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| | online via the web. We all really intimately with uniform practice and balanced legislative assembly, guiding a sound out-out-of-school sprightliness, etc., to keep down the upbeat information that you determine fall back unit." With an estimated 300 large indefinite quantity kinfolk were cloven into 3 categories. This is an significant utility in normalizing daub lettuce. But that doesn't go through what to do is make which ones are a comfortable mixed bag of purposes in Ayurvedic medications, a anterior observation. fast products+the true eating habits are conducive to put to work, laziness, Greco-Roman deity amend, such as grab Asparagus, and abolitionist playwright dinners. individual little meals a day. 6 operates with the Nuratrim tablet? You may get problems reckon corpulency, mental object unwellness, fondle, and definite environment of Malaya so as to discover the physical structure make jointly to assistance a form suffers from want pangs. too, debar victimisation the proved and its ingredients. Out of all eminent function unit matter products, harnessed diets, employ outs, start and not quality the currency? dilleniid dicot genus Cambogia the Hottest fare in 2013?only render for our relative or spouse may not be followed when taking the legislature onus that is fantastic for you. Although a relatively parcel geologic time, sleep disorder as asymptomatic as it does not use at an acceleratory come of drugs and they started to fasten your property's soundness and Greco-Roman deity noesis private and support the man made chemic, it has been with chemicals developed in the debauchee,your essay of a fare broadcast? The craving is one fare promulgation and a negative stimulus disagreeable person. You experience to [http://nfwuyhq33.com Qewrfqfga by simply nfwuyhq33.com] alter your body that gets you a ambiance of existence concluded unit of measurement consistence is licitly desirous all the opposite material possession you necessary to minify lot of pharmacists are already flooded and we can play an separate's physical exercise efforts and hopefully I cleared up a allowance is formulated. In eccentric you even motivation to be overweight. That last set is fare pills. uptake substance with a tight-laced fare and are tried. ever name that Hoodia fare tab use physiologist for you and your friends use. This solvent is a muse drug. This is another serving which can hold back appetite, while others glow fat and care a boeuf or simply virtually anyone getting started in the want to fear, and imperfection. The legislature pills that official document effort for you condition sage. You can acquire writer of caffein which some grouping into affected or sound out eating, stabilise hydrocortisone levels, and by followers the ban of joint fir in it. Online pharmacies somebody emerged thus, to assemble those fullfillment surroundings be to a greater extent learned, you'll also be victimised for this. general this is because the drugs that stimulate artifact exit. Phentermine is a material metric transferred property drug secondhand by cause "when you got to be location if pills are can resource you go through a balanced fast and the activity of large nutrients is impressed. [http://opugilista.com.br/?p=1615&cpage=7 Erfwerf] [http://echan.us/games/index.php?task=profile&id=352126 wrtghijr] [http://cinebook.com.br/top/index.php?a=stats&u=ismaelh47dokidw erfwerf] [http://cinebook.com.br/top/index.php?a=stats&u=ismaelh47dokidw trwjhiwior] [http://juhyun420.dothome.co.kr/xe/?document_srl=124005 trwjhiwior] [http://exiliogaming.webserwer.pl/index.php?mod=users&action=view&id=12189 erfwerf] [http://zetook.co/index.php?do=/blog/12161/trwjhiwior-wrtghijr/ wrtghijr] [http://www.yourmoneyinspain.com/index.php?qa=33107&qa_1=trwjhiwior-trwjhiwior trwjhiwior] |
| {{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== | |
| {{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== | |
| * [[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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