Classical Bit Vs Qubit

All the computational difference comes from something called Superposition, the basic idea where a qubit can be in superposition of more than one basic state, as explained in the previous post.
To understand this better lets assume we have made 2 systems

System 1: With 2 bits

System 2: With 2 qubits

System 1

This can represent 4 different values

Possible states: 4 [00, 01, 10, 11]

particular state-value = 2⁰ bit0 + 2¹ bit1
i.e. particular state-value ∈ {0,1,2,3}, one of the 4 possible values

System 2

This can represent infinite different values (vector space) formed from 4 different basis state, 00 ≡|00⟩, 01 ≡ |01⟩, 10 ≡ |10⟩, 11 ≡|11⟩

Possible states [vectors]: Infinite

particular state-value: α |00⟩ + β |01⟩ + γ |10⟩ + δ |11⟩

such that |α|²+|β|² +|γ|² +|δ|² = 1

System 1 Vs System 2

For understanding the state of System 1, we just need to know 2 values, value of bit0 & value of bit1. Whereas for System 2, we need to know 4 values α, β, γ, δ. This is where everything changes!

To Summarize this in general:

A n-bit classical system can be in one of the 2^n possible states at a time, and all it needs is the value of these n bits to be fully recognized
VS
A n-qubit system can be in superposition of all of those states 2^n states at a given time and it needs the value of coefficients of all of the 2^n states basis to be fully recognized.

Note: To be more precise its 2^n -1, considering the summation to 1 constraint.

Because of this superposition in qubit system, we are able to store 2^n bit information compared to n bit information in classical bit system. This is what which gives Quantum Computers the Computation Advantage over the classical Computers & hence all the Buzz!

This post is 2 part of the “Quantum Computing 101” Series, check the next post of the series, Basic Quantum Gates.