
    return circuit

Step 4: Define QNN (quantum Neural Network) - it simulates the quantum circuit, calculates probabilities, and computes the cost based on the differences between expected and observed outcomes.

def cost_function(params, data):
    circuit = qnn_circuit(params)
    backend = Aer.get_backend('qasm_simulator')
    job = execute(circuit, backend, shots=1000)
    result = job.result()
    counts = result.get_counts(circuit)
    prob_class_0 = counts.get('00', 0) / 1000.0
    prob_class_1 = counts.get('01', 0) / 1000.0
    cost = (prob_class_0 - data['class_0'][0])**2 + (prob_class_1 - data['class_1'][0])**2
    return cost
initial_params = np.random.rand(2)

Step 5: Optimize the QNN defined above and extract the optimized parameters. Here, I'm using COBYLA - Constrained Optimization BY Linear Approximations, an optimization algorithm.

result = minimize(cost_function, initial_params, args=(data,), method='COBYLA')
optimized_params = result.x

Step 6: Create the final quantum circuit

final_circuit = qnn_circuit(optimized_params)
job = execute(final_circuit, backend, shots=1000)
result = job.result()
counts = result.get_counts(final_circuit)

Step 7: Visualize the classification results using a histogram.

plot_histogram(counts)
plt.title('Classification Results')
plt.xlabel('Class')
plt.ylabel('Counts')
plt.show()

All right! We have developed a quantum binary classification model!