computer science//quantum computing//qubit

A qubit is the basic unit of quantum information, a two-level physical system (the two lowest energy states of a superconducting circuit, two levels of a trapped ion, two polarizations of a photon) that can be prepared, manipulated and measured, and it plays in a quantum computer the role a bit plays in a classical one. Where a bit is either 0 or 1, a qubit's state is described by two complex numbers, its **amplitudes**, one for each outcome.

A qubit is the basic unit of quantum information, a two-level physical system (the two lowest energy states of a superconducting circuit, two levels of a trapped ion, two polarizations of a photon) that can be prepared, manipulated and measured, and it plays in a quantum computer the role a bit plays in a classical one. Where a bit is either 0 or 1, a qubit's state is described by two complex numbers, its amplitudes, one for each outcome.

∣ψ⟩=α∣0⟩+β∣1⟩,∣α∣2+∣β∣2=1|\psi\rangle=\alpha|0\rangle+\beta|1\rangle,\qquad |\alpha|^2+|\beta|^2=1∣ψ⟩=α∣0⟩+β∣1⟩,∣α∣2+∣β∣2=1

The state is ∣ψ⟩|\psi\rangle∣ψ⟩, the two basis states are ∣0⟩|0\rangle∣0⟩ and ∣1⟩|1\rangle∣1⟩, and α\alphaα, β\betaβ are complex amplitudes. Measured in that basis, the qubit returns 0 with probability ∣α∣2|\alpha|^2∣α∣2 and 1 with probability ∣β∣2|\beta|^2∣β∣2, and afterwards it is in the state it reported: the measurement both reads and resets. A qubit with α=β=1/2\alpha=\beta=1/\sqrt2α=β=1/2​ gives 0 half the time and 1 half the time, like a fair coin, yet it is a definite state that a gate can turn back into a certain 0, which a coin cannot do.

The Bloch sphere draws every pure state of one qubit as a point on a unit sphere: 0 at the north pole, 1 at the south, equal mixtures around the equator with the phase as longitude. Single-qubit gates are rotations of that sphere, which is why a control engineer reads them as pulses of a given angle about a given axis.

The phase is what makes a qubit more than a probability. Two states with the same ∣α∣2|\alpha|^2∣α∣2 and different phases behave differently once they interfere (superposition), and losing that phase to the environment is the commonest way a qubit fails (decoherence).

The capacity is subtler than it looks. Describing nnn qubits takes 2n2^n2n amplitudes, so 50 qubits already hold more numbers than a laptop's memory, but a measurement returns only nnn classical bits; the power lies in shaping the amplitudes before reading, never in reading them all.

A physical qubit is the device itself, with its error rate; a logical qubit is a protected qubit built from many physical ones (quantum error correction). Counts of qubits in announcements are almost always physical, which is why the number alone says little about what a machine can compute.