Qubit

In quantum computing, a qubit (/ˈkjuːbɪt/) or quantum bit (sometimes qbit) is the basic unit of quantum information—the quantum version of the classical binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical system, one of the simplest quantum systems displaying the peculiarity of quantum mechanics. Examples include: the spin of the electron in which the two levels can be taken as spin up and spin down; or the polarization of a single photon in which the two states can be taken to be the vertical polarization and the horizontal polarization. In a classical system, a bit would have to be in one state or the other. However, quantum mechanics allows the qubit to be in a coherent superposition of both states/levels simultaneously, a property which is fundamental to quantum mechanics and quantum computing. In quantum computing, a qubit (/ˈkjuːbɪt/) or quantum bit (sometimes qbit) is the basic unit of quantum information—the quantum version of the classical binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical system, one of the simplest quantum systems displaying the peculiarity of quantum mechanics. Examples include: the spin of the electron in which the two levels can be taken as spin up and spin down; or the polarization of a single photon in which the two states can be taken to be the vertical polarization and the horizontal polarization. In a classical system, a bit would have to be in one state or the other. However, quantum mechanics allows the qubit to be in a coherent superposition of both states/levels simultaneously, a property which is fundamental to quantum mechanics and quantum computing. The coining of the term qubit is attributed to Benjamin Schumacher. In the acknowledgments of his 1995 paper, Schumacher states that the term qubit was created in jest during a conversation with William Wootters. The paper describes a way of compressing states emitted by a quantum source of information so that they require fewer physical resources to store. This procedure is now known as Schumacher compression. A binary digit, characterized as 0 and 1, is used to represent information in classical computers. A binary digit can represent up to one bit of Shannon information, where a bit is the basic unit of information.However, in this article, the word bit is synonymous with binary digit. In classical computer technologies, a processed bit is implemented by one of two levels of low DC voltage, and whilst switching from one of these two levels to the other, a so-called forbidden zone must be passed as fast as possible, as electrical voltage cannot change from one level to another instantaneously. There are two possible outcomes for the measurement of a qubit—usually taken to have the value '0' and '1', like a bit or binary digit. However, whereas the state of a bit can only be either 0 or 1, the general state of a qubit according to quantum mechanics can be a coherent superposition of both. Moreover, whereas a measurement of a classical bit would not disturb its state, a measurement of a qubit would destroy its coherence and irrevocably disturb the superposition state. It is possible to fully encode one bit in one qubit. However, a qubit can hold more information, e.g. up to two bits using superdense coding. For a system of n components, a complete description of its state in classical physics requires only n bits, whereas in quantum physics it requires 2n−1 complex numbers. In quantum mechanics, the general quantum state of a qubit can be represented by a linear superposition of its two orthonormal basis states (or basis vectors). These vectors are usually denoted as | 0 ⟩ = [ 1 0 ] {displaystyle |0 angle ={igl }} and | 1 ⟩ = [ 0 1 ] {displaystyle |1 angle ={igl }} . They are written in the conventional Dirac—or 'bra–ket'—notation; the | 0 ⟩ {displaystyle |0 angle } and | 1 ⟩ {displaystyle |1 angle } are pronounced 'ket 0' and 'ket 1', respectively. These two orthonormal basis states, { | 0 ⟩ , | 1 ⟩ } {displaystyle {|0 angle ,|1 angle }} , together called the computational basis, are said to span the two-dimensional linear vector (Hilbert) space of the qubit. Qubit basis states can also be combined to form product basis states. For example, two qubits could be represented in a four-dimensional linear vector space spanned by the following product basis states: | 00 ⟩ = [ 1 0 0 0 ] {displaystyle |00 angle ={iggl }} , | 01 ⟩ = [ 0 1 0 0 ] {displaystyle |01 angle ={iggl }} , | 10 ⟩ = [ 0 0 1 0 ] {displaystyle |10 angle ={iggl }} , and | 11 ⟩ = [ 0 0 0 1 ] {displaystyle |11 angle ={iggl }} . In general, n qubits are represented by a superposition state vector in 2n-dimensional Hilbert space.