Quantum Computing: Foundations continued..

Lets take a look into some of the key elements of quantum computing.

Qubits:

In quantum computing, the unit is a qubit, a quantum, which can exist in a superposition of both state at once: (Equation representing the state)

|ψ⟩ = α|0⟩ + β|1⟩

Here the ψ is the quantum state of the qubit, |0⟩ & |1⟩ are the basis state ( in classical computing, this is either 0 or 1), alph and beta (α, β) represents the complex numbers that decribes the probability amplitudes.

Superpositions:

Superposition means qubit can represent multiple classical states at once. If a classical bit 0 or 1 then qubit is like: both 0 and 1 simulteneously, untill measured.

What is superposition here?

while there is no specific definition about the superposition, lets take an anology of tossing a coin.

1. Here when the coin is tossed in the air and it's spinning, it is holding both heads and tails(0 & 1), the spinning coin in the air is called superposition.
2. Once the coin drops to the surface a result is obtained either head or teal (0 or 1), meaning it has collapsed from its superposition to a result.

Why superposition matters?

1. It represents many possible states simultaneously.
2. Performs computations in parallel.
3. Exploit interference to enhance correct results.

That’s the root of quantum parallelism, the reason quantum computers can potentially outperform classical ones.

The Bloch Sphere Representation

The Bloch sphere is a powerful geometric model of a qubit. You can visualise any qubit state as a point on the surface of a sphere, by providing conversion of a state-vector conversion from two-dimensional complex space to three-dimensional real vector space using 2 angles (theta and psi)

Measurement & what does it mean in quantum computing?

When a qubit is measured, it collapses from its superposition into one of the basis state 0 or 1. Lets understand this a bit more. this is the most important thing of quantum computing.

1. When a qubit is in superposition, we say its in both state ( 0 & 1), but only potentially.
2. It carries a possiblity of 0 or 1.
3. When qubit is measured, the act of measurement forces it to choose one of the two basis state.
4. After the measurement, the qubit collapses to whichever state it was observed, that it, if it was measured 0 the qubit becomes 0 and vice-versa. And it loses the memory or prior superposition.
5. For this reason (destruction of superposition), the algorithm, is designed to use interference before the final measurement, so that the correct result has highest probability when collapse occurs.

Author: Sanjay Kumar. | Knowledge source: www.cse.iitd.ac.in/, www.sciencedirect.com

In the next Article, I am going to take a look into Dirac notation and Single & Multiple qubit gates.