====================================================================== = Qubit = ====================================================================== Introduction ====================================================================== In quantum computing, a qubit () or quantum bit (sometimes qbit) is the basic unit of quantum informationâthe 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. Etymology ====================================================================== 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. Bit versus qubit ====================================================================== 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 qubitâusually 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 2'n'â1 complex numbers. Standard representation ====================================================================== 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 \rangle = \bigl[\begin{smallmatrix} 1\\ 0 \end{smallmatrix}\bigr] and | 1 \rangle = \bigl[\begin{smallmatrix} 0\\ 1 \end{smallmatrix}\bigr]. They are written in the conventional Diracâor "bra-ket"ânotation; the | 0 \rangle and | 1 \rangle are pronounced "ket 0" and "ket 1", respectively. These two orthonormal basis states, \ A number of qubits taken together is a qubit register. Quantum computers perform calculations by manipulating qubits within a register. A **qubyte** (quantum byte) is a collection of eight qubits.{{cite journal Similar to the qubit, the qutrit is the unit of quantum information that can be realized in suitable 3-level quantum systems. This is analogous to the unit of classical information trit of ternary computers. Note, however, that not all 3-level quantum systems are qutrits. The term "**qu-'d'-it**" (**'qu**antum' **d**'-g**it**') denotes the unit of quantum information that can be realized in suitable 'd'-level quantum systems. In 2017, scientists at the National Institute of Scientific Research constructed a pair of qudits with 10 different states each, giving more computational power than 6 qubits. Qubit states ============== Physical support Name Information support |0 \rangle |1 \ran gle rowspan=3 |Photon Polarization encoding Polarization of light Horizontal Vertical Number of photons Fock state Vacuum Single photon state Time-bin encoding Time of arrival Early Late Coherent state of light Squeezed light Quadrature Amplitude-squeezed state Phase-squeezed state rowspan=2|Electrons Electronic spin Spin Up Down Electron number Charge No electron One electron Nucleus Nuclear spin addressed through NMR Spin Up Down Optical lattices Atomic spin Spin Up Down rowspan=3|Josephson junction Superconducting charge qubit Charge Uncharged superconducting island ('Q'=0) Charged superconducting island ('Q'=2'e', one extra Cooper pair) Superconducting flux qubit Current Clockwise current Counterclockwise current Superconducting phase qubit Energy Ground state First excited state Singly charged quantum dot pair Electron localization Charge Electron on left dot Electron on right dot Quantum dot Dot spin Spin Down Up Gapped topological system Non-abelian anyons Braiding of Excitations Depends on specific topological system Depends on specific topological system |van der Waals heterostructure |Electron localization |Charge |Electron on bottom sheet |Electron on top sheet Qubit storage ====================================================================== In a paper entitled "Solid-state quantum memory using the 31P nuclear spin", published in the October 23, 2008, issue of the journal 'Nature', a team of scientists from the U.K. and U.S. reported the first relatively long (1.75 seconds) and coherent transfer of a superposition state in an electron spin "processing" qubit to a nuclear spin "memory" qubit. This event can be considered the first relatively consistent quantum data storage, a vital step towards the development of quantum computing. Recently, a modification of similar systems (using charged rather than neutral donors) has dramatically extended this time, to 3 hours at very low temperatures and 39 minutes at room temperature. Room temperature preparation of a qubit based on electron spins instead of nuclear spin was also demonstrated by a team of scientists from Switzerland and Australia. See also ====================================================================== * Two-state quantum system * Ancilla bit * Photonic computer * W state *Physical and logical qubits Further reading ====================================================================== *A good introduction to the topic is 'Quantum Computation and Quantum Information' by Nielsen and Chuang. *An excellent treatment of two-level quantum systems, decades before the term âqubitâ was coined, is found in the third volume of The Feynman Lectures on Physics [http://www.feynmanlectures.caltech.edu/III_toc.html (2013 ebook edition)]. *A non-traditional motivation of the qubit aimed at non-physicists is found in Quantum Computing Since Democritus, by Scott Aaronson, Cambridge University Press (2013). *A good introduction to qubits for non-specialists, by the person who coined the word, is found in Lecture 21 of ââThe science of information: from language to black holesââ, by Professor Benjamin Schumacher, The Great Courses, The Teaching Company (4DVDs, 2015). *A picture-book introduction to entanglement, contrasting classical systems and a Bell state, is found in âQuantum entanglement for babiesâ, by Chris Ferrie (2017). 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