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quantum computing Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though ...
, a qubit () or quantum bit is a basic unit of
quantum information Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both th ...
—the quantum version of the classic binary
bit The bit is the most basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represente ...
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 The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no kn ...
in which the two levels can be taken as spin up and spin down; or the polarization of a single
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always ...
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 simultaneously, a property that is fundamental to
quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
and
quantum computing Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though ...
.


Etymology

The coining of the term ''qubit'' is attributed to
Benjamin Schumacher Benjamin "Ben" Schumacher is an American theoretical physicist, working mostly in the field of quantum information theory. He discovered a way of interpreting quantum states as information. He came up with a way of compressing the information in ...
. In the acknowledgments of his 1995 paper, Schumacher states that the term ''qubit'' was created in jest during a conversation with
William Wootters William "Bill" Kent Wootters () is an American theoretical physicist, and one of the founders of the field of quantum information theory. In a 1982 joint paper with Wojciech H. Zurek, Wootters proved the no cloning theorem, at the same time as D ...
.


Bit versus qubit

A
binary digit Binary may refer to: Science and technology Mathematics * Binary number, a representation of numbers using only two digits (0 and 1) * Binary function, a function that takes two arguments * Binary operation, a mathematical operation that t ...
, characterized as 0 or 1, is used to represent information in classical computers. When averaged over both of its states (0,1), a binary digit can represent up to one bit of
Shannon information In information theory, the information content, self-information, surprisal, or Shannon information is a basic quantity derived from the probability of a particular event occurring from a random variable. It can be thought of as an alternative wa ...
, where a
bit The bit is the most basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represente ...
is the basic unit of
information Information is an abstract concept that refers to that which has the power to inform. At the most fundamental level information pertains to the interpretation of that which may be sensed. Any natural process that is not completely random ...
. However, in this article, the word bit is synonymous with a binary digit. In classical computer technologies, a ''processed'' bit is implemented by one of two levels of low DC
voltage Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to m ...
, and whilst switching from one of these two levels to the other, a so-called "forbidden zone" between two
logic level In digital circuits, a logic level is one of a finite number of states that a digital signal can inhabit. Logic levels are usually represented by the voltage difference between the signal and ground, although other standards exist. The range ...
s 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 qubit—usually 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 In quantum information theory, superdense coding (also referred to as ''dense coding'') is a quantum communication protocol to communicate a number of classical bits of information by only transmitting a smaller number of qubits, under the assum ...
. 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''
complex numbers In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form a ...
(or a single point in a 2''n''-dimensional
vector space In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called ''vectors'', may be added together and multiplied ("scaled") by numbers called '' scalars''. Scalars are often real numbers, but can ...
).


Standard representation

In quantum mechanics, the general
quantum state In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution in ...
of a qubit can be represented by a linear superposition of its two
orthonormal In linear algebra, two vectors in an inner product space are orthonormal if they are orthogonal (or perpendicular along a line) unit vectors. A set of vectors form an orthonormal set if all vectors in the set are mutually orthogonal and all of un ...
basis Basis may refer to: Finance and accounting * Adjusted basis, the net cost of an asset after adjusting for various tax-related items *Basis point, 0.01%, often used in the context of interest rates * Basis trading, a trading strategy consisting ...
states (or basis
vector Vector most often refers to: *Euclidean vector, a quantity with a magnitude and a direction *Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematic ...
s). These vectors are usually denoted as , 0 \rangle = \bigl begin 1\\ 0 \end\bigr/math> and , 1 \rangle = \bigl begin 0\\ 1 \end\bigr/math>. They are written in the conventional
Dirac Distributed Research using Advanced Computing (DiRAC) is an integrated supercomputing facility used for research in particle physics, astronomy and cosmology in the United Kingdom. DiRAC makes use of multi-core processors and provides a variety o ...
—or "bra–ket"—notation; the , 0 \rangle and , 1 \rangle are pronounced "ket 0" and "ket 1", respectively. These two orthonormal basis states, \, together called the computational basis, are said to span the two-dimensional linear vector (Hilbert) space of the qubit. Qubit basis states can also be combined to form product basis states. A set of qubits taken together is called a
quantum register In quantum computing, a quantum register is a system comprising multiple qubits. It is the quantum analogue of the classical processor register. Quantum computers perform calculations by manipulating qubits within a quantum register. Definition ...
. For example, two qubits could be represented in a four-dimensional linear vector space spanned by the following product basis states: , 00 \rangle = \biggl begin 1\\ 0\\ 0\\ 0 \end\biggr/math>, , 01 \rangle = \biggl begin 0\\ 1\\ 0\\ 0 \end\biggr/math>, , 10 \rangle = \biggl begin 0\\ 0\\ 1\\ 0 \end\biggr/math>, and , 11 \rangle = \biggl begin 0\\ 0\\ 0\\ 1 \end\biggr/math>. In general, ''n'' qubits are represented by a superposition state vector in 2''n'' dimensional Hilbert space.


Qubit states

A pure qubit state is a
coherent Coherence, coherency, or coherent may refer to the following: Physics * Coherence (physics), an ideal property of waves that enables stationary (i.e. temporally and spatially constant) interference * Coherence (units of measurement), a deri ...
superposition of the basis states. This means that a single qubit can be described by a linear combination of , 0 \rangle and , 1 \rangle : : , \psi \rangle = \alpha , 0 \rangle + \beta , 1 \rangle where α and β are the
probability amplitude In quantum mechanics, a probability amplitude is a complex number used for describing the behaviour of systems. The modulus squared of this quantity represents a probability density. Probability amplitudes provide a relationship between the quan ...
s, that are both
complex number In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form ...
s. When we measure this qubit in the standard basis, according to the
Born rule The Born rule (also called Born's rule) is a key postulate of quantum mechanics which gives the probability that a measurement of a quantum system will yield a given result. In its simplest form, it states that the probability density of findi ...
, the probability of outcome , 0 \rangle with value "0" is , \alpha , ^2 and the probability of outcome , 1 \rangle with value "1" is , \beta , ^2. Because the absolute squares of the amplitudes equate to probabilities, it follows that \alpha and \beta must be constrained according to the second axiom of probability theory by the equation : , \alpha , ^2 + , \beta , ^2 = 1. The probability amplitudes, \alpha and \beta, encode more than just the probabilities of the outcomes of a measurement; the ''relative phase'' between \alpha and \beta is for example responsible for
quantum interference In physics, interference is a phenomenon in which two waves combine by adding their displacement together at every single point in space and time, to form a resultant wave of greater, lower, or the same amplitude. Constructive and destructive ...
, as seen in the
two-slit experiment In modern physics, the double-slit experiment is a demonstration that light and matter can display characteristics of both classically defined waves and particles; moreover, it displays the fundamentally probabilistic nature of quantum mechanic ...
.


Bloch sphere representation

It might, at first sight, seem that there should be four degrees of freedom in , \psi \rangle = \alpha , 0 \rangle + \beta , 1 \rangle\,, as \alpha and \beta are
complex number In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form ...
s with two degrees of freedom each. However, one degree of freedom is removed by the normalization constraint . This means, with a suitable change of coordinates, one can eliminate one of the degrees of freedom. One possible choice is that of Hopf coordinates: :\begin \alpha &= e^ \cos\frac, \\ \beta &= e^ \sin\frac. \end Additionally, for a single qubit the ''global
phase Phase or phases may refer to: Science *State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter), a region of space throughout which all physical properties are essentially uniform * Phase space, a mathematic ...
'' of the state e^ has no physically observable consequences, so we can arbitrarily choose to be real (or in the case that is zero), leaving just two degrees of freedom: :\begin \alpha &= \cos\frac, \\ \beta &= e^ \sin\frac, \end where e^ is the physically significant ''relative phase''. The possible quantum states for a single qubit can be visualised using a
Bloch sphere In quantum quantum mechanics, mechanics and Quantum computing, computing, the Bloch sphere is a geometrical representation of the pure state space of a two-level system, two-level quantum mechanical system (qubit), named after the physicist Felix ...
(see picture). Represented on such a 2-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. This particular choice of the polar axis is arbitrary, however. The rest of the surface of the Bloch 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 + , 1 \rangle)/ would lie on the equator of the sphere at the positive X-axis. In the
classical limit The classical limit or correspondence limit is the ability of a physical theory to approximate or "recover" classical mechanics when considered over special values of its parameters. The classical limit is used with physical theories that predict n ...
, a qubit, which can have quantum states anywhere on the Bloch sphere, reduces to the classical bit, which can be found only at either poles. The surface of the Bloch sphere is a
two-dimensional space In mathematics, a plane is a Euclidean ( flat), two-dimensional surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. Planes can arise as ...
, which represents the observable
state space A state space is the set of all possible configurations of a system. It is a useful abstraction for reasoning about the behavior of a given system and is widely used in the fields of artificial intelligence and game theory. For instance, the toy ...
of the pure qubit states. This state space has two local degrees of freedom, which can be represented by the two angles \varphi and \theta.


Mixed state

A pure state is fully specified by a single ket, , \psi\rangle = \alpha , 0\rangle + \beta , 1\rangle,\, a coherent superposition, represented by a point on the surface of the Bloch sphere as described above. Coherence is essential for a qubit to be in a superposition state. With interactions,
quantum noise Quantum noise is noise arising from the indeterminate state of matter in accordance with fundamental principles of quantum mechanics, specifically the uncertainty principle and via zero-point energy fluctuations. Quantum noise is due to the appa ...
and
decoherence Quantum decoherence is the loss of quantum coherence. In quantum mechanics, particles such as electrons are described by a wave function, a mathematical representation of the quantum state of a system; a probabilistic interpretation of the wa ...
, it is possible to put the qubit in a mixed state, a statistical combination or “incoherent mixture” of different pure states. Mixed states can be represented by points ''inside'' the Bloch sphere (or in the Bloch ball). A mixed qubit state has three degrees of freedom: the angles \varphi and \theta , as well as the length r of the vector that represents the mixed state. Quantum error correction can be used to maintain the purity of qubits.


Operations on qubits

There are various kinds of physical operations that can be performed on qubits. *
Quantum logic gate In quantum computing and specifically the quantum circuit model of computation, a quantum logic gate (or simply quantum gate) is a basic quantum circuit operating on a small number of qubits. They are the building blocks of quantum circuits, lik ...
s, building blocks for a
quantum circuit In quantum information theory, a quantum circuit is a model for quantum computation, similar to classical circuits, in which a computation is a sequence of quantum gates, measurements, initializations of qubits to known values, and possibly othe ...
in a
quantum computer Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though ...
, operate on a set of qubits (a
register Register or registration may refer to: Arts entertainment, and media Music * Register (music), the relative "height" or range of a note, melody, part, instrument, etc. * ''Register'', a 2017 album by Travis Miller * Registration (organ), th ...
); mathematically, the qubits undergo a ( reversible)
unitary transformation In mathematics, a unitary transformation is a transformation that preserves the inner product: the inner product of two vectors before the transformation is equal to their inner product after the transformation. Formal definition More precisely, ...
described by multiplying the quantum gates
unitary matrix In linear algebra, a complex square matrix is unitary if its conjugate transpose is also its inverse, that is, if U^* U = UU^* = UU^ = I, where is the identity matrix. In physics, especially in quantum mechanics, the conjugate transpose is ...
with the
quantum state In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution in ...
vector. The result from this multiplication is a new quantum state. *
Quantum measurement In quantum physics, a measurement is the testing or manipulation of a physical system to yield a numerical result. The predictions that quantum physics makes are in general probabilistic. The mathematical tools for making predictions about what ...
is an irreversible operation in which information is gained about the state of a single qubit, and coherence is lost. The result of the measurement of a single qubit with the state \psi = \alpha , 0\rangle + \beta , 1\rangle will be either , 0\rangle with probability , \alpha, ^2 or , 1\rangle with probability , \beta, ^2. Measurement of the state of the qubit alters the magnitudes of α and β. For instance, if the result of the measurement is , 1\rangle, α is changed to 0 and β is changed to the phase factor e^ no longer experimentally accessible. If measurement is performed on a qubit that is entangled, the measurement may
collapse Collapse or its variants may refer to: Concepts * Collapse (structural) * Collapse (topology), a mathematical concept * Collapsing manifold * Collapse, the action of collapsing or telescoping objects * Collapsing user interface elements ** ...
the state of the other entangled qubits. * Initialization or re-initialization to a known value, often , 0\rangle. This operation collapses the quantum state (exactly like with measurement). Initialization to , 0\rangle may be implemented logically or physically: Logically as a measurement, followed by the application of the Pauli-X gate if the result from the measurement was , 1\rangle. Physically, for example if it is a
superconducting Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic flux fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike ...
phase qubit In quantum computing, and more specifically in superconducting quantum computing, the phase qubit is a superconducting device based on the superconductor–insulator–superconductor (SIS) Josephson junction, designed to operate as a quantum bit, ...
, by lowering the energy of the quantum system to its
ground state The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. ...
. * Sending the qubit through a
quantum channel In quantum information theory, a quantum channel is a communication channel which can transmit quantum information, as well as classical information. An example of quantum information is the state of a qubit. An example of classical information i ...
to a remote system or machine (an I/O operation), potentially as part of a
quantum network Quantum networks form an important element of quantum computing and quantum communication systems. Quantum networks facilitate the transmission of information in the form of quantum bits, also called qubits, between physically separated quantum ...
.


Quantum entanglement

An important distinguishing feature between qubits and classical bits is that multiple qubits can exhibit
quantum entanglement Quantum entanglement is the phenomenon that occurs when a group of particles are generated, interact, or share spatial proximity in a way such that the quantum state of each particle of the group cannot be described independently of the state of ...
. Quantum entanglement is a nonlocal property of two or more qubits that allows a set of qubits to express higher correlation than is possible in classical systems. The simplest system to display quantum entanglement is the system of two qubits. Consider, for example, two entangled qubits in the , \Phi^+\rangle
Bell state The Bell states or EPR pairs are specific quantum states of two qubits that represent the simplest (and maximal) examples of quantum entanglement; conceptually, they fall under the study of quantum information science. The Bell states are a form o ...
: :\frac (, 00\rangle + , 11\rangle). In this state, called an ''equal superposition'', there are equal probabilities of measuring either product state , 00\rangle or , 11\rangle, as , 1/\sqrt, ^2 = 1/2. In other words, there is no way to tell if the first qubit has value “0” or “1” and likewise for the second qubit. 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, i.e., she can now tell if her qubit has value “0” or “1”. Because of the qubits' entanglement, Bob must now get exactly the same measurement as Alice. For example, 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. In short, for these two entangled qubits, whatever Alice measures, so would Bob, with perfect correlation, in any basis, however far apart they may be and even though both can not tell if their qubit has value “0” or “1” — a most surprising circumstance that can not be explained by classical physics.


Controlled gate to construct the Bell state

Controlled gates act on 2 or more qubits, where one or more qubits act as a control for some specified operation. In particular, the
controlled NOT gate In computer science, the controlled NOT gate (also C-NOT or CNOT), controlled-''X'' gate'','' controlled-bit-flip gate, Feynman gate or controlled Pauli-X is a quantum logic gate that is an essential component in the construction of a gate-bas ...
(or CNOT or CX) acts on 2 qubits, and performs the NOT operation on the second qubit only when the first qubit is , 1\rangle, and otherwise leaves it unchanged. With respect to the unentangled product basis \, it maps the basis states as follows: : , 0 0 \rangle \mapsto , 0 0 \rangle : , 0 1 \rangle \mapsto , 0 1 \rangle : , 1 0 \rangle \mapsto , 1 1 \rangle : , 1 1 \rangle \mapsto , 1 0 \rangle . A common application of the CNOT gate is to maximally entangle two qubits into the , \Phi^+\rangle
Bell state The Bell states or EPR pairs are specific quantum states of two qubits that represent the simplest (and maximal) examples of quantum entanglement; conceptually, they fall under the study of quantum information science. The Bell states are a form o ...
. To construct , \Phi^+\rangle, the inputs A (control) and B (target) to the CNOT gate are: \frac(, 0\rangle + , 1\rangle)_A and , 0\rangle_B After applying CNOT, the output is the , \Phi^+\rangle Bell State: \frac(, 00\rangle + , 11\rangle).


Applications

The , \Phi^+\rangle
Bell state The Bell states or EPR pairs are specific quantum states of two qubits that represent the simplest (and maximal) examples of quantum entanglement; conceptually, they fall under the study of quantum information science. The Bell states are a form o ...
forms part of the setup of the
superdense coding In quantum information theory, superdense coding (also referred to as ''dense coding'') is a quantum communication protocol to communicate a number of classical bits of information by only transmitting a smaller number of qubits, under the assum ...
, quantum teleportation, and entangled
quantum cryptography Quantum cryptography is the science of exploiting quantum mechanical properties to perform cryptographic tasks. The best known example of quantum cryptography is quantum key distribution which offers an information-theoretically secure solution ...
algorithms. Quantum entanglement also allows multiple states (such as the
Bell state The Bell states or EPR pairs are specific quantum states of two qubits that represent the simplest (and maximal) examples of quantum entanglement; conceptually, they fall under the study of quantum information science. The Bell states are a form o ...
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 In quantum information theory, superdense coding (also referred to as ''dense coding'') is a quantum communication protocol to communicate a number of classical bits of information by only transmitting a smaller number of qubits, under the assum ...
, make use of entanglement, suggesting that entanglement is a
resource Resource refers to all the materials available in our environment which are technologically accessible, economically feasible and culturally sustainable and help us to satisfy our needs and wants. Resources can broadly be classified upon their ...
that is unique to quantum computation. A major hurdle facing quantum computing, as of 2018, in its quest to surpass classical digital computing, is noise in quantum gates that limits the size of
quantum circuit In quantum information theory, a quantum circuit is a model for quantum computation, similar to classical circuits, in which a computation is a sequence of quantum gates, measurements, initializations of qubits to known values, and possibly othe ...
s that can be executed reliably.


Quantum register

A number of qubits taken together is a qubit register.
Quantum computer Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though ...
s perform calculations by manipulating qubits within a register.


Qudits and qutrits

The term qudit denotes the unit of quantum information that can be realized in suitable ''d''-level quantum systems. A qubit register that can be measured to ''N'' states is identical to an ''N''-level qudit. A rarely used
synonym A synonym is a word, morpheme, or phrase that means exactly or nearly the same as another word, morpheme, or phrase in a given language. For example, in the English language, the words ''begin'', ''start'', ''commence'', and ''initiate'' are all ...
for qudit is quNit, since both ''d'' and ''N'' are frequently used to denote the dimension of a quantum system. Qudits are similar to the integer types in classical computing, and may be mapped to (or realized by) arrays of qubits. Qudits where the ''d''-level system is not an exponent of 2 can not be mapped to arrays of qubits. It is for example possible to have 5-level qudits. In 2017, scientists at the
National Institute of Scientific Research The Institut national de la recherche scientifique (English: 'National Institute of Scientific Research') is the research-oriented constituent university of the Université du Québec system that offers only graduate studies. INRS conducts res ...
constructed a pair of qudits with 10 different states each, giving more computational power than 6 qubits. In 2022, researchers at the
University of Innsbruck The University of Innsbruck (german: Leopold-Franzens-Universität Innsbruck; la, Universitas Leopoldino Franciscea) is a public research university in Innsbruck, the capital of the Austrian federal state of Tyrol, founded on October 15, 1669. ...
succeeded in developing a universal qudit quantum processor with trapped ions. In the same year, researchers at Tsinghua University's Center for Quantum Information implemented the dual-type qubit scheme in trapped ion quantum computers using the same ion species. Similar to the qubit, the
qutrit A qutrit (or quantum trit) is a unit of quantum information that is realized by a 3-level quantum system, that may be in a superposition of three mutually orthogonal quantum states. The qutrit is analogous to the classical radix-3 trit, just as ...
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 computer A ternary computer, also called trinary computer, is one that uses ternary logic (i.e., base 3) instead of the more common binary system (i.e., base 2) in its calculations. This means it uses trits (instead of bits, as most computers do). Types ...
s.


Physical implementations

Any two-level quantum-mechanical 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 that 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 A hard disk drive (HDD), hard disk, hard drive, or fixed disk is an electro-mechanical data storage device that stores and retrieves digital data using magnetic storage with one or more rigid rapidly rotating platters coated with magnet ...
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.


Qubit storage

In 2008 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 Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though ...
. In 2013, 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. An increased coherence of qubits is being explored by researchers who are testing the limitations of a Ge
hole A hole is an opening in or through a particular medium, usually a solid body. Holes occur through natural and artificial processes, and may be useful for various purposes, or may represent a problem needing to be addressed in many fields of en ...
spin-orbit qubit structure.


See also

*
Ancilla bit Ancilla bits are some extra bits being used to achieve some specific goals in computation (e.g. reversible computation). In classical computation, any memory bit can be turned on or off at will, requiring no prior knowledge or extra complexity. ...
*
Bell state The Bell states or EPR pairs are specific quantum states of two qubits that represent the simplest (and maximal) examples of quantum entanglement; conceptually, they fall under the study of quantum information science. The Bell states are a form o ...
,
W state The W state is an entangled quantum state of three qubits which in the bra-ket notation has the following shape : , \mathrm\rangle = \frac(, 001\rangle + , 010\rangle + , 100\rangle) and which is remarkable for representing a specific type of ...
and
GHZ state The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that on ...
*
Bloch sphere In quantum quantum mechanics, mechanics and Quantum computing, computing, the Bloch sphere is a geometrical representation of the pure state space of a two-level system, two-level quantum mechanical system (qubit), named after the physicist Felix ...
*
Physical and logical qubits In quantum computing, a ''qubit'' is a unit of information analogous to a bit (binary digit) in classical computing, but it is affected by quantum mechanical properties such as superposition and entanglement which allow qubits to be in some ...
*
Quantum register In quantum computing, a quantum register is a system comprising multiple qubits. It is the quantum analogue of the classical processor register. Quantum computers perform calculations by manipulating qubits within a quantum register. Definition ...
*
Two-state quantum system In quantum mechanics, a two-state system (also known as a two-level system) is a quantum system that can exist in any quantum superposition of two independent (physically distinguishable) quantum states. The Hilbert space describing such a sys ...
* The elements of the
group A group is a number of persons or things that are located, gathered, or classed together. Groups of people * Cultural group, a group whose members share the same cultural identity * Ethnic group, a group whose members share the same ethnic ide ...
U(2) In mathematics, the unitary group of degree ''n'', denoted U(''n''), is the group of unitary matrices, with the group operation of matrix multiplication. The unitary group is a subgroup of the general linear group . Hyperorthogonal group is ...
are all possible single-qubit
quantum gate In quantum computing and specifically the quantum circuit model of computation, a quantum logic gate (or simply quantum gate) is a basic quantum circuit operating on a small number of qubits. They are the building blocks of quantum circuits, lik ...
s * The circle group
U(1) In mathematics, the circle group, denoted by \mathbb T or \mathbb S^1, is the multiplicative group of all complex numbers with absolute value 1, that is, the unit circle in the complex plane or simply the unit complex numbers. \mathbb T = \. ...
define the phase about the qubits basis states


Notes


References


Further reading

* * * * A treatment of two-level quantum systems, decades before the term “qubit” was coined, is found in the third volume of ''
The Feynman Lectures on Physics ''The Feynman Lectures on Physics'' is a physics textbook based on some lectures by Richard Feynman, a Nobel laureate who has sometimes been called "The Great Explainer". The lectures were presented before undergraduate students at the Californ ...
'
(2013 ebook edition)
in chapters 9-11. * A non-traditional motivation of the qubit aimed at non-physicists is found in ''
Quantum Computing Since Democritus Quantum Computing Since Democritus is a 2013 book on quantum information science written by Scott Aaronson. It is loosely based on a course Aaronson taught at the University of Waterloo, Canada, the lecture notes for which are available online. ...
'', by
Scott Aaronson Scott Joel Aaronson (born May 21, 1981) is an American theoretical computer scientist and David J. Bruton Jr. Centennial Professor of Computer Science at the University of Texas at Austin. His primary areas of research are quantum computing an ...
, Cambridge University Press (2013). * An introduction to qubits for non-specialists, by the person who coined the word, is found in Lecture 21 of ''The science of information: from language to black holes'', by Professor
Benjamin Schumacher Benjamin "Ben" Schumacher is an American theoretical physicist, working mostly in the field of quantum information theory. He discovered a way of interpreting quantum states as information. He came up with a way of compressing the information in ...
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The Great Courses The Teaching Company, doing business as Wondrium, is a media production company that produces educational, video and audio content in the form of courses, documentaries, series under two content brands - Wondrium and The Great Courses. The compa ...
, The Teaching Company (4DVDs, 2015). * A
picture book A picture book combines visual and verbal narratives in a book format, most often aimed at young children. With the narrative told primarily through text, they are distinct from comics, which do so primarily through sequential images. The images ...
introduction to entanglement, showcasing a Bell state and the measurement of it, is found in ''Quantum entanglement for babies'', by Chris Ferrie (2017). . {{Authority control Quantum computing Quantum states Teleportation Units of information Australian inventions