The Power of Information Encoding - Classical Bits Vs Qubits

Classical BIT / Binary Digit) / Directional Binary Pointers / Scalar / O or 1 / Up or Down

Classical bits, represented as BITS, are akin to directional binary pointers. They offer a simple choice between two options, such as pointing Up or Down, North or South. In the context of locating a position on Earth, classical bits provide a binary indication, like stating whether you are in the Northern Hemisphere (Up) or the Southern Hemisphere (Down). However, they do not convey precise location information beyond this binary choice.

Qubit (Quantum Bits)- Precise Location Pointers (Vector) -

In the context of locating a position on Earth, envision a qubit as a vector pointer that combines latitude and longitude coordinates, pointing to a specific location on the Earth. A single qubit vector state can convey both latitude and longitude (2 real numbers), providing a multidimensional representation that goes beyond the binary scope of classical bits. This expanded encoding capability of qubits ushers in a new realm of possibilities in information processing.

Classical Bit:  Information Content is just one Bit
Qubit:             Information Content is 2 real numbers
This offers a simplified understanding of the Bloch Sphere representation, making the concept more accessible to individuals without extensive technical knowledge.

This example serves as a simplified illustration to highlight the fundamental difference between classical bits and qubits.

Appendix - Understanding the Bloch Sphere

The Bloch sphere is a powerful tool for visualizing quantum states and operations. By mapping the state vector of a qubit to a point on the surface of the sphere, we can easily visualize the state of the qubit and gain insight into its behavior. By visualizing quantum gates as rotations of the Bloch sphere, we can understand how they transform the state of the qubit and gain insight into the behavior of quantum systems.

Bloch Sphere, is a sphere where each point represents a possible state of a qubit.  Imagine each qubit as a vector on this sphere. The position of the vector is determined by two angles, denoted by θ and ϕ.

1. The angle θ: This is the angle made by the vector with the z-axis. The range of θ is from 0 to π, inclusive.

2. The angle ϕ: This is the azimuthal angle, measured counter-clockwise from the positive x-axis in the x-y plane. The range of ϕ is from 0 to 2π, inclusive.

The state of a qubit is expressed using these angles in the following equation:

$\mathrm{\mid }\psi ⟩=cos(\frac{\theta }{\mathrm{/2}})\mathrm{\mid }0⟩+sin(\frac{\mathrm{\theta /}}{2})e^{i\varphi }\mathrm{\mid }1⟩$

Here, |0⟩ and |1⟩ are the basis states that correspond to the classical bits in classical computing. These states are represented by the top (North Pole) and bottom (South Pole) points on the Bloch Sphere's z-axis.

Bloch Sphere Cheat Sheet 

Author: Ganesh Swaminathan | Created on: 18 August 2018 | Source: Link to Source Document by Ganesh.

This piece is the result of extensive study in Quantum Physics, Qubits, Matrices and Matrix Transformation, Vector Algebra, Complex Numbers, Probability, and Geometry/Trigonometry.

Conclusion and Key Takeaways

The Bloch Sphere is a vital tool in quantum computing. It visualizes the states of a qubit, moving beyond the 0 or 1 of classical bits to a vast range of possibilities. A qubit can exist in a superposition of states, a fundamental trait of quantum computing.

As we delve deeper into quantum computing, we encounter complex concepts like superposition and entanglement, and explore quantum gates and quantum algorithms. Understanding these ideas is key to unlocking the potential of quantum computing across various fields.