Classical Bit Vs Qubit

In the realm of computing, the fundamental building blocks of information are bits. But what happens when we introduce the concept of qubits (Quantum Bits), the quantum counterparts of classical bits? Enter the fascinating world of quantum computing, where the power of superposition unlocks extraordinary computational possibilities.

In this article, we will explore the key differences between classical bits and qubits.

Classical Bit and Quantum Bit

A classical bit can be either 0 or 1.?A quantum bit, or qubit, is a superposition of 0?and?1.

A single qubit therefore takes 2 classical values at once.?Every operation on the qubit is done on both values at once.

System A: Classical Bit

Let's start by examining a classical system composed of 2 bits. In this system, we can represent 4 different values or states: 00, 01, 10, and 11. Each state corresponds to a particular value based on the bit positions.

For example, the state 01 represents the value 2^0 * bit0 + 2^1 * bit1. In this case, the possible values are 0, 1, 2, or 3.

System B: Qubit

Now, let's shift our focus to a quantum system composed of 2 qubits. Unlike classical bits, qubits can exist in a superposition of multiple basic states. In this system, we can form an infinite number of different values or states using 4 distinct basis states:

00 ≡ |00?, 01 ≡ |01?, 10 ≡ |10?, and 11 ≡ |11?

Each qubit state is represented as

α |00? + β |01? + γ |10? + δ |11?

where α, β, γ, and δ are complex numbers that satisfy the normalization condition |α|^2 + |β|^2 + |γ|^2 + |δ|^2 = 1.

The qubit system allows for the superposition of all 2^2 = 4 possible states simultaneously.

System A vs System B

The crucial distinction between System 1 and System 2 lies in the amount of information they can represent. In System 1, a classical n-bit system can exist in one of the 2^n possible states at any given time, and we only need to know the values of the n bits to recognize the state. In contrast, System 2, with n qubits, can be in a superposition of all 2^n states simultaneously. To fully recognize the state of the qubit system, we need to know the values of the coefficients (α, β, γ, and δ) associated with each basis state.

Summary;

• In classical computing, bits are the fundamental units of information, represented as 0 or 1. They can only exist in one of these states at a time. In contrast, qubits in quantum computing can exist in a superposition of 0 and 1 simultaneously, enabling parallel computation and increased information storage capacity.
• Measurement of a classical bit always yields a definite result, either 0 or 1, while measurement of a qubit in superposition can yield a probabilistic result based on the coefficients of its basis states. Quantum gates manipulate qubits using quantum operations, whereas classical logic gates operate on bits using classical operations.
• Quantum computing employs error correction techniques to mitigate the effects of quantum noise, while classical computing relies on error correction mechanisms to handle errors.

Here's a simple Python program that demonstrates the concept of qubits and superposition:

import numpy as np
# Define the basis states
basis_0 = np.array([1, 0])? # |0?
basis_1 = np.array([0, 1])? # |1?
# Define the coefficients for superposition
alpha = 0.6
beta = 0.8

# Create a qubit in superposition
qubit = alpha * basis_0 + beta * basis_1
# Measure the qubit (collapse the superposition)
measurement = np.random.choice([0, 1], p=[abs(alpha) ** 2, abs(beta) ** 2])

# Print the results
print("Qubit in superposition state:", qubit)
print("Measurement result:", measurement)
        

Note: This simple example demonstrates the principles of superposition and measurement in qubits, showcasing how a qubit can exist in multiple states simultaneously until measured.