Quantum Gates and Quantum Circuits

Abstract Quantum gates, equivalent to logic gates, operate on and modify the state vectors. Alice and Bob explain what quantum gates do and illustrate their action on states describing a single qubit. These gates include the NOT gate, the Pauli gates, and the Hadamard gate. The operations of the gates are represented both as abstract symbols and by matrices multiplying state vectors (expressed as column vectors). Alice and Bob also provide a simple introduction to some of the mathematical aspects of quantum gates and what happens when several gates act successively on the state describing a qubit, a feature which appears again and again in quantum computing. Cardy wants to know how quantum measurements are related to quantum gates. Alice and Bob point out important differences between measurement devices and quantum gates. Those differences foreshadow the deep conceptual divide between quantum and classical physics.