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Quantum basics
What a qubit is, how it differs from a bit, and why adding qubits makes a quantum computer so hard to simulate.
Written by Bhumipat Nunthaboct
A bit is a switch. A qubit is a direction.
A classical bit is always exactly 0 or 1. A qubit is described by two amplitudes, one for 0 and one for 1, so it can be in a superposition of both. Measuring it gives a single 0 or 1, with probabilities set by those amplitudes.
- 1A bit is 0 or 1A classical bit is always in one definite state. Reading it doesn't change it.
- 2A qubit can be in betweenA qubit's state is a combination of 0 and 1. The arrow's angle sets how likely each result is.
- 3Measuring forces a choiceMeasurement gives 0 or 1 at random with those probabilities, and the in-between state is gone. Measuring again gives the same answer.
Classical bit
Two states. Reading it doesn't change it.
Qubit
Tilt the state, then measure. Each measurement gives one answer.
- P(|0⟩)
- 75%
- P(|1⟩)
- 25%
Simplified. A full qubit state also has a phase (picture a sphere, not a circle). Phase is what lets quantum algorithms make wrong answers cancel out.
| Property | Bit | Qubit |
|---|---|---|
| Possible states | 0 or 1 | A weighted combination of 0 and 1 |
| Reading it | Doesn't change it | Gives 0 or 1 and destroys the superposition |
| Copying | Copy freely | Impossible (no-cloning theorem) |
| n of them describe | One of 2ⁿ values at a time | 2ⁿ amplitudes at once |
| Errors | Extremely rare | Fragile. Needs error correction: many physical qubits per reliable logical qubit |
n qubits, 2ⁿ amplitudes
Every qubit you add doubles the number of amplitudes needed to describe the system. That exponential growth is why quantum computers are hard to simulate, and why they can be powerful.
24 =amplitudes to track
Each square is one amplitude.
MythA quantum computer tries every answer in parallel.
FactMeasurement returns one answer. Speedups come from interference, and only for problems with the right mathematical structure.
MythQuantum computers will be faster at everything.
FactFor most tasks there is no advantage. The threat to cryptography comes from two specific algorithms.
Technical deep dive
A qubit's state is |ψ⟩ = α|0⟩ + β|1⟩, where α and β are complex amplitudes with |α|² + |β|² = 1. Measuring gives 0 with probability |α|² and 1 with probability |β|².
Up to an unobservable global phase, any single-qubit state can be written cos(θ/2)|0⟩ + e^{iφ} sin(θ/2)|1⟩, a point on the Bloch sphere. The demo shows θ only (φ = 0).
An n-qubit state needs 2ⁿ complex amplitudes. Storing 50 qubits exactly at double precision takes 2⁵⁰ × 16 bytes ≈ 18 PB.