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A qubit is not just a fancier bit

Every computer you've ever used stores information as bits: each one is a 0 or a 1, nothing in between. A quantum computer uses qubits, which can sit in a weighted blend of 0 and 1 until the moment you look. That one change is why the number of qubits matters so much more than the number of bits.

Sinclair College - Dr. Mike Libassi

Qubit (quantum bit) — the basic unit of quantum information. Physically it can be an ion, a photon, or a tiny superconducting circuit. Mathematically it's a pair of complex numbers (amplitudes). Their squared sizes give the odds of reading 0 or 1, and the angle between them, the phase, decides how they interfere.

CLASSICAL BIT

Always exactly one value. Flip it, and it's the other one.

QUBIT

|0⟩

|1⟩

A weighted blend of both. Measuring it forces a single answer.

01 · Refresher

The classical bit

Click a term to see how it fits together.

Try it: flip four bits

Four bits can represent 16 different values, but they hold only one of them at any moment. Watch the grid below: exactly one cell is ever lit.

binary=0000 decimal=0

02 · The core idea

Writing a qubit down: ket notation

Physicists write quantum states inside a ket, the | ⟩ symbol. The two basic states are |0⟩ and |1⟩, the quantum versions of a classical 0 and 1. Each is really a two-row column of numbers, called a vector.

Ket — the |name⟩ symbol from Dirac (bra-ket) notation. It just labels a state. |0⟩ is read "ket zero." Underneath, every ket is a column vector.

|0⟩=10 |1⟩=01

|ψ⟩=α|0⟩ + β|1⟩=αβ

rule: |α|² + |β|² = 1 · P(read 0) = |α|² · P(read 1) = |β|²

The numbers α and β are called amplitudes. Squaring an amplitude gives a probability, which is why they must square-and-add to exactly 1. A qubit with both amplitudes nonzero is in superposition (the next page covers it in depth).

Amplitude — the number in front of each ket. Amplitudes can be negative or even complex, which is what lets quantum algorithms make wrong answers cancel out. On this page we keep them positive to focus on probability.

Try it: build a qubit, then measure it

Drag the slider to set the chance of reading 0. The ket and the vector update together. Then measure: each measurement uses a fresh qubit prepared the same way, because measuring destroys the blend.

P(read 0)50%

|ψ⟩=

|0⟩

|1⟩

No measurements yet.

Common misconception: a qubit does not "store 0 and 1 at the same time" in a way you can read out. Every measurement gives you one ordinary bit. The amplitudes only show up as statistics across many runs, which is exactly what the tally above demonstrates.

03 · More than one qubit

Two qubits need four numbers

Combine qubits with the tensor product (written ⊗) and the vector doubles in length each time. Two qubits have four basis states, |00⟩ |01⟩ |10⟩ |11⟩, and a two-qubit state carries an amplitude for each one.

Tensor product (⊗) — the way quantum states combine. Multiply each entry of the first vector by the whole second vector and stack the results. A 2-row vector ⊗ a 2-row vector gives a 4-row vector.

|0⟩⊗|1⟩= 10⊗01= 1·01·10·00·1= 0100=|01⟩

Try it: count the basis states

Pick a number of qubits. Each chip is one basis state, shown with its amplitude in an even blend of all of them.

04 · Scaling

Add one qubit, double the work

Describing n classical bits takes n numbers. Describing n qubits takes 2ⁿ amplitudes. To simulate a quantum computer on a normal one, you must store every amplitude, roughly 16 bytes each (two 64-bit floating-point numbers). Every added qubit doubles the memory, so storing every amplitude runs out of room somewhere around 45–50 qubits (2⁵⁰ amplitudes × 16 bytes ≈ 16 PiB). Clever simulators can go further for some circuits, but not for all of them.

Try it: how many qubits can you simulate?

Drag to add qubits and watch the memory a classical simulator would need.

number of qubits (n)10

CLASSICAL: n BITS NEED

QUANTUM: 2ⁿ AMPLITUDES

MEMORY TO SIMULATE

Machine sizes are rounded reference points. Clever simulation tricks can stretch these limits a few qubits further, but the doubling always wins.

05 · Reality check

Why more qubits doesn't mean infinite power

The 2ⁿ amplitudes are real, but you can't simply read them all out. Measuring n qubits gives back exactly n ordinary bits. Quantum algorithms win by arranging amplitudes so that wrong answers cancel and the right answer is likely to be measured. That trick only works for certain problems, and one of those problems happens to be the math behind RSA.

Click a term to see what limits real machines today.

WHAT QUBITS GIVE YOU

A state space that doubles with every qubit, which classical computers can't track at scale.

WHAT THEY DON'T

Free access to all 2ⁿ answers. You still read out only n bits per run.

Security connection: breaking RSA-2048 with Shor's algorithm needs a large number of error-corrected qubits. Recent estimates, which depend on assumed hardware error rates and speeds, put that around a million noisy physical qubits, far beyond today's machines. The Shor's Algorithm page in this series walks through why.