Quantum Basics

Learning goal: why quantum basics matter

In this lesson, you will learn the basic principles of quantum mechanics and see how those principles affect computing, which is the foundation for the rest of a quantum computing course. Classical computing is built on bits that are either 0 or 1. Quantum computing is built on qubits, which follow the rules of quantum mechanics.

The story begins in the early 1900s, when physicists such as Max Planck, Albert Einstein, and Niels Bohr found that light and matter do not always behave like smooth, predictable waves or tiny billiard balls. At very small scales, particles can act in ways that seem strange: they can exist in superposition, show probabilistic outcomes, and become entangled.

For computing, this matters because the hardware is no longer just electrical switches. It becomes a physical system—such as trapped ions, superconducting circuits, or photons—whose information is shaped by quantum rules.

Superposition: more than "both at once"

A qubit can be in state |0⟩, state |1⟩, or a combination of both called a superposition. We often write a qubit as:

|ψ⟩ = α|0⟩ + β|1⟩

Here, α and β are numbers called amplitudes. Their squared magnitudes give probabilities, and they must satisfy:

|α|^2 + |β|^2 = 1

Worked example

Suppose a qubit has amplitudes:

• α = 0.8
• β = 0.6

Then:

• Probability of measuring 0 = 0.8^2 = 0.64
• Probability of measuring 1 = 0.6^2 = 0.36

So the qubit is not 64% 0 and 36% 1 in a classical sense. Before measurement, it is a genuine quantum state. But when you measure it, you get one definite result.

This is the first big computational shift: quantum information can be prepared and transformed in ways classical bits cannot.

Measurement, interference, and why quantum algorithms can help

Quantum mechanics is probabilistic, but quantum computing is not just “random computing.” The key is interference: amplitudes can combine so that some outcomes become more likely and others cancel out.

A famous historical example is the double-slit experiment, first explored in the 1800s and later understood quantum mechanically. Even single electrons fired one at a time create an interference pattern, showing that quantum states combine like waves until measured.

Quantum algorithms exploit this. Instead of checking every possibility one by one, they manipulate amplitudes so that wrong answers interfere destructively and right answers interfere constructively.

For example, a simple quantum gate can create superposition:

# Conceptual example
state = "|0>"
state = "Hadamard(state)"  # becomes an equal superposition
measure(state)              # returns 0 or 1 with equal probability

This does not solve a hard problem by itself, but it shows the basic trick: prepare, transform, then measure.

Entanglement and the computing difference

The other major quantum idea is entanglement, a correlation stronger than anything possible with ordinary classical bits. If two qubits are entangled, describing one qubit separately is no longer enough; the pair must be treated as a single quantum system.

A common example is the Bell state:

(|00⟩ + |11⟩) / √2

If you measure the first qubit and get 0, the second will also be 0. If you get 1, the second will also be 1. Before measurement, neither qubit has a definite classical value on its own.

This matters for computing because multiple qubits can represent structured correlations that are hard to simulate classically. That is why systems with even 50 to 100 high-quality qubits can already challenge classical simulation in specific tasks.

So the big picture is this: superposition expands possible states, interference shapes probabilities, and entanglement links qubits into richer computational systems. Next, you will build on these ideas by learning how quantum gates and circuits control qubits step by step.