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In quantum computing, a qubit/ˈkjuːbɪt/ or quantum bit is a unit of quantum information—the quantum analogue of the classical bit. A qubit is a twostate quantummechanical system, such as the 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 superposition of both states at the same time, a property which is fundamental to quantum computing.
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.
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 superposition of both. This happens in basic math. (squareroot of 1)+(squareroot of 1) is normally thought to have only 2 solutions 1+1 and 1 + 1, but 0 is also a solution (1 + 1) and (1 + 1). These squareroots 1^(1/2) or 1^(1/32) for example are roots of unity and expand to more solutions to the same equation with each squareroot, later collapsing the wavefunction with squaring.
The two states in which a qubit may be measured are known as basis states (or basis vectors). As is the tradition with any sort of quantum states, they are represented by Dirac—or "braket"—notation. This means that the two computational basis states are conventionally written as and (pronounced "ket 0" and "ket 1").
A pure qubit state is a linear superposition of the basis states. This means that the qubit can be represented as a linear combination of and :
where α and β are probability amplitudes and can in general both be complex numbers.
When we measure this qubit in the standard basis, the probability of outcome is and the probability of outcome is . Because the absolute squares of the amplitudes equate to probabilities, it follows that α and β must be constrained by the equation
simply because this ensures you must measure either one state or the other.
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 and 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 would lie on the equator of the sphere, on the positive y axis.
The surface of the sphere is twodimensional space, which represents the state space of the pure qubit states. This state space has two local 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 . Another, the overall phase of the state, has no physically observable consequences, so we can arbitrarily choose α to be real, leaving just two degrees of freedom.
It is possible to put the qubit in a mixed state, a statistical combination of different pure states. Mixed states can be represented by points inside the Bloch sphere.
There are various kinds of physical operations that can be performed on pure qubit states.^{[citation needed]}
An important distinguishing feature between a qubit and a classical bit is that multiple qubits can exhibit quantum entanglement. Entanglement is a 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
In this state, called an equal superposition, there are equal probabilities of measuring either or , as .
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 or . Because of the qubits' entanglement, Bob must now get exactly the same measurement as Alice; i.e., if she measures a , Bob must measure the same, as is the only state where Alice's qubit is a .
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.
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 resource that is unique to quantum computation.
A number of entangled qubits taken together is a qubit register. Quantum computers perform calculations by manipulating qubits within a register. A qubyte is a collection of eight 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.^{[1]}
Similar to the qubit, a qutrit is a unit of quantum information in a 3level quantum system. This is analogous to the unit of classical information trit. The term "qudit" is used to denote a unit of quantum information in a dlevel quantum system.
List of unsolved problems in physics
Is it possible to have threedimensional, selfcorrecting, quantum memory? 
Any twolevel 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 twolevel 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.
The following is an incomplete list of physical implementations of qubits, and the choices of basis are by convention only.
Physical support  Name  Information support  

Photon  Polarization encoding  Polarization of light  Horizontal  Vertical 
Number of photons  Fock state  Vacuum  Single photon state  
Timebin encoding  Time of arrival  Early  Late  
Coherent state of light  Squeezed light  Quadrature  Amplitudesqueezed state  Phasesqueezed state 
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 
Josephson junction  Superconducting charge qubit  Charge  Uncharged superconducting island (Q=0)  Charged superconducting island (Q=2e, 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  Electron spin  Spin  Projection of spin orientation in "z" direction  Projection of spin orientation in "+z" direction 
In a paper titled "Solidstate quantum memory using the ^{31}P nuclear spin," published in the October 23, 2008 issue of the journal Nature,^{[2]} 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.^{[3]}
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.^{[4]}^{[5]}
The coining of the term "qubit" is attributed to Benjamin Schumacher.^{[6]} 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.
