Qubit

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Not to be confused with Cubit or Q*bert.
This article is about the quantum computing unit. For other uses, see Qubit (disambiguation).

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 two-state quantum-mechanical 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.

Bit versus qubit[edit]

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.

Representation[edit]

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 "bra–ket"—notation. This means that the two computational basis states are conventionally written as | 0 \rangle and | 1 \rangle (pronounced "ket 0" and "ket 1").

Qubit states[edit]

Bloch sphere representation of a qubit. The probability amplitudes in the text are given by  \alpha = \cos\left(\frac{\theta}{2}\right) and  \beta = e^{i \phi}  \sin\left(\frac{\theta}{2}\right) .

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 |0 \rangle and |1 \rangle  :

| \psi \rangle = \alpha |0 \rangle + \beta |1 \rangle,\,

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 |0 \rangle is | \alpha |^2 and the probability of outcome |1 \rangle is | \beta |^2. Because the absolute squares of the amplitudes equate to probabilities, it follows that α and β must be constrained by the equation

| \alpha |^2 + | \beta |^2 = 1 \,

simply because this ensures you must measure either one state or the other.

Bloch sphere[edit]

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 |0 \rangle and |1 \rangle 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 {|0 \rangle +i|1 \rangle}\over{\sqrt{2}}  would lie on the equator of the sphere, on the positive y axis.

The surface of the sphere is two-dimensional 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 | \alpha |^2 + | \beta |^2 = 1 \,. 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.

Operations on pure qubit states[edit]

There are various kinds of physical operations that can be performed on pure qubit states.[citation needed]

Entanglement[edit]

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

\frac{1}{\sqrt{2}} (|00\rangle + |11\rangle).

In this state, called an equal superposition, there are equal probabilities of measuring either |00\rangle or |11\rangle, as |1/\sqrt{2}|^2 = 1/2.

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 |0\rangle or |1\rangle. Because of the qubits' entanglement, Bob must now get exactly the same measurement as Alice; i.e., if she measures a |0\rangle, Bob must measure the same, as |00\rangle is the only state where Alice's qubit is a |0\rangle.

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.

Quantum register[edit]

A number of 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]

Variations of the qubit[edit]

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 trit. The term "qudit" is used to denote a unit of quantum information in a d-level quantum system.

Physical representation[edit]

List of unsolved problems in physics

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.

The following is an incomplete list of physical implementations of qubits, and the choices of basis are by convention only.

Physical supportNameInformation support|0 \rangle|1 \rangle
PhotonPolarization encodingPolarization of lightHorizontalVertical
Number of photonsFock stateVacuumSingle photon state
Time-bin encodingTime of arrivalEarlyLate
Coherent state of lightSqueezed lightQuadratureAmplitude-squeezed statePhase-squeezed state
ElectronsElectronic spinSpinUpDown
Electron numberChargeNo electronOne electron
NucleusNuclear spin addressed through NMRSpinUpDown
Optical latticesAtomic spinSpinUpDown
Josephson junctionSuperconducting charge qubitChargeUncharged superconducting island (Q=0)Charged superconducting island (Q=2e, one extra Cooper pair)
Superconducting flux qubitCurrentClockwise currentCounterclockwise current
Superconducting phase qubitEnergyGround stateFirst excited state
Singly charged quantum dot pairElectron localizationChargeElectron on left dotElectron on right dot
Quantum dotElectron spinSpinProjection of spin orientation in "-z" directionProjection of spin orientation in "+z" direction

Qubit storage[edit]

In a paper titled "Solid-state quantum memory using the 31P 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, 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.[3]

Origin of the concept and term[edit]

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.

See also[edit]

References[edit]

  1. ^ UIBK.ac.at
  2. ^ J. J. L. Morton; et al. (2008). "Solid-state quantum memory using the 31P nuclear spin". Nature 455 (7216): 1085–1088. arXiv:0803.2021. Bibcode:2008Natur.455.1085M. doi:10.1038/nature07295. 
  3. ^ Kamyar Saeedi; et al. (2013). "Room-Temperature Quantum Bit Storage Exceeding 39 Minutes Using Ionized Donors in Silicon-28". Science 342 (6160): 830–833. doi:10.1126/science.1239584. 
  4. ^ S. Weisner (1983). "Conjugate coding". Association for Computing Machinery, Special Interest Group in Algorithms and Computation Theory 15: 78–88. 
  5. ^ A. Zelinger, Dance of the Photons: From Einstein to Quantum Teleportation, Farrar, Straus & Giroux, New York, 2010, pp. 189, 192, ISBN 0374239665
  6. ^ B. Schumacher (1995). "Quantum coding". Physical Review A 51 (4): 2738–2747. Bibcode:1995PhRvA..51.2738S. doi:10.1103/PhysRevA.51.2738. 

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