The Qubit
A qubit is the basic unit of quantum information: a two-level quantum system that can hold any superposition of its two basis states.
What a qubit is
A classical bit is either 0 or 1. A qubit is a quantum system with two distinguishable states, written |0> and |1>, that can also exist in a linear combination of both at once. Its general pure state is |psi> = a|0> + b|1>, where a and b are complex numbers called probability amplitudes.
Normalisation requires |a|^2 + |b|^2 = 1, because |a|^2 is the probability of measuring 0 and |b|^2 the probability of measuring 1. The amplitudes carry more than probabilities: their relative phase governs interference, which is what makes quantum computation more than randomised classical computation.
Physical realisations
Any quantum system with two cleanly addressable energy levels can serve as a qubit: the spin of an electron or nucleus, two energy levels of a trapped ion, the polarisation of a photon, or the two lowest states of a superconducting circuit. The abstraction |0>/|1> lets algorithms be written once and run on any of these.
- Superconducting transmons — two lowest circuit energy levels
- Trapped ions — internal electronic states
- Photons — horizontal and vertical polarisation
- Spin qubits — up and down of a confined electron
Why one qubit is not much, but many are
A single qubit holds only one bit of extractable classical information: a measurement yields one outcome, 0 or 1. The power appears with many qubits, because n qubits span a state space of dimension 2^n. Describing a general 300-qubit state would require more complex numbers than there are atoms in the observable universe, yet the physical register is only 300 two-level systems.
This exponential state space is the resource quantum algorithms exploit, but it is not freely readable — measurement collapses the state and returns only n classical bits. Designing algorithms is largely the art of arranging interference so the useful answer is the likely measurement outcome.