QuBits

Qubits are the basic units of quantum information. A qubit is a two-level quantum system described by a state in a two-dimensional Hilbert space. In the computational basis {|0>, |1>}, its state is |ψ> = α|0> + β|1>, with complex amplitudes α and β satisfying |α|^2 + |β|^2 = 1. Measurement in this basis yields 0 with probability |α|^2 and 1 with probability |β|^2. Unlike a classical bit, a qubit can be in a superposition, and the relative phase between α and β influences interference.

Qubits can be represented on the Bloch sphere, with pure states on the surface. Multi-qubit states may be entangled, meaning the state cannot be written as a product of single-qubit states. Entanglement enables correlations with no classical counterpart and is central to quantum algorithms.

Quantum gates implement unitary transformations on qubits. Common single-qubit gates include X, Y, Z, H, and phase gates; two-qubit gates such as CNOT or CZ generate entanglement. A universal gate set can approximate any quantum computation.

Physical realizations span several platforms. Superconducting circuits and trapped ions are leading processor technologies; photonic qubits are well suited for communication; other approaches include quantum dots and color centers in diamond.

Challenges include decoherence and operational errors. Quantum error correction and fault-tolerant architectures aim to protect information. No-cloning prevents copying unknown quantum states. Beyond computing, qubits enable quantum simulation and advances in secure communication.