What it means for a qubit to be in two states at once, and why measurement is what makes the difference.
A qubit in superposition is described by two numbers at once. Mathematically, it's a vector in two-dimensional complex space — the "0 state" times one amplitude plus the "1 state" times another. When you measure it, you get 0 or 1 with probabilities set by those amplitudes. Until you measure, both values are present.
Schrödinger's cat is the standard analogy: a cat in a sealed box with a quantum-triggered mechanism is, until observed, in a superposition of alive and dead. The thought experiment was meant to highlight how strange quantum mechanics is when applied to everyday objects. For a single qubit, the strangeness is verified — interference experiments have confirmed superposition for photons, electrons, and increasingly large molecules.
A qubit's state is written as α|0⟩ + β|1⟩, where α and β are complex numbers with |α|² + |β|² = 1. The |α|² is the probability of measuring 0, |β|² is the probability of measuring 1. Operations on the qubit are matrices that rotate these amplitudes.
Two amplitudes might sound unimpressive. The interesting part is what happens with multiple qubits. Two qubits in superposition have four amplitudes. Ten qubits have 1,024 amplitudes. Fifty qubits have over 10¹⁵ amplitudes. That exponential growth is the resource quantum algorithms exploit.
But here's the catch: you can't read out all those amplitudes at the end. Measurement gives you one bitstring. The algorithm has to arrange the amplitudes so that the right answer has a high probability and the wrong answers have very low probabilities. That choreography is what quantum algorithm design is about.
Consider a problem with N possible answers. A classical computer checks them one by one, taking N steps in the worst case. A naive reading of superposition says "a quantum computer tries all N at once" — but that's wrong. The quantum computer sets up amplitudes for all N answers and then uses interference to boost the right ones and cancel the wrong ones. The total work is still proportional to N in some sense, but the constant factors are very different.
Searching an unsorted database of N items takes N/2 checks classically. Grover's algorithm finds the right item in about √N steps using amplitude amplification. For N = 1 million, that's 1,000 instead of 500,000. The speedup is quadratic, not exponential.
The biggest practical use of superposition is simulating other quantum systems. A 100-qubit register can hold the state of a 100-particle quantum system — something a classical computer can't do at all, because the state would require 2¹⁰⁰ complex numbers to describe. Chemistry and materials science simulations are the most promising near-term applications.
For ordinary data processing, superposition offers no speedup. Word processors, spreadsheets, web servers, and most database queries aren't well-suited to quantum algorithms. Quantum computers aren't "faster computers" — they're different computers for different problems.
Measurement in quantum mechanics isn't passive observation. It's an interaction that entangles the qubit with the measuring device. The result is that the original qubit's superposition becomes correlated with a definite state in the device, and from the outside we only see the device's reading.
This is called wave function collapse, and it's the part of quantum mechanics physicists argue about most. The Copenhagen interpretation says the superposition simply stops existing when measured. The many-worlds interpretation says it continues, just in a different branch of reality. The decoherence view says the superposition leaks into the environment and stops being coherent before measurement ever happens. All three predict the same experimental results.
For practical purposes, the takeaway is the same: once you measure a qubit, you get one definite value and the quantum information about the other amplitude is gone forever. You can't copy a qubit's state (no-cloning theorem), and you can't measure it without disturbing it. Quantum algorithms have to extract the answer through clever patterns of constructive and destructive interference, not by reading out all the amplitudes directly.