You only get one peek
Here is the rule that shapes everything else in quantum computing: when you read a qubit, you get one plain, classical bit back — a 0 or a 1. Not a fraction, not a blend, not a list of possibilities. One bit.
That feels unfair, because a qubit before you read it can be in a superposition — a genuine mix of |0> and |1> at the same time. You might hope to pull that whole rich quantum state out and inspect it. You can't. The measurement hands you a single bit and nothing more, and you can't rewind to ask again.
The Born rule
So if reading gives you a random-looking bit, what decides which one? The state itself. A qubit is written with two numbers called amplitudes, one attached to |0> and one to |1>:
|psi> = a|0> + b|1>
The Born rule says: the probability of reading 0 is |a|^2, and the probability of reading 1 is |b|^2. You square the size of the amplitude to get the chance. Because *something* must happen when you measure, those probabilities have to add to 1: |a|^2 + |b|^2 = 1.
Collapse
Measurement doesn't just *report* a value — it changes the state. The instant you read 0, the qubit truly becomes |0>. Read it again and you'll get 0 every time. The superposition is gone; this irreversible jump is called collapse.
That's a hard ceiling on what one run can tell you. Whatever delicate blend of |0> and |1> the qubit held, collapse flattens it into a single definite bit, and the other possibility is simply lost. You never see the amplitudes directly — only the outcome they made likely.
No-cloning: you can't copy first
A tempting escape: if measuring destroys the state, why not copy the qubit a hundred times first, then measure the copies and reconstruct the original blend? It would work in a classical computer. It is impossible here.
The [[no-cloning-theorem|no-cloning theorem]] proves there is no operation that takes an unknown quantum state and produces a second, independent copy of it. The laws that make quantum information useful also forbid duplicating an unknown state. So the single measurement you get really is your only window — there's no backup copy to study on the side.
Designing around measurement
Put the three rules together and the design problem becomes clear. You get one peek (one collapsed bit per run), the bit you get is governed by |amplitude|^2 (the Born rule), and you can't copy an unknown state to check it first (no-cloning). A quantum computer is not a faster classical CPU that secretly evaluates every option — it's a machine for shaping amplitudes.
So the entire job of a quantum algorithm is to arrange, through interference, for the right answer's amplitude to be large *before* you measure. Grover's search does this gently, nudging the target's amplitude up over many steps for a quadratic (square-root) speedup — not a magic exponential one. Shor's algorithm gets its famous exponential edge only because factoring has hidden structure its interference pattern can exploit; most problems have no such structure.