What is a qubit?
A qubit is the quantum version of a bit. When you measure it you always get 0 or 1, but before that it can be in a superposition α|0⟩ + β|1⟩, where two complex numbers α and β set the odds: |α|² for 0 and |β|² for 1.
From bits to qubits
Every classical computer is built from bits. A bit is always in exactly one of two states, 0 or 1 — a switch that is off or on. Everything else, from photos to this web page, is long strings of those switches.
A qubit (short for quantum bit) also has two basic states. Physicists write them as |0⟩ and |1⟩. The difference is what is allowed between measurements: a qubit can be in a combination of both basic states, called a superposition.
Reading the notation: |0⟩ and |1⟩
The angle-bracket symbol |ψ⟩ is called a ket (from Dirac’s “bra-ket” notation). It simply means “the quantum state named ψ”. For one qubit, the two basis states are column vectors:
A general qubit state is a weighted sum of the two:
The weights α (alpha) and β (beta) are called amplitudes. They are complex numbers — each has a size and an angle.
Amplitudes become probabilities
Amplitudes are not probabilities themselves, but they tell you the probabilities. This is the Born rule:
For example, the state 0.6|0⟩ + 0.8|1⟩ gives 0 with probability 0.6² = 36% and 1 with probability 0.8² = 64%. The last condition (the probabilities add up to 1) is why a valid state always has “length” one.
| State | α | β | P(0) | P(1) |
|---|---|---|---|---|
| |0⟩ | 1 | 0 | 100% | 0% |
| |1⟩ | 0 | 1 | 0% | 100% |
| |+⟩ | 1/√2 | 1/√2 | 50% | 50% |
| |−⟩ | 1/√2 | −1/√2 | 50% | 50% |
| 0.6|0⟩ + 0.8|1⟩ | 0.6 | 0.8 | 36% | 64% |
Try it: flip and split a qubit
Below is a live qubit. The arrow shows its state (the next lesson explains the sphere in detail). Press X to flip |0⟩ into |1⟩ — the quantum NOT. Press H to put it into an equal superposition, then Measure a few times after resetting.
The arrow points at the north pole, so measuring now gives 0 every time. Press a gate to rotate it, or drag the sphere to look around.
Why the minus sign matters
Look at |+⟩ and |−⟩ in the table. They give exactly the same measurement statistics — 50/50 — yet they are different states. The only difference is the sign (more generally, the phase) of β.
You can see the difference by applying one more gate. Hadamard turns |+⟩ into |0⟩ but turns |−⟩ into |1⟩: the amplitudes add up in one case and cancel in the other. That adding and cancelling is called interference, and it is the engine behind every quantum algorithm.
Superposition is not a hidden coin
A tempting picture is a coin under a cup: it is “really” heads or tails, we just do not know which. If qubits worked like that, |+⟩ and |−⟩ would be the same thing — both just “unknown, 50/50” — and the experiment above could not tell them apart. It can, so superposition is something richer than ignorance.
Summary
- A qubit has two basis states, |0⟩ and |1⟩.
- Its general state is α|0⟩ + β|1⟩ with complex amplitudes α and β.
- Measurement gives 0 with probability |α|² and 1 with probability |β|².
- The phase of the amplitudes is invisible in a single measurement but changes what later gates do.
Next, we turn those two amplitudes into a single point you can see and rotate: the Bloch sphere.
Frequently asked questions
Is a qubit 0 and 1 at the same time?
Not in the everyday sense. A qubit in superposition is described by two amplitudes, one for 0 and one for 1. It is a genuinely new kind of state: when you measure it you get just one answer, but before that the two amplitudes can interfere with each other, which a hidden “it was really 0 all along” could never do.
How much information can one qubit store?
Describing a qubit takes two real numbers (two angles), so its state holds a continuum of possibilities. But when you measure it you only ever get one classical bit out. Holevo’s theorem makes this precise: one qubit can carry at most one bit of retrievable classical information.
What are qubits made of in real quantum computers?
Any physical system with two well-separated states can serve: tiny superconducting circuits cooled close to absolute zero, single trapped ions or neutral atoms held by lasers, the polarization of a photon, or the spin of an electron. The maths in this lesson is the same for all of them.
Why do qubits use complex numbers?
Because amplitudes have a phase as well as a size. The phase does not change the odds of a single measurement, but it decides how amplitudes add up or cancel after further gates. Complex numbers are the natural bookkeeping for “size plus angle”.