Qubits and Superposition · Quantum Computing Fundamentals

A normal bit is a switch. It is off (0) or on (1), and that is all there is to it.

A qubit is different. Until you look at it, it holds a mixture of both — and the recipe for that mixture is what the machine actually computes with.

Bit vs qubit

	Classical bit	Qubit
State	Exactly 0 or 1	α\|0⟩ + β\|1⟩, with α and β complex
Read it	You see what is there	You get 0 or 1; the superposition is gone
Copy it	Freely	Impossible — the no-cloning theorem
Two of them	2 numbers	4 amplitudes; n qubits need 2ⁿ

A bit is one of two points. A qubit is any point on the sphere — but you only ever get one bit back out of it.

The mixture has two numbers in it

Each qubit carries two numbers, one for "how much 0" and one for "how much 1". Physicists call them amplitudes.

They are not the odds. To get the odds, you square them. And because something has to happen when you look, the two squares always add up to 1.

H|0⟩ — a balanced superposition

The Hadamard gate moves the state from the north pole to the equator. Both outcomes are now equally likely, but the qubit is not secretly a 0 or a 1 — it is genuinely both amplitudes at once.

It is not a spinning coin

A spinning coin is already heads or tails — you just cannot see which yet. It feels like the obvious explanation for a qubit, and for about thirty years the smartest people alive argued about it.

Experiments settled it. A qubit is genuinely not secretly one or the other. The three physicists who proved it shared the 2022 Nobel Prize in Physics for the work.

Here is the strange part

Odds are never negative. You cannot have a minus-30% chance of rain.

Amplitudes can be negative. And that changes everything, because two negatives and positives can cancel.

An amplitude of +½ gives the same odds as −½. But add the two together and you get zero. Two ways of reaching the same answer can wipe each other out completely.

Amplitude

The two numbers a qubit carries. Square one and you get the chance of that result. Unlike a chance, an amplitude can be negative — which is exactly what lets things cancel.

Why more qubits get out of hand fast

One qubit needs 2 numbers. Two qubits need 4. Ten need 1,024. Three hundred qubits would need more numbers than there are atoms in the universe.

That is why ordinary computers choke on this stuff. It is also why building the real thing is worth the trouble.

Worth remembering

A qubit holds two numbers — amplitudes — one for 0 and one for 1.
Square an amplitude to get the chance of that result. The two squares add to 1.
A qubit is not secretly one or the other. Experiments proved that.
Amplitudes can be negative, so they can cancel. Odds never can.
Each qubit you add doubles the numbers involved — but you still only get one answer out.