In quantum computing, a qubit (/ˈkjuːbɪt/) or quantum bit is a basic unit of quantum information—the quantum version of the classic 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 spin states (left-handed and the right-handed circular polarization) can also be measured as horizontal and vertical linear 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 multiple states simultaneously, a property that is fundamental to quantum mechanics and quantum computing.

Etymology

The coining of the term qubit is attributed to Benjamin Schumacher.^[1] In the acknowledgments of his 1995 paper, Schumacher states that the term qubit was created in jest during a conversation with William Wootters.

Bit versus qubit

A binary digit, characterized as 0 or 1, is used to represent information in classical computers. When averaged over both of its states (0,1), 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 a 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" between two logic levels 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. However, whereas the state of a bit can only be binary (either 0 or 1), the general state of a qubit according to quantum mechanics can arbitrarily be a coherent superposition of all computable states simultaneously.^[2] 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. Respectively, 8 qubits is called a lnq.

For a system of n components, a complete description of its state in classical physics requires only n bits, whereas in quantum physics a system of n qubits requires 2ⁿ complex numbers (or a single point in a 2ⁿ-dimensional vector space).^{[3] [clarification needed]}

Standard representation

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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 ${\displaystyle |0\rangle ={\bigl }}$ and ${\displaystyle |1\rangle ={\bigl }}$. They are written in the conventional Dirac—or "bra–ket"—notation; the ${\displaystyle |0\rangle }$ and ${\displaystyle |1\rangle }$ are pronounced "ket 0" and "ket 1", respectively. These two orthonormal basis states, ${\displaystyle \{|0\rangle ,|1\rangle \}}$, 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. A set of qubits taken together is called a quantum register. For example, two qubits could be represented in a four-dimensional linear vector space spanned by the following product basis states:

${\displaystyle |00\rangle ={\biggl }}$, ${\displaystyle |01\rangle ={\biggl }}$, ${\displaystyle |10\rangle ={\biggl }}$, and ${\displaystyle |11\rangle ={\biggl }{\begin{smallmatrix}0\\0\\0\\1\end{smallmatrix}}{\biggr }}$.

In general, n qubits are represented by a superposition state vector in 2ⁿ dimensional Hilbert space.

Qubit statesedit

A pure qubit state is a coherent superposition of the basis states. This means that a single qubit (${\displaystyle \psi }$) can be described by a linear combination of ${\displaystyle |0\rangle }$ and ${\displaystyle |1\rangle }$:

${\displaystyle |\psi \rangle =\alpha |0\rangle +\beta |1\rangle }$

where α and β are the probability amplitudes, and are both complex numbers. When we measure this qubit in the standard basis, according to the Born rule, the probability of outcome ${\displaystyle |0\rangle }$ with value "0" is ${\displaystyle |\alpha |^{2}}$ and the probability of outcome ${\displaystyle |1\rangle }$ with value "1" is ${\displaystyle |\beta |^{2}}$. Because the absolute squares of the amplitudes equate to probabilities, it follows that ${\displaystyle \alpha }$ and ${\displaystyle \beta }$ must be constrained according to the second axiom of probability theory by the equation^[5]

${\displaystyle |\mathrm{\alpha <!--\; \alpha \; -->}{|}^{}}$Zdroj:https://en.wikipedia.org?pojem=Quantum_bit
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