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Topological Quantum Computation
A topological quantum computer is a type of quantum computer. It utilizes anyons, a type of quasiparticle that occurs in two-dimensional systems. The anyons' world lines intertwine to form braid theory, braids in a three-dimensional spacetime (one temporal and two spatial dimensions). The braids act as the logic gates of the computer. The primary advantage of using quantum braids over Trapped-ion quantum computer, trapped quantum particles is in their stability. While small but cumulative perturbations can cause quantum states to quantum decoherence, decohere and introduce errors in traditional quantum computations, such perturbations do not alter the topological properties of the braids. This stability is akin to the difference between cutting and reattaching a string to form a different braid versus a ball (representing an ordinary quantum particle in four-dimensional spacetime) colliding with a wall. It was proposed by Russian-American physicist Alexei Kitaev in 1997. While the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological Quantum Computer
A topological quantum computer is a type of quantum computer. It utilizes anyons, a type of quasiparticle that occurs in two-dimensional systems. The anyons' world lines intertwine to form braids in a three-dimensional spacetime (one temporal and two spatial dimensions). The braids act as the logic gates of the computer. The primary advantage of using quantum braids over trapped quantum particles is in their stability. While small but cumulative perturbations can cause quantum states to decohere and introduce errors in traditional quantum computations, such perturbations do not alter the topological properties of the braids. This stability is akin to the difference between cutting and reattaching a string to form a different braid versus a ball (representing an ordinary quantum particle in four-dimensional spacetime) colliding with a wall. It was proposed by Russian-American physicist Alexei Kitaev in 1997. While the elements of a topological quantum computer originate in a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Fermion
In particle physics, a fermion is a subatomic particle that follows Fermi–Dirac statistics. Fermions have a half-integer spin (spin 1/2, spin , Spin (physics)#Higher spins, spin , etc.) and obey the Pauli exclusion principle. These particles include all quarks and leptons and all composite particles made of an even and odd, odd number of these, such as all baryons and many atoms and atomic nucleus, nuclei. Fermions differ from bosons, which obey Bose–Einstein statistics. Some fermions are elementary particles (such as electrons), and some are composite particles (such as protons). For example, according to the spin-statistics theorem in Theory of relativity, relativistic quantum field theory, particles with integer Spin (physics), spin are bosons. In contrast, particles with half-integer spin are fermions. In addition to the spin characteristic, fermions have another specific property: they possess conserved baryon or lepton quantum numbers. Therefore, what is usually referr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Topological Degeneracy
In quantum many-body physics, topological degeneracy is a phenomenon in which the ground state of a gapped many-body Hamiltonian becomes degenerate in the limit of large system size such that the degeneracy cannot be lifted by any local perturbations. Applications Topological degeneracy can be used to protect qubits which allows topological quantum computation. It is believed that topological degeneracy implies topological order (or long-range entanglement ) in the ground state. Many-body states with topological degeneracy are described by topological quantum field theory at low energies. Background Topological degeneracy was first introduced to physically define topological order. In two-dimensional space, the topological degeneracy depends on the topology of space, and the topological degeneracy on high genus Riemann surfaces encode all information on the quantum dimensions and the fusion algebra of the quasiparticles. In particular, the topological degeneracy on torus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Toric Code
The toric code is a topological quantum error correcting code, and an example of a stabilizer code, defined on a two-dimensional spin lattice. It is the simplest and most well studied of the quantum double models. It is also the simplest example of topological order—''Z''2 topological order (first studied in the context of ''Z''2 spin liquid in 1991). The toric code can also be considered to be a ''Z''2 lattice gauge theory in a particular limit. It was introduced by Alexei Kitaev. The toric code gets its name from its periodic boundary conditions, giving it the shape of a torus. These conditions give the model translational invariance, which is useful for analytic study. However, some experimental realizations require open boundary conditions, allowing the system to be embedded on a 2D surface. The resulting code is typically known as the planar code. This has identical behaviour to the toric code in most, but not all, cases. Error correction and computation The toric co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantinuum
Quantinuum is a quantum computing company formed by the merger of Cambridge Quantum and Honeywell Quantum Solutions. The company's H-Series trapped-ion quantum computers set the highest quantum volume to date of 1,048,576 in April 2024. This architecture supports all-to-all qubit connectivity, allowing entangled states to be created between all qubits, and enables a high fidelity of quantum states. Quantinuum has developed middleware and software products that run on trapped-ion and other quantum computing platforms for cybersecurity, quantum chemistry, quantum machine learning, quantum Monte Carlo integration, and quantum artificial intelligence. The company also offers quantum-computing-hardened encryption keys designed to protect data assets and enhance cryptographic defenses. History Formed in 2021, Quantinuum is the combination of the quantum hardware team from Honeywell Quantum Solutions (HQS) and the quantum software team at Cambridge Quantum Computing (CQC). HQS was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Google
Google LLC (, ) is an American multinational corporation and technology company focusing on online advertising, search engine technology, cloud computing, computer software, quantum computing, e-commerce, consumer electronics, and artificial intelligence (AI). It has been referred to as "the most powerful company in the world" by the BBC and is one of the world's List of most valuable brands, most valuable brands. Google's parent company, Alphabet Inc., is one of the five Big Tech companies alongside Amazon (company), Amazon, Apple Inc., Apple, Meta Platforms, Meta, and Microsoft. Google was founded on September 4, 1998, by American computer scientists Larry Page and Sergey Brin. Together, they own about 14% of its publicly listed shares and control 56% of its stockholder voting power through super-voting stock. The company went public company, public via an initial public offering (IPO) in 2004. In 2015, Google was reorganized as a wholly owned subsidiary of Alphabet Inc. Go ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quanta Magazine
''Quanta Magazine'' is an editorially independent online publication of the Simons Foundation covering developments in physics, mathematics, biology and computer science. History ''Quanta Magazine'' was initially launched as ''Simons Science News'' in October 2012, but it was renamed to its current title in July 2013. It was founded by the former ''New York Times'' journalist Thomas Lin, who was the magazine's editor-in-chief until 2024. The two deputy editors are John Rennie and Michael Moyer, formerly of ''Scientific American'', and the art director is Samuel Velasco. In 2024, Samir Patel became the magazine's second editor in chief. Content The articles in the magazine are freely available to read online. ''Scientific American'', ''Wired'', ''The Atlantic'', and ''The Washington Post'', as well as international science publications like '' Spektrum der Wissenschaft'', have reprinted articles from the magazine. In November 2018, MIT Press The MIT Press is the uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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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, where 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. See also * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Chetan Nayak
Chetan Nayak (born 1971) is an Indian-American physicist and computer scientist specializing in quantum computing. He is a professor at the University of California, Santa Barbara and a technical fellow and distinguished engineer on the Microsoft Azure Quantum hardware team. He joined Microsoft in 2005 and became director and general manager of Quantum Hardware at Microsoft Station Q at Microsoft Research in 2014. Education and career Nayak was born in New York City in 1971. He earned a bachelor's degree from Harvard University in 1992 and a Ph.D. in physics from Princeton University in 1996. His dissertation on "Theories of the half-filled Landau level" was completed under Frank Wilczek. In 1996, he was a post-doctoral fellow at the Institute for Theoretical Physics at the University of California, Berkeley (UCSB) and a professor of physics at the University of California, Los Angeles from 1997 to 2006. He joined Microsoft in 2005 as a visiting researcher in Redmond, Washingt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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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 University professor at the time, and was admitted to the university's graduate school, where in 1968 he continued his studies and received a Ph.D. in 1973 for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Sankar Das Sarma
Sankar Das Sarma () is an India-born American theoretical condensed matter physicist. He has been a member of the department of physics at University of Maryland, College Park since 1980. Das Sarma is the Richard E. Prange Chair in Physics, a distinguished university professor, a Fellow of the Joint Quantum Institute (JQI), and the director of the Condensed Matter Theory Center at the University of Maryland, College Park. Career Das Sarma came to the United States from India as a physics graduate student in 1974 after finishing his secondary school (Hare School in Kolkata) and undergraduate education at Presidency College in Calcutta, India (now Presidency University in Kolkata) where he was born. He received his PhD in theoretical physics from Brown University in 1979 as a doctoral student of John Quinn. In collaboration with Chetan Nayak and Michael Freedman of Microsoft Research, Das Sarma introduced the \nu=5/2 topological qubit in 2005, which has led to experim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Braid Group
In mathematics, the braid group on strands (denoted B_n), also known as the Artin braid group, is the group whose elements are equivalence classes of Braid theory, -braids (e.g. under ambient isotopy), and whose group operation is composition of braids (see ). Example applications of braid groups include knot theory, where any knot may be represented as the closure of certain braids (a result known as Alexander's theorem); in mathematical physics where Emil Artin, Artin's canonical presentation of the braid group corresponds to the Yang–Baxter equation (see ); and in monodromy invariants of algebraic geometry. Introduction In this introduction let ; the generalization to other values of will be straightforward. Consider two sets of four items lying on a table, with the items in each set being arranged in a vertical line, and such that one set sits next to the other. (In the illustrations below, these are the black dots.) Using four strands, each item of the first set is connec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |