Section 1.4 Classical Computing
Before diving into the basics of quantum computing, we must first discuss how computing is done classically. On non-quantum computers, information is stored in strings of bits, where each bit is either a 0 or a 1. These strings of bits represent numbers in binary and they provide computers with instructions on what to do. The notable difference on a quantum computer is that quantum bits (qubits) exist in a superposition of states that allows them to be both a 0 and a 1 until they are measured and this superposition collapses. This unique property of qubits allows quantum computers to perform multiple processes simultaneously.
When describing the state of a qubit, instead of writing 0 and 1, we use \(\ket{0}\) and \(\ket{1}\text{.}\) These quantum states belong to a vector space, which means that multiplying states by a constant coefficient and adding states together will result in another valid quantum state. This is how a superposition is formed, by creating a linear combination of the states \(\ket{0}\) and \(\ket{1}\text{.}\)
