Classical Bits vs Qubits
A bit holds one value you can read: 0 or 1. A qubit carries two amplitudes, one for each outcome. An amplitude is a number that says how strongly the qubit leans toward that outcome. Measuring a qubit gives back a single bit. The chance of each result is its amplitude's size, squared.
What is a bit, and what is a qubit?
Why care? Every quantum program is built from qubits. If you know what a qubit really holds, the rest of this course makes sense.
An ordinary bit holds one value, 0 or 1. Think of a light switch: up or down. A program can read a bit, copy it, and make choices based on it at any time.
A qubit is a tiny physical system with two setups you can always tell apart. We label them |0⟩ and |1⟩. The bracket is just a way to name a quantum state.
A qubit's state is described by two numbers called amplitudes. The amplitude α (the Greek letter "alpha") goes with |0⟩. The amplitude β ("beta") goes with |1⟩. We write the state as α|0⟩ + β|1⟩. The + does not add anything here. It just lists the two outcomes side by side, each with its amplitude.
Amplitudes can be negative. They can even be complex numbers, which have two parts. They are hidden bookkeeping. You never read them directly off one qubit. Unlike a light switch, a qubit has these hidden numbers behind its answer.
- How do amplitudes turn into readout?
- Which one-qubit states should you know by name?
- Run it: prepare |+⟩INTERACTIVE
- Try this: hide a sign in the stateINTERACTIVE
- What does a qubit not give you?
- Is a qubit "both 0 and 1"?
You’ve read the opening of chapter 2. Pro unlocks the other 6 sections — plus every chapter of every course, with circuits you can run right on the page. That’s $11.99 a month, about the price of a coffee, or $99.99 a year (save 30%). The first chapter of every course, and the whole math course, stay free.