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| {{distinguish|Cubit}}
| | My name is Lou (22 years old) and my hobbies are Gardening and Amateur geology.<br><br>Here is my website ... FIFA coin generator ([http://www.chinatablecloth.net/en/plus/guestbook.php navigate to this website]) |
| {{about|the quantum computing unit}}
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| {{Fundamental info units}}
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| In [[quantum computing]], a '''qubit''' {{IPAc-en|ˈ|k|juː|b|ɪ|t}} or '''quantum bit''' is a unit of [[quantum information]]—the quantum analogue of the classical [[bit]]. A qubit is a [[Two-state quantum system|two-state quantum-mechanical system]], such as the [[Photon polarization|polarization ]] of a single [[photon]]: here the two states are vertical polarization and horizontal polarization. In a classical system, a bit would have to be in one state or the other, but quantum mechanics allows the qubit to be in a [[Quantum superposition|superposition ]] of both states at the same time, a property which is fundamental to quantum computing.
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| ==Bit versus qubit==
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| A [[bit]] is the basic unit of information. It is used to represent information by computers. Regardless of its physical realization, a bit is always understood to be either a 0 or a 1. An analogy to this is a light switch— with the off position representing 0 and the on position representing 1.
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| A qubit has a few similarities to a classical bit, but is overall very different. Like a bit, a qubit can have two possible values—normally a 0 or a 1. The difference is that whereas a bit ''must be'' either 0 or 1, a qubit ''can be'' 0, 1, or a [[Quantum superposition|superposition]] of both.
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| ==Representation==
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| The two states in which a qubit may be measured are known as [[Basis (linear algebra)|basis]] states (or basis [[vector space|vector]]s). As is the tradition with any sort of [[quantum states]], they are represented by Dirac—or [[bra-ket notation|"bra-ket"]]—notation. This means that the two computational basis states are conventionally written as <math>| 0 \rangle </math> and <math>| 1 \rangle </math> (pronounced "ket 0" and "ket 1").
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| ==Qubit states==
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| [[Image:Bloch Sphere.svg|thumb|[[Bloch sphere]] representation of a qubit. The probability amplitudes in the text are given by <math> \alpha = \cos\left(\frac{\theta}{2}\right) </math> and <math> \beta = e^{i \phi} \sin\left(\frac{\theta}{2}\right) </math>.]]
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| A pure qubit state is a linear [[quantum superposition|superposition]] of the basis states. This means that the qubit can be represented as a [[linear combination]] of <math>|0 \rangle </math> and <math>|1 \rangle </math> :
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| : <math>| \psi \rangle = \alpha |0 \rangle + \beta |1 \rangle,\,</math>
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| where <var>α</var> and <var>β</var> are [[probability amplitude]]s and can in general both be [[complex number]]s.
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| When we measure this qubit in the standard basis, the probability of outcome <math>|0 \rangle </math> is <math>| \alpha |^2</math> and the probability of outcome <math>|1 \rangle </math> is <math>| \beta |^2</math>. Because the absolute squares of the amplitudes equate to probabilities, it follows that <var>α</var> and <var>β</var> must be constrained by the equation
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| : <math>| \alpha |^2 + | \beta |^2 = 1 \,</math>
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| simply because this ensures you must measure either one state or the other.
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| ===Bloch sphere===
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| The possible states for a single qubit can be visualised using a [[Bloch sphere]] (see diagram). Represented on such a sphere, a classical bit could only be at the "North Pole" or the "South Pole", in the locations where <math>|0 \rangle </math> and <math>|1 \rangle </math> are respectively. The rest of the surface of the sphere is inaccessible to a classical bit, but a pure qubit state can be represented by any point on the surface. For example, the pure qubit state <math>{|0 \rangle +i|1 \rangle}\over{\sqrt{2}} </math> would lie on the equator of the sphere, on the positive y axis.
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| The surface of the sphere is two-dimensional space, which represents the [[state space (physics)|state space]] of the pure qubit states. This state space has two local [[Degrees of freedom (physics and chemistry)|degrees of freedom]]. It might at first sight seem that there should be four degrees of freedom, as α and β are [[complex numbers]] with two degrees of freedom each. However, one degree of freedom is removed by the constraint <math>| \alpha |^2 + | \beta |^2 = 1 \,</math>. Another, the overall [[phase factor|phase]] of the state, has no physically observable consequences, so we can arbitrarily choose α to be real, leaving just two degrees of freedom.
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| It is possible to put the qubit in a [[Mixed state (physics)|mixed state]], a statistical combination of different pure states. Mixed states can be represented by points inside the Bloch sphere.
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| ===Operations on pure qubit states===
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| There are various kinds of physical operations that can be performed on pure qubit states.{{Citation needed|date=August 2009}}
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| * A [[quantum logic gate]] can operate on a qubit: mathematically speaking, the qubit undergoes a [[unitary transformation]]. Unitary transformations correspond to rotations of the qubit vector in the Bloch sphere.
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| * [[Quantum measurement|Standard basis measurement]] is an operation in which information is gained about the state of the qubit. The result of the measurement will be either <math>| 0 \rangle </math>, with probability <math>|\alpha|^2</math>, or <math>| 1 \rangle </math>, with probability <math>|\beta|^2</math>. Measurement of the state of the qubit alters the values of <var>α</var> and <var>β</var>. For instance, if the result of the measurement is <math>| 0 \rangle </math>, <var>α</var> is changed to 1 (up to phase) and <var>β</var> is changed to 0. Note that a measurement of a qubit state entangled with another quantum system transforms a pure state into a [[Mixed state (physics)|mixed state]].
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| ==Entanglement==
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| An important distinguishing feature between a qubit and a classical bit is that multiple qubits can exhibit [[quantum entanglement]]. Entanglement is a [[quantum nonlocality|nonlocal]] property that allows a set of qubits to express higher correlation than is possible in classical systems. Take, for example, two entangled qubits in the [[Bell state]]
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| :<math>\frac{1}{\sqrt{2}} (|00\rangle + |11\rangle).</math>
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| In this state, called an ''equal superposition,'' there are equal probabilities of measuring either <math>|00\rangle</math> or <math>|11\rangle</math>, as <math>|1/\sqrt{2}|^2 = 1/2</math>.
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| Imagine that these two entangled qubits are separated, with one each given to Alice and Bob. Alice makes a measurement of her qubit, obtaining—with equal probabilities—either <math>|0\rangle</math> or <math>|1\rangle</math>. Because of the qubits' entanglement, Bob must now get exactly the same measurement as Alice; i.e., if she measures a <math>|0\rangle</math>, Bob must measure the same, as <math>|00\rangle</math> is the only state where Alice's qubit is a <math>|0\rangle</math>.
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| Entanglement also allows multiple states (such as the [[Bell state]] mentioned above) to be acted on simultaneously, unlike classical bits that can only have one value at a time. Entanglement is a necessary ingredient of any quantum computation that cannot be done efficiently on a classical computer.
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| Many of the successes of quantum computation and communication, such as [[quantum teleportation]] and [[superdense coding]], make use of entanglement, suggesting that entanglement is a [[Computational resource|resource]] that is unique to quantum computation.
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| ===Quantum register===
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| A number of entangled qubits taken together is a [[quantum register|qubit register]]. [[Quantum computer]]s perform calculations by manipulating qubits within a register. A ''qubyte'' is a collection of eight [[Quantum entanglement|entangled]] qubits. It was first demonstrated by a team at the Institute of Quantum Optics and Quantum Information at the [[University of Innsbruck]] in Austria in December 2005.<ref>[http://heart-c704.uibk.ac.at/index.html UIBK.ac.at]</ref>
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| ==Variations of the qubit==
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| Similar to the qubit, a [[qutrit]] is a unit of quantum information in a 3-level quantum system. This is analogous to the unit of classical information [[Ternary numeral system|trit]]. The term "'''qudit'''" is used to denote a unit of quantum information in a ''d''-level quantum system.
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| ==Physical representation==
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| {{Unsolved|physics|Is it possible to have three-dimensional, [[Stabilizer code|self-correcting]], quantum memory?}}
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| Any two-level quantum system can be used as a qubit. Multilevel systems can be used as well, if they possess two states that can be effectively decoupled from the rest (e.g., ground state and first excited state of a nonlinear oscillator). There are various proposals. Several physical implementations which approximate two-level systems to various degrees were successfully realized. Similarly to a classical bit where the state of a transistor in a processor, the magnetization of a surface in a hard disk and the presence of current in a cable can all be used to represent bits in the same computer, an eventual quantum computer is likely to use various combinations of qubits in its design.
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| The following is an incomplete list of physical implementations of qubits, and the choices of basis are by convention only.
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| {| align="center" class="wikitable"
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| |-
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| ! scope="col" | Physical support
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| ! scope="col" | Name
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| ! scope="col" | Information support
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| ! scope="col" style="background: white;" | <math>|0 \rangle</math>
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| ! scope="col" style="background: white;" | <math>|1 \rangle</math>
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| |-
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| | rowspan=3 |[[Photon]]
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| | Polarization encoding
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| | [[Polarization of light]]
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| | Horizontal
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| | Vertical
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| |-
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| | Number of photons
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| | [[Fock state]]
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| | Vacuum
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| | Single photon state
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| |-
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| | [[Time-bin encoding]]
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| | Time of arrival
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| | Early
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| | Late
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| |-
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| | Coherent state of light
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| | [[Squeezed coherent state|Squeezed light]]
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| | Quadrature
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| | Amplitude-squeezed state
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| | Phase-squeezed state
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| |-
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| | rowspan=2|[[Electron]]s
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| | [[Spin quantum number|Electronic spin]]
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| | Spin
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| | Up
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| | Down
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| |-
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| | Electron number
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| | [[charge (physics)|Charge]]
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| | No electron
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| | One electron
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| |-
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| | [[Atomic nucleus|Nucleus]]
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| | [[Nuclear spin]] addressed through [[Nuclear magnetic resonance|NMR]]
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| | Spin
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| | Up
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| | Down
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| |-
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| | [[Optical lattice]]s
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| | Atomic spin
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| | Spin
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| | Up
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| | Down
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| |-
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| | rowspan=3|[[Josephson junction]]
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| | Superconducting [[charge qubit]]
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| | Charge
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| | Uncharged superconducting island (''Q''=0)
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| | Charged superconducting island (''Q''=2''e'', one extra Cooper pair)
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| |-
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| | Superconducting [[flux qubit]]
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| | Current
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| | Clockwise current
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| | Counterclockwise current
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| |-
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| | Superconducting [[phase qubit]]
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| | Energy
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| | Ground state
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| | First excited state
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| |-
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| | Singly charged [[quantum dot]] pair
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| | Electron localization
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| | Charge
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| | Electron on left dot
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| | Electron on right dot
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| |-
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| | Quantum dot
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| | Electron spin
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| | Spin
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| | Projection of spin orientation in "-z" direction
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| | Projection of spin orientation in "+z" direction
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| |}
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| ==Qubit storage==
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| In a paper titled "Solid-state quantum memory using the <sup>31</sup>P nuclear spin," published in the October 23, 2008 issue of the journal ''[[Nature (journal)|Nature]]'',<ref>
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| {{cite journal
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| |author=J. J. L. Morton
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| |coauthors=''et al.''
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| |year=2008
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| |title=Solid-state quantum memory using the <sup>31</sup>P nuclear spin |journal=[[Nature (journal)|Nature]]
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| |volume=455 |pages=1085–1088
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| |doi=10.1038/nature07295
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| |bibcode = 2008Natur.455.1085M
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| |issue=7216|arxiv = 0803.2021 }}</ref> an international team of scientists that included researchers with the U.S. Department of Energy's [[Lawrence Berkeley National Laboratory]] (Berkeley Lab) 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 modification of similar systems (using charged rather than neutral donors) have dramatically extended this time, to 3 hours at very low temperatures and 39 minutes at room temperature.<ref>{{cite journal |author=Kamyar Saeedi |coauthors=''et al.''|year=2013|title=Room-Temperature Quantum Bit Storage Exceeding 39 Minutes Using Ionized Donors in Silicon-28|volume=342|pages=830–833|doi=10.1126/science.1239584|issue=6160|journal=[[Science (journal)|Science]]}}</ref>
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| ==Origin of the concept and term==
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| The concept of the qubit was unknowingly introduced by [[Stephen Wiesner]] in 1983, in his proposal for unforgeable [[quantum money]], which he had tried to publish for over a decade.<ref>
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| {{cite journal
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| |author=S. Weisner | authorlink=Stephen Wiesner
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| |year=1983
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| |title=Conjugate coding
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| |journal=[[Association for Computing Machinery]], Special Interest Group in Algorithms and Computation Theory
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| |volume=15 |pages=78–88
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| }}</ref><ref name="Zeilinger">A. Zelinger, ''Dance of the Photons: From Einstein to Quantum Teleportation'', Farrar, Straus & Giroux, New York, 2010, pp. 189, 192, ISBN 0374239665</ref>
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| The coining of the term "qubit" is attributed to [[Benjamin Schumacher]].<ref>
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| {{cite journal
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| |author=B. Schumacher | authorlink=Benjamin Schumacher
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| |year=1995
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| |title=Quantum coding
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| |journal=[[Physical Review A]]
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| |volume=51 |pages=2738–2747
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| |doi=10.1103/PhysRevA.51.2738
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| |bibcode = 1995PhRvA..51.2738S
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| |issue=4 }}</ref> In the acknowledgments of his paper, Schumacher states that the term ''qubit'' was invented in jest (due to its phonological resemblance with an ancient unit of length called [[cubit]]), 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]].
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| ==See also==
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| * [[W state]]
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| * [[Quantum computer]]
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| * [[Photonic computer]]
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| ==References==
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| {{Reflist}}
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| ==External links==
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| * [http://www.sciam.com/article.cfm?chanID=sa006&colID=5&articleID=000D4372-A8A9-1330-A54583414B7F0000 An update on qubits in the Oct 2005] issue of [[Scientific American]]
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| * [http://www.qubit.org/ Qubit.org] cofounded by one of the pioneers in quantum computation, [[David Deutsch]]
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| {{quantum computing}}
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| [[Category:Units of information]]
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| [[Category:Quantum information science]]
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| [[Category:Australian inventions]]
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| [[Category:Quantum states]]
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| {{Link GA|de}}
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| {{Link GA|es}}
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