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Bacon–Shor Code
The Bacon–Shor code is a subsystem Quantum error correction, error correcting code. In a subsystem code, information is encoded in a System#Subsystem, subsystem of a Hilbert space. Subsystem codes lend to simplified error correcting procedures unlike codes which encode information in the Space (mathematics), 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. Given the Stabilizer code, stabilizer generators of Quantum error correction#Shor code, 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 symmetry, 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 correction is now simplified because 4 stabilizers are needed to measure errors instead of 8. A gauge group can be created from the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Error Correction
Quantum error correction (QEC) is 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 preparation, and faulty measurements. Classical error correction employs redundancy. The simplest albeit inefficient approach is the repetition code. The idea is to store the information multiple times, and—if these copies are later found to disagree—take a majority vote; e.g. suppose we copy a bit in the one state three times. Suppose further that a noisy error corrupts the three-bit state so that one of the copied bits is equal to zero but the other two are equal to one. Assuming that noisy errors are independent and occur with some sufficiently low probability ''p'', it is most likely that the error is a single-bit error and the tran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
System
A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment (systems), environment, is described by its boundaries, structure and purpose and 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 Per ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hilbert Space
In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as function spaces. Formally, a Hilbert space is a vector space equipped with an inner product that defines a distance function for which the space is a complete metric space. The earliest Hilbert spaces were studied from this point of view 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, 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 term ''Hilbert space'' for the abstract concept that under ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Space (mathematics)
In mathematics, a space is a set (sometimes called a universe) with some added 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 be elements of a set, 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 between the points of a three-dimensional Euclidean space are uniquely determined by Euclid's axioms, and all three-dimensional Euclidean spac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dave Bacon
Dave may refer to: Film, television, and theater * ''Dave'' (film), a 1993 film starring Kevin Kline and Sigourney Weaver * ''Dave'' (musical), a 2018 stage musical adaptation of the film * Dave (TV channel), a digital television channel in the United Kingdom and Ireland * ''Dave'' (TV series), a 2020 American comedy series * "Dave" (Lost), an episode of ''Lost'' * ''Meet Dave'', a 2008 film starring Eddie Murphy People * Dave (given name), a list of people and fictional characters * Dave (surname), a common Gujarati surname * 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 * DAVE (CP-7), a 1U CubeSat * "Dave", a 1984 song by the Boomtown Rats from ''In the Lon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Shor
Peter Williston Shor (born August 14, 1959) is an American professor of applied mathematics at MIT. He is 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. Early life and education Shor was born in New York City to Joan Bopp Shor and S. W. Williston Shor, of Jewish descent. He grew up in Washington, D.C. and Mill Valley, California. While attending Tamalpais High School, he placed third in the 1977 USA Mathematical Olympiad. After graduation that year, he won a silver medal at the International Math Olympiad in Yugoslavia (the U.S. team achieved the most points per country that year). He received his B.S. in Mathematics in 1981 for undergraduate work at Caltech, and was a Putnam Fellow in 1978. He earned his PhD in Applied Mathematics from MIT in 1985. His doctoral advisor was F. Thomson Leighton, and his thesi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stabilizer Code
The theory of quantum error correction plays a prominent role in the practical realization and engineering of quantum computing and quantum communication devices. The first quantum error-correcting codes are strikingly similar to classical block codes in their operation and performance. Quantum error-correcting codes restore a noisy, decohered quantum state to a pure quantum state. A stabilizer quantum error-correcting code appends ancilla qubits to qubits that we want to protect. A unitary encoding circuit rotates the global state into a subspace of a larger Hilbert space. This highly entangled, encoded state corrects for local noisy errors. A quantum error-correcting code makes quantum computation and quantum communication practical by providing a way for a sender and receiver to simulate a noiseless qubit channel given a noisy qubit channel whose noise conforms to a particular error model. The stabilizer theory of quantum error correction allows one to import some class ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gauge Symmetry
In physics, a gauge theory is a type of field theory in which the Lagrangian (and hence the dynamics of the system itself) does not change (is invariant) under local transformations according to certain smooth families of operations (Lie groups). The term ''gauge'' refers to any specific mathematical formalism to regulate redundant degrees of freedom in the Lagrangian of a physical system. The transformations between possible gauges, called ''gauge transformations'', form a Lie group—referred to as the ''symmetry group'' or the ''gauge group'' of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises a corresponding field (usually a vector field) called the ''gauge field''. Gauge fields are included in the Lagrangian to ensure its invariance under the local group transformations (called ''gauge invariance''). When such a theory is quantized, the quanta of the gauge fields are called ''gauge bosons' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gauge Group
In physics, a gauge theory is a type of field theory in which the Lagrangian (and hence the dynamics of the system itself) does not change (is invariant) under local transformations according to certain smooth families of operations ( Lie groups). The term ''gauge'' refers to any specific mathematical formalism to regulate redundant degrees of freedom in the Lagrangian of a physical system. The transformations between possible gauges, called ''gauge transformations'', form a Lie group—referred to as the '' symmetry group'' or the ''gauge group'' of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises a corresponding field (usually a vector field) called the ''gauge field''. Gauge fields are included in the Lagrangian to ensure its invariance under the local group transformations (called ''gauge invariance''). When such a theory is quantized, the quanta of the gauge fields are called '' gauge bo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Five-qubit Error Correcting Code
The five-qubit error correcting code is the smallest quantum error correcting code that can protect a logical qubit from any arbitrary single qubit error. In this code, 5 physical qubits are used to encode the logical qubit. With X and Z being Pauli matrices and I the Identity matrix, this code's generators are \langle XZZXI, IXZZX, XIXZZ,ZXIXZ \rangle. Its logical operators are \bar = XXXXX and \bar = ZZZZZ. Once the logical qubit is encoded, errors on the physical qubits can be detected via stabilizer measurements. A lookup table that maps the results of the stabilizer measurements to the types and locations of the errors gives the control system of the quantum computer enough information to correct errors. Measurements Stabilizer measurements are parity measurements that measure the stabilizers of physical qubits. For example, to measure the first stabilizer (XZZXI), a parity measurement of X of the first qubit, Z on the second, Z on the third, X on the fourth , and I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
