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Topological Quantum Computer
A topological quantum computer is a theoretical quantum computer proposed by Russian-American physicist Alexei Kitaev in 1997. It employs quasiparticles in two-dimensional systems, called anyons, whose world lines pass around one another to form braids in a three-dimensional spacetime (i.e., one temporal plus two spatial dimensions). These braids form the logic gates that make up the computer. The advantage of a quantum computer based on quantum braids over using trapped quantum particles is that the former is much more stable. Small, cumulative perturbations can cause quantum states to decohere and introduce errors in the computation, but such small perturbations do not change the braids' topological properties. This is like the effort required to cut a string and reattach the ends to form a different braid, as opposed to a ball (representing an ordinary quantum particle in four-dimensional spacetime) bumping into a wall. While the elements of a topological quantum computer o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 current quantum computers may be too small to outperform usual (classical) computers for practical applications, larger realizations are believed to be capable of solving certain computational problems, such as integer factorization (which underlies RSA encryption), substantially faster than classical computers. The study of quantum computing is a subfield of quantum information science. There are several models of quantum computation with the most widely used being quantum circuits. Other models include the quantum Turing machine, quantum annealing, and adiabatic quantum computation. Most models are based on the quantum bit, or " qubit", which is somewhat analogous to the bit in classical computation. A qubit can be in a 1 or 0 qu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
World Lines
The world line (or worldline) of an object is the path that an object traces in 4-dimensional spacetime. It is an important concept in modern physics, and particularly theoretical physics. The concept of a "world line" is distinguished from concepts such as an "orbit" or a "trajectory" (e.g., a planet's ''orbit in space'' or the ''trajectory'' of a car on a road) by the ''time'' dimension, and typically encompasses a large area of spacetime wherein perceptually straight paths are recalculated to show their ( relatively) more absolute position states—to reveal the nature of special relativity or gravitational interactions. The idea of world lines originates in physics and was pioneered by Hermann Minkowski. The term is now most often used in relativity theories (i.e., special relativity and general relativity). Usage in physics In physics, a world line of an object (approximated as a point in space, e.g., a particle or observer) is the sequence of spacetime events corresp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chern–Simons Theory
The Chern–Simons theory is a 3-dimensional topological quantum field theory of Schwarz type developed by Edward Witten. It was discovered first by mathematical physicist Albert Schwarz. It is named after mathematicians Shiing-Shen Chern and James Harris Simons, who introduced the Chern–Simons 3-form. In the Chern–Simons theory, the action is proportional to the integral of the Chern–Simons 3-form. In condensed-matter physics, Chern–Simons theory describes the topological order in fractional quantum Hall effect states. In mathematics, it has been used to calculate knot invariants and three-manifold invariants such as the Jones polynomial. Particularly, Chern–Simons theory is specified by a choice of simple Lie group G known as the gauge group of the theory and also a number referred to as the ''level'' of the theory, which is a constant that multiplies the action. The action is gauge dependent, however the partition function of the quantum theory is well-defined wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fibonacci Anyons
Fibonacci (; also , ; – ), also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano ('Leonardo the Traveller from Pisa'), was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Western mathematician of the Middle Ages". The name he is commonly called, ''Fibonacci'', was made up in 1838 by the Franco-Italian historian Guillaume Libri and is short for ('son of Bonacci'). However, even earlier in 1506 a notary of the Holy Roman Empire, Perizolo mentions Leonardo as "Lionardo Fibonacci". Fibonacci popularized the Indo–Arabic numeral system in the Western world primarily through his composition in 1202 of ''Liber Abaci'' (''Book of Calculation''). He also introduced Europe to the sequence of Fibonacci numbers, which he used as an example in ''Liber Abaci''. Biography Fibonacci was born around 1170 to Guglielmo, an Italian merchant and customs official. Guglielmo directed a trading post in Bugia (Béjaïa) in modern- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael J
Michael may refer to: People * Michael (given name), a given name * Michael (surname), including a list of people with the surname Michael Given name "Michael" * Michael (archangel), ''first'' of God's archangels in the Jewish, Christian and Islamic religions * Michael (bishop elect), English 13th-century Bishop of Hereford elect * Michael (Khoroshy) (1885–1977), cleric of the Ukrainian Orthodox Church of Canada * Michael Donnellan (1915–1985), Irish-born London fashion designer, often referred to simply as "Michael" * Michael (footballer, born 1982), Brazilian footballer * Michael (footballer, born 1983), Brazilian footballer * Michael (footballer, born 1993), Brazilian footballer * Michael (footballer, born February 1996), Brazilian footballer * Michael (footballer, born March 1996), Brazilian footballer * Michael (footballer, born 1999), Brazilian footballer Rulers =Byzantine emperors= *Michael I Rangabe (d. 844), married the daughter of Emperor Nikephoros I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael H
Michael may refer to: People * Michael (given name), a given name * Michael (surname), including a list of people with the surname Michael Given name "Michael" * Michael (archangel), ''first'' of God's archangels in the Jewish, Christian and Islamic religions * Michael (bishop elect), English 13th-century Bishop of Hereford elect * Michael (Khoroshy) (1885–1977), cleric of the Ukrainian Orthodox Church of Canada * Michael Donnellan (1915–1985), Irish-born London fashion designer, often referred to simply as "Michael" * Michael (footballer, born 1982), Brazilian footballer * Michael (footballer, born 1983), Brazilian footballer * Michael (footballer, born 1993), Brazilian footballer * Michael (footballer, born February 1996), Brazilian footballer * Michael (footballer, born March 1996), Brazilian footballer * Michael (footballer, born 1999), Brazilian footballer Rulers =Byzantine emperors= *Michael I Rangabe (d. 844), married the daughter of Emperor Nikephoros I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jones Polynomial
In the mathematical field of knot theory, the Jones polynomial is a knot polynomial discovered by Vaughan Jones in 1984. Specifically, it is an invariant of an oriented knot or link which assigns to each oriented knot or link a Laurent polynomial in the variable t^ with integer coefficients. Definition by the bracket Suppose we have an oriented link L, given as a knot diagram. We will define the Jones polynomial, V(L), using Louis Kauffman's bracket polynomial, which we denote by \langle~\rangle. Here the bracket polynomial is a Laurent polynomial in the variable A with integer coefficients. First, we define the auxiliary polynomial (also known as the normalized bracket polynomial) :X(L) = (-A^3)^\langle L \rangle, where w(L) denotes the writhe of L in its given diagram. The writhe of a diagram is the number of positive crossings (L_ in the figure below) minus the number of negative crossings (L_). The writhe is not a knot invariant. X(L) is a knot invariant since it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Turing Machine
A quantum Turing machine (QTM) or universal quantum computer is an abstract machine used to model the effects of a quantum computer. It provides a simple model that captures all of the power of quantum computation—that is, any quantum algorithm can be expressed formally as a particular quantum Turing machine. However, the computationally equivalent quantum circuit is a more common model. Quantum Turing machines can be related to classical and probabilistic Turing machines in a framework based on transition matrices. That is, a matrix can be specified whose product with the matrix representing a classical or probabilistic machine provides the quantum probability matrix representing the quantum machine. This was shown by Lance Fortnow. Informal sketch A way of understanding the quantum Turing machine (QTM) is that it generalizes the classical Turing machine (TM) in the same way that the quantum finite automaton (QFA) generalizes the deterministic finite automaton (DFA). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 other actions. The minimum set of actions that a circuit needs to be able to perform on the qubits to enable quantum computation is known as DiVincenzo's criteria. Circuits are written such that the horizontal axis is time, starting at the left hand side and ending at the right. Horizontal lines are qubits, doubled lines represent classical bits. The items that are connected by these lines are operations performed on the qubits, such as measurements or gates. These lines define the sequence of events, and are usually not physical cables. The graphical depiction of quantum circuit elements is described using a variant of the Penrose graphical notation. Richard Feynman used an early version of the quantum circuit notation in 1986. Rever ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-abelian Group
In mathematics, and specifically in group theory, a non-abelian group, sometimes called a non-commutative group, is a group (''G'', ∗) in which there exists at least one pair of elements ''a'' and ''b'' of ''G'', such that ''a'' ∗ ''b'' ≠ ''b'' ∗ ''a''. This class of groups contrasts with the abelian groups. (In an abelian group, all pairs of group elements commute). Non-abelian groups are pervasive in mathematics and physics. One of the simplest examples of a non-abelian group is the dihedral group of order 6. It is the smallest finite non-abelian group. A common example from physics is the rotation group SO(3) in three dimensions (for example, rotating something 90 degrees along one axis and then 90 degrees along a different axis is not the same as doing them in reverse order). Both discrete groups and continuous groups may be non-abelian. Most of the interesting Lie groups are non-abelian, and these play an important role in gauge theory ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chetan Nayak
Chetan may refer to: * Chetan (name), an Indian and Nepalese given name * Chetan, Iran, a village in Mazandaran Province, Iran * Chetan, Kurdistan, a village in Kurdistan Province, Iran * Lucian Chetan Lucian of Samosata, '; la, Lucianus Samosatensis ( 125 – after 180) was a Hellenized Syrian satirist, rhetorician and pamphleteer who is best known for his characteristic tongue-in-cheek style, with which he frequently ridiculed supersti ... (born 1985), Romanian football player See also * Cheta (other) {{dab, geo, surname ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael Freedman
Michael Hartley Freedman (born April 21, 1951) is an American mathematician, at Microsoft Station Q, a research group at the University of California, Santa Barbara. In 1986, he was awarded a Fields Medal for his work on the 4-dimensional generalized Poincaré conjecture. Freedman and Robion Kirby showed that an exotic ℝ4 manifold exists. Life and career Freedman was born in Los Angeles, California, in the United States. His father, Benedict Freedman, was an American Jewish aeronautical engineer, musician, writer, and mathematician. His mother, Nancy Mars Freedman, performed as an actress and also trained as an artist. His parents cowrote a series of novels together. . He entered the University of California, Berkeley, but dropped out after two semesters. In the same year he wrote a letter to Ralph Fox, a Princeton professor at the time, and was admitted to graduate school so in 1968 he continued his studies at Princeton University where he received Ph.D. degree in 1973 f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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