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Bacon–Shor Code
The Bacon–Shor code is a subsystem error correcting code. In a subsystem code, information is encoded in a subsystem of a Hilbert space. Subsystem codes lend to simplified error correcting procedures unlike codes which encode information in the subspace of a Hilbert space. This simplicity led to the first claim of fault tolerant circuit demonstration on a quantum computer. It is named after Dave Bacon and Peter Shor Peter Williston Shor (born August 14, 1959) is an American theoretical computer scientist known for his work on quantum computation, in particular for devising Shor's algorithm, a quantum algorithm for factoring exponentially faster than the .... Given the stabilizer generators of Shor's code: \langle X_X_X_X_X_X_, X_X_X_X_X_X_, Z_Z_, Z_Z_, Z_Z_, Z_Z_, Z_Z_, Z_Z_\rangle, 4 stabilizers can be removed from this generator by recognizing gauge symmetries in the code to get: \langle X_X_X_X_X_X_, X_X_X_X_X_X_, Z_Z_Z_Z_Z_Z_, Z_Z_Z_Z_Z_Z_ \rangle. Error correc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Quantum Error Correction
Quantum error correction (QEC) is a set of techniques used in quantum computing to protect quantum information from errors due to decoherence and other quantum noise. Quantum error correction is theorised as essential to achieve fault tolerant quantum computing that can reduce the effects of noise on stored quantum information, faulty quantum gates, faulty quantum state preparation, and faulty measurements. Effective quantum error correction would allow quantum computers with low qubit fidelity to execute algorithms of higher complexity or greater circuit depth. Classical error correction often employs redundancy. The simplest albeit inefficient approach is the repetition code. A repetition code stores the desired (logical) information as multiple copies, and—if these copies are later found to disagree due to errors introduced to the system—determines the most likely value for the original data by majority vote. For instance, suppose we copy a bit in the one (on) state thr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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System
A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its open system (systems theory), environment, is described by its boundaries, structure and purpose and is expressed in its functioning. Systems are the subjects of study of systems theory and other systems sciences. Systems have several common properties and characteristics, including structure, function(s), behavior and interconnectivity. Etymology The term ''system'' comes from the Latin word ''systēma'', in turn from Greek language, Greek ''systēma'': "whole concept made of several parts or members, system", literary "composition"."σύστημα" , Henry George Liddell, Robert Scott, ''A Greek–English Lexicon'', on Pers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Hilbert Space
In mathematics, a Hilbert space is a real number, real or complex number, complex inner product space that is also a complete metric space with respect to the metric induced by the inner product. It generalizes the notion of Euclidean space. The inner product allows lengths and angles to be defined. Furthermore, Complete metric space, completeness means that there are enough limit (mathematics), limits in the space to allow the techniques of calculus to be used. A Hilbert space is a special case of a Banach space. Hilbert spaces were studied beginning in the first decade of the 20th century by David Hilbert, Erhard Schmidt, and Frigyes Riesz. They are indispensable tools in the theories of partial differential equations, mathematical formulation of quantum mechanics, quantum mechanics, Fourier analysis (which includes applications to signal processing and heat transfer), and ergodic theory (which forms the mathematical underpinning of thermodynamics). John von Neumann coined the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Space (mathematics)
In mathematics, a space is a set (sometimes known as a ''universe'') endowed with a structure defining the relationships among the elements of the set. A subspace is a subset of the parent space which retains the same structure. While modern mathematics uses many types of spaces, such as Euclidean spaces, linear spaces, topological spaces, Hilbert spaces, or probability spaces, it does not define the notion of "space" itself. A space consists of selected mathematical objects that are treated as points, and selected relationships between these points. The nature of the points can vary widely: for example, the points can represent numbers, functions on another space, or subspaces of another space. It is the relationships that define the nature of the space. More precisely, isomorphic spaces are considered identical, where an isomorphism between two spaces is a one-to-one correspondence between their points that preserves the relationships. For example, the relationships b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Dave Bacon
Dave may refer to: Arts and entertainment * ''Dave'' (film), a 1993 film starring Kevin Kline and Sigourney Weaver * ''Dave'' (musical), a 2018 stage musical adaptation of the 1993 film * ''Dave'' (TV series), a 2020 American comedy series * "Dave" (''Lost''), an episode of ''Lost'' * Dave, a digital television channel in the United Kingdom and Ireland now rebranded as U&Dave People * Dave (given name), a list of people and fictional characters * Dave (surname), a common Gujarati surname * Dave (American rapper), aka David Jolicoeur (1967–2023), of the hip hop group De La Soul * Dave (artist) (born 1969), Swiss artist * Dave (rapper) (born 1998), English rapper from London * Dave (singer) (born 1944), Dutch-born French singer Software * Dave (company), a digital banking service * DAvE (Infineon), a C-language software development tool * Thursby DAVE, a Windows file and printer sharing for Macs Other uses * Dave (Belgium), a town in Belgium * Damping and Vibrations ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Peter Shor
Peter Williston Shor (born August 14, 1959) is an American theoretical computer scientist known for his work on quantum computation, in particular for devising Shor's algorithm, a quantum algorithm for factoring exponentially faster than the best currently-known algorithm running on a classical computer. He has been a professor of applied mathematics at the Massachusetts Institute of Technology (MIT) since 2003. Early life and education Shor was born on August 14, 1959, in New York City, to Joan Bopp Shor and S. W. Williston Shor.Joan Shor Obituary He grew up in Washington, D.C. and |
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Stabilizer Code
Stabilizer, stabiliser, stabilisation or stabilization may refer to: Chemistry and food processing * Stabilizer (chemistry), a substance added to prevent unwanted change in state of another substance ** Polymer stabilizers are stabilizers used specifically in plastic or other polymers * Stabilizer (food), a type of food additive * Wood stabilization, a wood preservation process to prevent distortion caused by moisture * Clarification and stabilization of wine Mathematics * Stabilization (category theory) * Stabilizer subgroup Technology * Buoyancy compensator (diving) adjusts buoyancy. * Stabilizer (aircraft), surfaces to help keep aircraft under control. Includes: ** Vertical stabilizer of airplanes ** Tailplane or horizontal stabilizer * Stabilizer (ship), fins on ships to counteract roll * Stabilizer, another name for bicycle training wheels * Stabilizers, the extendable legs mounted on a land vehicle which are folded out when stabilization is required; see Outrigger ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |