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Featured Article

A qubit is a quantum system in which the Boolean states 0 and 1 are represented by a prescribed pair of normalised and mutually orthogonal quantum states labeled as \{|0\rangle ,|1\rangle \}

The two states form a `computational basis' and any other (pure) state of the qubit can be written as a superposition \alpha |0\rangle +\beta |1\rangle for some α and β such that | α | 2 + | β | 2 = 1. A qubit is typically a microscopic system, such as an atom, a nuclear spin, or a polarised photon. A collection of n qubits is called a quantum register of size n.

We shall assume that information is stored in the registers in binary form. For example, the number 6 is represented by a register in state |1\rangle \otimes |1\rangle \otimes |0\rangle . In more compact notation: |a\rangle stands for the tensor product |a_{n-1}\rangle \otimes |a_{n-2}\rangle \ldots |a_{1}\rangle \otimes |a_{0}\rangle , where a_i\in\{0,1\}, and it represents a quantum register prepared with the value a=2^{0}a_{0}+2^{1}a_{1}+\ldots2^{n-1}a_{n-1}. There are 2n states of this kind, representing all binary strings of length n or numbers from 0 to 2n − 1, and they form a convenient computational basis. In the following a\in \{0,1\}^n (a is a binary string of length n) implies that \left| a \right\rangle belongs to the computational basis.

Read more about the Basic concepts in quantum computation


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