Quantum Computing Foundations and Models

Quantum computers represent information with quantum states

Quantum computers represent and process information using quantum states rather than classical bits. The basic unit is the qubit, which can be in a superposition of two basis states, typically written as |ψ⟩ = α|0⟩ + β|1⟩. Geometrically, such a state corresponds to a point on the Bloch sphere, and the coefficients α and β are complex probability amplitudes whose magnitudes determine measurement probabilities via the Born rule. Computation is performed by manipulating qubits with quantum logic gates (unitary operations) and then measuring them. Because qubits carry relative phase information, quantum interference can amplify the probability of desired outcomes when algorithms are designed to exploit superposition, interference, and entanglement. Although quantum computers can, in principle, offer exponential or other significant speedups for certain problems, practical implementations are still experimental and limited by noise and decoherence.

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Superposition, interference, and entanglement enable quantum computation

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