The quantum version of a bit. Instead of being 0 or 1, a qubit carries two numbers (amplitudes) that say how much of "0" and how much of "1" it holds — including negative and complex values.
Why it matters
The amplitudes are the whole game. Probabilities can only add up; amplitudes can cancel. That difference is the source of every quantum speedup.
After this you will be able to
A classical bit is one number that is either 0 or 1. A qubit is described by two numbers — one attached to the outcome 0, one attached to the outcome 1. Those numbers are called amplitudes, and they can be negative, or even complex.
Think of a dial rather than a switch. A switch is up or down. A dial has a direction, and "pointing halfway between up and down" is a real, definite setting — not indecision about which way it is really pointing.
A qubit is secretly 0 or 1 and we just do not know which.
If that were true, quantum computers would be no more powerful than randomised classical ones. The amplitudes are physically real: they interfere with each other, which random hidden values cannot do.
A qubit always has a perfectly definite state. What is uncertain is only what you get when you measure it.
To get the probability of an outcome, you square the size of its amplitude. Because amplitudes can be negative, two contributions to the same outcome can add up to zero — an event that could have happened two ways can end up never happening at all.
Two water waves meeting crest-to-trough produce flat water. Two ways of winning a lottery never make your chance of winning zero. Amplitudes behave like the waves, not like the lottery.
Drag to change the qubit’s state. Watch what the two panels do differently.
Now apply a Hadamard gate first, then measure:
Compare θ = 90° with θ = 270°. Before the gate they are indistinguishable — both give a 50/50 coin flip. After the Hadamard, one is a certainty and the other is impossible. The only difference between them is a minus sign on one amplitude, and probabilities alone cannot see it. That hidden sign is the resource every quantum algorithm spends.
Amplitudes are just probabilities written in a fancy way.
Probabilities are non-negative and only ever accumulate. Amplitudes are signed, and that signed-ness is the entire mechanism behind every quantum speedup.
Squaring is why the minus sign matters: -0.7 and +0.7 give the same probability but behave completely differently when combined with something else.
Hand-picked and ordered. If you only have time for one, take the first.
The single best starting point in existence. An essay built on spaced-repetition flashcards embedded in the text, so you actually remember it a month later. Assumes nothing but curiosity, and gets you honestly to quantum teleportation.
A rigorous but genuinely well-taught course by John Watrous covering single systems, multiple systems, quantum circuits and the core protocols. The cleanest bridge from intuition to real notation.
Microsoft's concept documentation is unusually well written for docs — the pages on qubits, entanglement and the Q# language work as standalone explanations.
A polished, heavily visual self-paced program aimed squarely at newcomers without a physics background. The interactive Bloch sphere and noise demos are the standouts.
IBM's free structured course platform and the successor to the old Qiskit Textbook. Mixes written lessons, videos and runnable notebooks, and takes you from 'what is a qubit' to running jobs on real hardware.
A free, complete undergraduate textbook with worked exercises. Uniquely, it teaches classical computing alongside quantum, so the comparison is always concrete rather than hand-waved.
A hands-on Jupyter-based workshop run worldwide by a volunteer community. Strong on doing rather than watching, and the free live cohorts give you people to get stuck with.
Interactive, visual and gentle, built in collaboration with quantum researchers. Worth it if you learn best by poking at widgets; everything it covers is available free elsewhere with more effort.
Twenty-two short videos taking you from the basic postulates through to quantum teleportation, taught by the co-author of Nielsen & Chuang. Whiteboard-paced and easy to follow.
Free lecture videos from the Delft MOOCs, organised by topic. Uniquely strong on the hardware side — how you actually build and control a qubit — and on quantum internet.
Topics that list Qubits as a prerequisite.
A qubit holding a nonzero amount of both 0 and 1 at the same time — not "secretly one of them", and not "both in separate universes", but a genuine third kind of state with no classical counterpart.
BeginnerReversible operations that rotate qubit states. X flips, H creates superposition, Z flips a sign, and CNOT lets one qubit control another — that small set already gets you a long way.
BeginnerQubits leak their quantum information into the environment within microseconds to milliseconds, and every gate applied to them is slightly wrong. That is why building a useful quantum computer is hard.
BeginnerThe compact notation physicists use for quantum states: |psi> is a column vector, <psi| its conjugate transpose, and <a|b> their inner product.
Intermediate