What is a Qubit?

A qubit (quantum bit) is the basic unit of quantum information. It generalizes the classical bit by allowing states that are not merely 0 or 1, but normalized vectors in a two-dimensional complex Hilbert space.

Classical bit vs quantum bit

A classical bit is in one of two definite states: 0 or 1. You can copy it arbitrarily and read it without disturbing it.

A qubit can be prepared in a superposition of $\lvert 0 \rangle$ and $\lvert 1 \rangle$. You still obtain a classical outcome (0 or 1) when you measure in the computational basis, but the pre-measurement state carries more information in the amplitudes.

Where the term comes from

The word qubit is commonly attributed to the theoretical physicist Benjamin Schumacher, and it is short for quantum bit.

Mathematical representation (Dirac notation)

We write an arbitrary single-qubit pure state as a ket:

The bra $\langle \psi \rvert$ is the conjugate-transpose row vector. Inner products use the braket $\langle \phi \vert \psi \rangle$.

Superposition

Superposition means $\alpha$ and $\beta$ can both be non-zero. A measurement in the computational basis yields:

• outcome 0 with probability $\lvert \alpha \rvert^2$
• outcome 1 with probability $\lvert \beta \rvert^2$

Even though only one outcome is observed, the quantum description before measurement is the full normalized vector $\lvert \psi \rangle$.

Bloch sphere (introduction)

Up to a global phase, any pure single-qubit state can be written as

with $0 \le \theta \le \pi$ and $0 \le \phi < 2\pi$. The pair $(\theta, \phi)$ maps to a point on the Bloch sphere: a geometric picture of single-qubit pure states as points on a unit sphere.

How qubits are built (physical platforms)

In hardware, a qubit is implemented by choosing two well-controlled quantum states of a physical system and manipulating them with precisely engineered control signals. Common platforms include:

• Superconducting circuits (microwave control, cryogenic temperatures)
• Trapped ions (laser control, long coherence, high-fidelity operations)
• Neutral atoms (laser arrays, promising scaling routes)
• Photons (good for communication and networking)
• Quantum dots / spins (semiconductor compatibility, active research)

Each platform makes different trade-offs in coherence time, gate fidelity, connectivity, and scalability.

Why qubits are hard (coherence and noise)

Qubits are powerful but fragile. They must maintain coherence long enough to execute a circuit; interactions with the environment introduce noise and cause decoherence.

Python / Qiskit example

The snippet below prepares a superposition with a Hadamard gate and prints the statevector (ideal noise-free simulation).

from qiskit import QuantumCircuit
from qiskit.quantum_info import Statevector

qc = QuantumCircuit(1)
qc.h(0)

psi = Statevector(qc)
print(psi)

You should obtain amplitudes consistent with $\lvert + \rangle = \frac{1}{\sqrt{2}}(\lvert 0 \rangle + \lvert 1 \rangle)$ up to numerical formatting. To see random 0/1 outcomes from measurement, run the circuit on a simulator or device with shots after you add a measurement instruction.

Exercise

Thought question: Suppose you are given many copies of an unknown qubit state $\lvert \psi \rangle$. Why is it impossible to learn $\alpha$ and $\beta$ perfectly from a single measurement on one copy? What kind of repeated experiment would let you estimate $\lvert \alpha \rvert^2$ and $\lvert \beta \rvert^2$?

Next

Continue with Superposition for more intuition before you formalize gates as matrices.