What is a quantum computer?

A quantum computer is a machine that processes information using the rules of quantum mechanics — the physics that governs atoms, electrons and photons. That sounds exotic, but the idea we will build on throughout this course is simple to state:

A quantum computer manipulates amplitudes — numbers that behave like probabilities but can be negative or even complex — and uses interference between them to make right answers likely and wrong answers unlikely.

This lesson gives you the big picture. Every idea here will be made precise, with full mathematics, in later modules.

Bits: the classical starting point

Every classical computer — your laptop, a phone, a GPU cluster — stores information in bits. A bit is always in exactly one of two states, which we label 0 and 1. Three bits are always in exactly one of $2^3 = 8$ configurations, such as 101.

Even a random classical bit is simple to describe. A coin that is heads with probability $p$ and tails with probability $1-p$ is fully described by the single number $p$ . For $n$ random bits, a full description is a probability for each of the $2^n$ configurations — but at any moment the physical bits are still in one configuration; the probabilities just describe our ignorance.

Qubits: the quantum version

A qubit (quantum bit) also has two special states, written $|0\rangle$ and $|1\rangle$ (read "ket zero" and "ket one"). But a qubit can also be in a superposition of them:

|\psi\rangle = \alpha\,|0\rangle + \beta\,|1\rangle

where $\alpha$ and $\beta$ are amplitudes. Two facts about amplitudes drive everything that follows:

Measurement gives probabilities. When you measure the qubit you get 0 with probability $|\alpha|^2$ and 1 with probability $|\beta|^2$ (so $|\alpha|^2 + |\beta|^2 = 1$ ). This is the Born rule, which you will study in Module 3.
Amplitudes can cancel. Unlike probabilities, amplitudes can be negative (or complex). When two computational paths lead to the same outcome, their amplitudes add — and a positive and a negative amplitude can cancel to zero. This is interference.

Why quantum states are expensive to describe

For $n$ qubits there is one amplitude for every $n$ -bit string, so a general state needs $2^n$ complex amplitudes:

|\psi\rangle = \sum_{x \in \{0,1\}^n} \alpha_x\,|x\rangle, \qquad \sum_x |\alpha_x|^2 = 1.

Storing each amplitude as a double-precision complex number takes 16 bytes, so writing down the state of

Qubits	Amplitudes	Memory for the full state
10	1,024	16 KB
30	about 1.07 billion	16 GiB
50	about 1.13 × 10¹⁵	16 PiB (about 18 PB)

Every additional qubit doubles the memory. This is the observation Feynman made in 1982: nature seems to "compute" with exponentially many amplitudes, so perhaps a computer built from quantum parts could simulate nature efficiently where classical computers cannot.

The "parallel universes" misconception

You will often read that a quantum computer "tries every possible answer at once". That is misleading. It is true that one operation can act on all $2^n$ amplitudes, but if you simply prepare an equal superposition of all answers and measure, you get a uniformly random answer — no better than guessing.

What a quantum algorithm actually does is:

Prepare a superposition.
Apply operations that make the amplitudes of wrong answers interfere destructively (cancel) and those of right answers interfere constructively (reinforce).
Measure, obtaining a right answer with high probability.

This only works for problems with special structure that interference can exploit — which is why quantum computers are not faster at everything. The next lesson maps out where they help.

Knowledge check

Which statement best describes how a quantum algorithm gets its advantage?

It evaluates all 2ⁿ answers simultaneously and reads them all outIt prepares a superposition and then uses interference to make correct answers likely before measuringIt measures the qubits many times per second so it can check every answer quicklyIt stores 2ⁿ bits of classical information in n qubits and reads them back

Three quantum ingredients

Throughout the course we will keep returning to three resources:

Superposition — a qubit's state is a combination of $|0\rangle$ and $|1\rangle$ with amplitudes.
Interference — amplitudes for the same outcome add, and can cancel or reinforce.
Entanglement — the joint state of several qubits can have correlations that cannot be described by giving each qubit its own state. You will meet entanglement properly in Module 5.

What the hardware looks like

A quantum computer is a physical device that holds qubits, applies controlled operations called gates to them, and measures them. Several technologies are competing, each with trade-offs:

Technology	Qubit is…	Examples of companies
Superconducting circuits	a tiny electrical circuit cooled to about 10 millikelvin	IBM, Google, Rigetti
Trapped ions	the internal state of an individual charged atom held by electric fields	Quantinuum, IonQ
Neutral atoms	an atom held by focused laser beams ("optical tweezers")	QuEra, Pasqal, Atom Computing
Photonics	properties of individual particles of light	PsiQuantum, Xanadu
Spin qubits	the spin of an electron in silicon	Intel, Diraq

In this course you will run circuits on a simulator in your browser, on IBM's high-performance simulators, and on real IBM superconducting quantum processors.