Because amplitudes can be negative (or complex), contributions to a wrong answer can cancel each other out while contributions to the right answer add up.
Why it matters
This is the actual mechanism of quantum speedup. If you only remember one thing from the beginner level, remember that a quantum algorithm is an interference pattern engineered so the answer survives.
After this you will be able to
A quantum algorithm arranges the computation so that the amplitudes leading to wrong answers cancel out, while those leading to the right answer reinforce. When you finally measure, the right answer is overwhelmingly likely.
Noise-cancelling headphones generate a sound wave precisely shaped to cancel the noise. A quantum algorithm generates a computational wave precisely shaped to cancel the wrong answers.
The speedup comes from having lots of qubits.
Qubit count sets the size of the space. Whether you can engineer useful interference within that space is a separate question, and it is the hard one — which is why only a handful of algorithms exist.
Every quantum speedup you will ever read about is an interference pattern in disguise. Grover, Shor and phase estimation are all just different cancellation schemes.
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.
Drag gates onto wires and watch amplitudes, Bloch spheres and probabilities update live. Nothing else builds gate intuition this fast, and it needs no install or account.
A drag-and-drop optical table in the browser — lasers, beam splitters, polarisers — that lets you build interference and Bell-test experiments and see the physics rather than the algebra.