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A qubit is the fundamental unit of quantum information, analogous to a classical bit but capable of existing in a superposition of |0> and |1>. The general state of a single qubit is alpha|0> + beta|1>, where alpha and beta are complex amplitudes satisfying |alpha|^2 + |beta|^2 = 1. Multi-qubit systems live in tensor-product Hilbert spaces whose dimension grows exponentially: n qubits span a 2n-dimensional space. This exponential state space is the source of quantum computing's potential power over classical computation.
A classical bit is either 0 or 1. A qubit can be in a superposition of both: the general single-qubit state is alpha|0> + beta|1>, where alpha and beta are complex numbers called amplitudes. The constraint |alpha|^2 + |beta|^2 = 1 ensures that the probabilities of measuring 0 or 1 sum to one. From your study of quantum superposition and Dirac notation, you know the formalism; quantum computing repurposes it as information processing. The states |0> and |1> are the computational basis — column vectors [1,0]T and [0,1]T in the two-dimensional Hilbert space C2.
The Bloch sphere provides geometric intuition for single-qubit states. Any pure state can be parameterized as cos(theta/2)|0> + ei*phi sin(theta/2)|0>, where theta is the polar angle and phi is the azimuthal angle. The north pole is |0>, the south pole is |1>, and equal superpositions live on the equator. Quantum gates correspond to rotations of this sphere. The Bloch sphere works only for single qubits — multi-qubit states cannot be visualized this simply because of entanglement.
When multiple qubits are combined, the state space grows exponentially. Two qubits live in C2 tensor C2 = C4, spanned by |00>, |01>, |10>, |11>. Three qubits span C8. In general, n qubits require 2n complex amplitudes to describe. This is the fundamental resource of quantum computing: a 300-qubit system has more amplitudes than there are atoms in the observable universe. But this exponential richness is not freely accessible — measurement collapses the state to a single basis vector, and the art of quantum algorithm design is arranging interference so that the measurement outcome is useful.
The distinction between a qubit and a classical probabilistic bit is critical. A coin that is 50% heads and 50% tails is described by a probability distribution — a statistical mixture with no internal structure. The state |+> = (|0> + |1>)/sqrt(2) is also measured as 0 or 1 with equal probability, but its amplitudes are complex numbers with definite phases. Two amplitude paths to the same outcome can reinforce or cancel depending on their relative phase. This interference is the engine of quantum speedups: algorithms like Deutsch-Jozsa and Grover's search work by arranging phases so that correct answers receive constructive interference and wrong answers receive destructive interference. Without interference — if qubits were just probabilistic bits — no quantum advantage would exist.
Multi-qubit states can also be entangled, meaning the joint state cannot be factored as a product of individual qubit states. The Bell state (|00> + |11>)/sqrt(2) has this property: neither qubit has a definite state on its own, but measuring one instantly determines the other. Entanglement is a uniquely quantum resource with no classical analog, and it plays a central role in quantum teleportation, superdense coding, and quantum error correction. The combination of superposition, interference, and entanglement in an exponentially large state space is what gives quantum computing its distinctive character.