A qubit representation by a Bloch sphere.

A qubit is not to be confused with a cubit, which is an ancient measure of length.

A quantum bit, or qubit (sometimes qbit) ['kju.bɪt] or [k'bɪt] is a unit of quantum information. That information is described by a state vector in a two-level quantum mechanical system which is formally equivalent to a two-dimensional vector space over the complex numbers. Image File history File links Blochsphere. ... Image File history File links Blochsphere. ... Bloch sphere In quantum mechanics, the Bloch sphere is a geometrical representation of the pure state space of a 2-level quantum mechanical system. ... This derivation of the Vitruvian Man by Leonardo da Vinci, depicts nine historical units of measurement: the Yard, the Span, the Cubit, the Flemish Ell, the English Ell, the French Ell, the Fathom, the Hand , and the Foot. ... In quantum mechanics, quantum information is physical information that is held in the state of a quantum system. ... Probability densities for the electron at different quantum numbers (l) In quantum mechanics, the quantum state of a system is a set of numbers that fully describe a quantum system. ... In quantum mechanics, a two-state system is a system which has two possible states. ... In mathematics, a vector space (or linear space) is a collection of objects (called vectors) that, informally speaking, may be scaled and added. ... In mathematics, a complex number is a number which is often formally defined to consist of an ordered pair of real numbers , often written: In mathematics, the adjective complex means that the underlying number field is complex numbers, for example complex analysis, complex matrix, complex polynomial and complex Lie algebra. ...

Benjamin Schumacher discovered a way of interpreting quantum states as information. He came up with a way of compressing the information in a state, and storing the information on a smaller number of states. This is now known as Schumacher compression. In the acknowledgments of his paper (Phys. Rev. A 51, 2738), Schumacher states that the term qubit was invented in jest, during his conversations with Bill Wootters. Benjamin Schumacher discovered a way of interpreting quantum states as information. ... William Kent Wootters is an American physicist, and a leading contributor to the field of quantum information theory. ...

Bit versus qubit

A bit is the base of computer information. Regardless of its physical representation, it is always read as either a 0 or a 1. An analogy to this is a light switch–the down position can represent 0 (normally equated to off) and the up position can represent 1 (normally equated to on). This article is about the unit of information. ...

A qubit has some similarities to a classical bit, but is overall very different. Like a bit, a qubit can have only 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. Quantum superposition is the application of the superposition principle to quantum mechanics. ...

Representation

The states a qubit may be measured in are known as basis states (or vectors). As is the tradition with any sort of quantum states, Dirac, or bra-ket notation is used to represent them. In linear algebra, a basis is a set of vectors that, in a linear combination, can represent every vector in a given vector space, and such that no element of the set can be represented as a linear combination of the others. ... In mathematics, a vector space (or linear space) is a collection of objects (called vectors) that, informally speaking, may be scaled and added. ... Quite literally, quantum state describes the state of a quantum system. ... Bra-ket notation is the standard notation for describing quantum states in the theory of quantum mechanics. ...

This means that the two computational basis states are conventionally written as and (pronounced: 'ket 0' and 'ket 1').

The French Commissariat à l'Énergie Atomique have created a representation of the superposition. [1] The Commissariat à lÉnergie Atomique or CEA, the Atomic Energy Commisson, in English, is a French public establishment of an industrial and commercial character whose mission is to develop all applications of atomic energy, both civilian and military. ...

Qubit states

A pure qubit state is a linear superposition of those two states. This means that the qubit can be represented as a linear combination of and : In quantum information processing, a pure qubit state is a non-zero superposition of two basis states, conventionally written in bra-ket notation notation as and . ... Quantum superposition is the application of the superposition principle to quantum mechanics. ...

where α and β are probability amplitudes and can in general both be complex numbers. In quantum mechanics, a probability amplitude is a complex-valued function that describes an uncertain or unknown quantity. ... In mathematics, a complex number is a number which is often formally defined to consist of an ordered pair of real numbers , often written: In mathematics, the adjective complex means that the underlying number field is complex numbers, for example complex analysis, complex matrix, complex polynomial and complex Lie algebra. ...

When we measure this qubit in the standard basis, the probability of outcome is | α | ² and the probability of outcome is | β | ². 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 state space of a single qubit register can be represented geometrically by the Bloch sphere. This is a two dimensional space which has an underlying geometry of the surface of a sphere. This essentially means that the single qubit register space has two local degrees of freedom. Represented on such a sphere, a classical bit could only lie on one of the poles. An n-qubit register space has 2ⁿ⁺¹ − 2 degrees of freedom. This is much larger than 2n, which is what one would expect classically with no entanglement (i.e. using the cartesian product instead of the tensor product for combining the qubit states.) In physics, a state space is a complex Hilbert space within which the possible instantaneous states of the system may be described by a unit vector. ... Bloch sphere In quantum mechanics, the Bloch sphere is a geometrical representation of the pure state space of a 2-level quantum mechanical system. ... It has been suggested that Quantum coherence be merged into this article or section. ...

Entanglement

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 It has been suggested that Quantum coherence be merged into this article or section. ... Nonlocality in quantum mechanics, refers to the property of entangled quantum states in which both the entangled states collapse simultaneously upon measurement of one of their entangled components, regardless of the spatial separation of the two states. ... The Bell states are a concept in quantum information science and represent the simplest possible examples of entanglement. ...

(Note that in this state, there are equal probabilities of measuring either or .)

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 the exact same measurement as Alice, i.e. if she measured a , Bob must measure the same, as is the only state where Alice's qubit is a .

Entanglement also allows multiple states (such as are 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. The Bell states are a concept in quantum information science and represent the simplest possible examples of entanglement. ...

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. In quantum information, quantum teleportation, or entanglement-assisted teleportation, is a technique that transfers a quantum state to an arbitrarily distant location using a distributed entangled state and the transmission of some classical information. ... Superdense coding is a technique used in quantum information theory. ... In computational complexity theory, a computational resource is a resource used by some computational model in the solution of computational problems. ...

Quantum register

A number of entangled qubits taken together is a qubit register. Quantum computers perform calculations by manipulating qubits within a register. A quantum register is the quantum computing analogue of a classical processor register. ... The Bloch sphere is a representation of a qubit, the fundamental building block of quantum computers. ...

Variations of the qubit

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. A qutrit is a unit of quantum information. ... Ternary is the base 3 numeral system. ...

Physical representation

Any two-level 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.

This is an incomplete list of physical implementation of qubits:

In modern physics the photon is the elementary particle responsible for electromagnetic phenomena. ... A Fock state, in quantum mechanics, is any state of the Fock space with a well-defined number of particles in each state. ... This article is about electromagnetic waves; for other senses of this term, see polarization (disambiguation). ... Time-bin encoding is a technique used in Quantum information science to encode a qubit of information on a photon. ... In physics, a squeezed coherent state is any state of the quantum mechanical Hilbert space such that the uncertainty principle is saturated. ... For other uses, see Electron (disambiguation). ... In atomic physics, the spin quantum number is a quantum number that parametrizes the intrinsic angular momentum (or spin angular momentum, or simply spin) of a given particle. ... Look up charge in Wiktionary, the free dictionary. ... The nucleus of an atom is the very small dense region, of positive charge, in its centre consisting of nucleons (protons and neutrons). ... In physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is generated by the motion of its center of mass about an external point. ... NMR redirects here. ... An optical lattice is formed by using counterpropagating laser beams to create a periodic (in space) intensity pattern. ... Josephson junctions, first postulated by B. D. Josephson and first made by John Rowell and Philip Anderson, are quantum-mechanical circuit elements of superconducting devices. ... Circuit diagram of a cooper pair box circuit. ... // Introduction Flux Qubits (also known as Persistent Current Qubits) are micro-metre sized loops of superconducting metal interrupted by a number of Josephson junctions. ... A quantum dot is made from a semiconductor nanostructure that confines the motion of conduction band electrons, valence band holes, or excitons (bound pairs of conduction band electrons and valence band holes) in all three spatial directions. ...

External links

• An update on qubits in the Jan 2005 issue of Scientific American
• An update on qubits in the Oct 2005 issue of Scientific American
• The organization cofounded by one of the pioneers in quantum computation, David Deutsch

Scientific American is a popular-science magazine, published (first weekly and later monthly) since August 28, 1845, making it the oldest continuously published magazine in the United States. ... Scientific American is a popular-science magazine, published (first weekly and later monthly) since August 28, 1845, making it the oldest continuously published magazine in the United States. ... David Deutsch (born 1953) is a physicist at Oxford University. ... Molecule of alanine used in NMR implementation of error correction. ... In quantum mechanics, a quantum circuit is a specific model for a quantum computational device. ... The Bloch sphere is a representation of a qubit, the fundamental building block of quantum computers. ... Quantum cryptography, or quantum key distribution (QKD), uses quantum mechanics to guarantee secure communication. ... In quantum mechanics, quantum information is physical information that is held in the state of a quantum system. ... It has been suggested that Quantum programming language be merged into this article or section. ... In quantum information, quantum teleportation, or entanglement-assisted teleportation, is a technique that transfers a quantum state to an arbitrarily distant location using a distributed entangled state and the transmission of some classical information. ... A Quantum Virtual Machine (QVM) is a virtual machine which emulates a quantum computer. ... Timeline of quantum computers // 1970 - Stephen Wiesner invents conjugate coding. ... The Deutsch-Jozsa algorithm is a quantum algorithm, proposed by David Deutsch and Richard Jozsa in 1992. ... Grovers algorithm is a quantum algorithm for searching an unsorted database with N entries in O(N1/2) time and using O(logN) storage space (see big O notation). ... Shors algorithm is a quantum algorithm for factoring an integer N in O((log N)3) time and O(log N) space, named after Peter Shor. ... BQP, in computational complexity theory, stands for Bounded error, Quantum, Polynomial time. It denotes the class of problems solvable by a quantum computer in polynomial time, with an error probability of at most 1/4 for all instances. ... Molecule of alanine used in NMR implementation of quantum computing. ... Todays computers use the movement of electrons in-and-out of transistors to do logic. ... Nonlinear optics is the branch of optics that describes the behaviour of light in nonlinear media, that is, media in which the polarization P responds nonlinearly to the electric field E of the light. ... A Trapped ion quantum computer is a type of quantum computer. ... The Kane quantum computer is a proposal for a scalable quantum computer proposed by Bruce Kane in 19981, then at the University of New South Wales. ... A double quantum dot. ... Journal articles on Superconducting qubits Y. Nakamura, Yu. ... Circuit diagram of a cooper pair box circuit. ... // Introduction Flux Qubits (also known as Persistent Current Qubits) are micro-metre sized loops of superconducting metal interrupted by a number of Josephson junctions. ...