THE POLES: |0⟩ AND |1⟩
Where quantum states behave exactly like classical bits.
Before going further, let's fully de-mystify the |0⟩ notation, since you've now seen it several times.
What a "Ket" Actually Is
|0⟩ is called a ket. Don't let the exotic-looking bars and angle brackets intimidate you — a ket is nothing more than a labeled container for a quantum state, similar to how a variable name like x in code just labels some value without you needing to think about the label's shape.
|0⟩ simply means "the specific quantum state we've agreed to call zero." The full mathematical content that goes inside those brackets (a vector, described properly with numbers) is the subject of Module 2. For this entire module, all you need is: |0⟩ and |1⟩ are just names for two specific points on the Bloch sphere — the two poles.
The Poles Are Where "Quantum" Meets "Classical"
The Key Insight: At the poles, a qubit behaves exactly like an ordinary classical bit.
This is a reassuring and important fact: quantum computing doesn't throw away classical computing — it contains it as a special case.
|0⟩ — North Pole (θ = 0°)
- P(0) = 100%
- P(1) = 0%
- Always measures as 0
|1⟩ — South Pole (θ = 180°)
- P(0) = 0%
- P(1) = 100%
- Always measures as 1
Any classical bit can be represented exactly by a qubit sitting at one of these two poles, and it will behave in every measurable way exactly like a classical bit. The "quantum weirdness" only shows up once a qubit moves away from the poles — which is exactly what the Hadamard gate (Module 4) is built to do.
The Z-Basis / Computational Basis
The pair {|0⟩, |1⟩} is called the computational basis or Z-basis (because the poles sit on the Z-axis). It's the default, standard way of measuring a qubit.
A quick, self-contained definition of basis: a basis is simply a chosen pair of reference points that you measure "against" — like deciding to describe a location using North/South instead of some rotated pair of directions.
The computational basis (|0⟩/|1⟩) is the default choice, corresponding to the ordinary, standard measurement. In Lesson 5 you'll meet two other important bases (X and Y), and Module 8 formalizes what "measuring in a basis" precisely means.
It's called the computational basis because it's the basis in which we ultimately always read out answers on real hardware. No matter what fancy rotations a quantum circuit performs internally, the very last step — the physical measurement — is always a Z-basis measurement in practice. Other "bases" are simulated by rotating the qubit before this final Z-measurement.
Practice Questions
Test your understanding
KEY TAKEAWAYS
Remember these points
|0⟩ and |1⟩ are just names ("kets") for the North and South poles of the Bloch sphere — full ket mathematics comes in Module 2
At these two poles, and only at these two poles, a qubit measurement is 100% certain — this is where quantum states reduce exactly to classical bits
The pair {|0⟩, |1⟩} is called the computational basis or Z-basis — the default, standard way of measuring a qubit
Quantum computing doesn't discard classical computing; classical bits are a special case (the poles) of the richer qubit state space