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Decoherence-free Subspaces
A decoherence-free subspace (DFS) is a subspace of a quantum system's Hilbert space that is invariant to non-unitary dynamics. Alternatively stated, they are a small section of the system Hilbert space where the system is decoupled from the environment and thus its evolution is completely unitary. DFSs can also be characterized as a special class of quantum error correcting codes. In this representation they are ''passive'' error-preventing codes since these subspaces are encoded with information that (possibly) won't require any ''active'' stabilization methods. These subspaces prevent destructive environmental interactions by isolating quantum information. As such, they are an important subject in quantum computing, where (coherent) control of quantum systems is the desired goal. Decoherence creates problems in this regard by causing loss of coherence between the quantum states of a system and therefore the decay of their interference terms, thus leading to loss of information ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Subspace
In mathematics, and more specifically in linear algebra, a linear subspace, also known as a vector subspaceThe term ''linear subspace'' is sometimes used for referring to flats and affine subspaces. In the case of vector spaces over the reals, linear subspaces, flats, and affine subspaces are also called ''linear manifolds'' for emphasizing that there are also manifolds. is a vector space that is a subset of some larger vector space. A linear subspace is usually simply called a ''subspace'' when the context serves to distinguish it from other types of subspaces. Definition If ''V'' is a vector space over a field ''K'' and if ''W'' is a subset of ''V'', then ''W'' is a linear subspace of ''V'' if under the operations of ''V'', ''W'' is a vector space over ''K''. Equivalently, a nonempty subset ''W'' is a subspace of ''V'' if, whenever are elements of ''W'' and are elements of ''K'', it follows that is in ''W''. As a corollary, all vector spaces are equipped with at least two ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vlatko Vedral
Vlatko Vedral is a Serbian-born (and naturalised British citizen) physicist and Professor in the Department of Physics at the University of Oxford and a Fellow of Wolfson College, Oxford. Until the summer of 2022 he also held a joint appointment at the Centre for Quantum Technologies (CQT) at the National University of Singapore. He is known for his research on the theory of quantum entanglement and quantum information theory. He has published numerous research papers, which are regularly cited, in quantum mechanics and quantum information, and was awarded the Royal Society Wolfson Research Merit Award in 2007. He has held a lectureship and readership at Imperial College, a professorship at Leeds and visiting professorships in Vienna, Singapore (NUS) and at the Perimeter Institute for Theoretical Physics in Canada. He is the author of several books, including '' Decoding Reality''. Education After completing secondary education at Mathematical Grammar School (Matematička gim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eigenvector
In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by \lambda, is the factor by which the eigenvector is scaled. Geometrically, an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation and the eigenvalue is the factor by which it is stretched. If the eigenvalue is negative, the direction is reversed. Loosely speaking, in a multidimensional vector space, the eigenvector is not rotated. Formal definition If is a linear transformation from a vector space over a field into itself and is a nonzero vector in , then is an eigenvector of if is a scalar multiple of . This can be written as T(\mathbf) = \lambda \mathbf, where is a scalar in , known as the eigenvalue, characteristic value, or characteristic root ass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Degenerate Energy Levels
In quantum mechanics, an energy level is degenerate if it corresponds to two or more different measurable states of a quantum system. Conversely, two or more different states of a quantum mechanical system are said to be degenerate if they give the same value of energy upon measurement. The number of different states corresponding to a particular energy level is known as the degree of degeneracy of the level. It is represented mathematically by the Hamiltonian for the system having more than one linearly independent eigenstate with the same energy eigenvalue. When this is the case, energy alone is not enough to characterize what state the system is in, and other quantum numbers are needed to characterize the exact state when distinction is desired. In classical mechanics, this can be understood in terms of different possible trajectories corresponding to the same energy. Degeneracy plays a fundamental role in quantum statistical mechanics. For an -particle system in three dimens ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Span
In mathematics, the linear span (also called the linear hull or just span) of a set of vectors (from a vector space), denoted , pp. 29-30, §§ 2.5, 2.8 is defined as the set of all linear combinations of the vectors in . It can be characterized either as the intersection of all linear subspaces that contain , or as the smallest subspace containing . The linear span of a set of vectors is therefore a vector space itself. Spans can be generalized to matroids and modules. To express that a vector space is a linear span of a subset , one commonly uses the following phrases—either: spans , is a spanning set of , is spanned/generated by , or is a generator or generator set of . Definition Given a vector space over a field , the span of a set of vectors (not necessarily infinite) is defined to be the intersection of all subspaces of that contain . is referred to as the subspace ''spanned by'' , or by the vectors in . Conversely, is called a ''spanning set'' of , and we ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Singlet State
In quantum mechanics, a singlet state usually refers to a system in which all electrons are paired. The term 'singlet' originally meant a linked set of particles whose net angular momentum is zero, that is, whose overall spin quantum number s=0. As a result, there is only one spectral line of a singlet state. In contrast, a doublet state contains one unpaired electron and shows splitting of spectral lines into a doublet; and a triplet state has two unpaired electrons and shows threefold splitting of spectral lines. History Singlets and the related spin concepts of doublets and triplets occur frequently in atomic physics and nuclear physics, where one often needs to determine the total spin of a collection of particles. Since the only observed fundamental particle with zero spin is the extremely inaccessible Higgs boson, singlets in everyday physics are necessarily composed of sets of particles whose individual spins are non-zero, e.g. or 1. The origin of the term "singlet" is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebra
Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary algebra deals with the manipulation of variables (commonly represented by Roman letters) as if they were numbers and is therefore essential in all applications of mathematics. Abstract algebra is the name given, mostly in education, to the study of algebraic structures such as groups, rings, and fields (the term is no more in common use outside educational context). Linear algebra, which deals with linear equations and linear mappings, is used for modern presentations of geometry, and has many practical applications (in weather forecasting, for example). There are many areas of mathematics that belong to algebra, some having "algebra" in their name, such as commutative algebra, and some not, such as Galois theory. The word ''algebra'' is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Irreducible Representation
In mathematics, specifically in the representation theory of groups and algebras, an irreducible representation (\rho, V) or irrep of an algebraic structure A is a nonzero representation that has no proper nontrivial subrepresentation (\rho, _W,W), with W \subset V closed under the action of \. Every finite-dimensional unitary representation on a Hilbert space V is the direct sum of irreducible representations. Irreducible representations are always indecomposable (i.e. cannot be decomposed further into a direct sum of representations), but converse may not hold, e.g. the two-dimensional representation of the real numbers acting by upper triangular unipotent matrices is indecomposable but reducible. History Group representation theory was generalized by Richard Brauer from the 1940s to give modular representation theory, in which the matrix operators act on a vector space over a field K of arbitrary characteristic, rather than a vector space over the field of real numbers or o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lorenza Viola
Lorenza Viola is an Italian-US theoretical physicist who works in quantum information science at Dartmouth College in Hanover, United States as the James Frank Family Professor of Physics. Education and career Viola earned a master's degree (''laurea summa cum laude'') in physics from the University of Trento in 1991. She completed her Ph.D. in 1996 at the University of Padua with a dissertation ''Relativistic stochastic quantization through co-moving coordinates'' supervised by Laura M. Morato. After postdoctoral research at the Massachusetts Institute of Technology and the Los Alamos National Laboratory, and then working for three more years at Los Alamos as a J. Robert Oppenheimer Fellow, she joined Dartmouth as an associate professor in 2004. She was promoted to full professor in 2012. Recognition In 2014, Viola was named a Fellow of the American Physical Society The American Physical Society honors members with the designation ''Fellow'' for having made significant accompli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Raymond Laflamme
Raymond Laflamme (born 1960), Officer of the Order of Canada, OC, Royal Society of Canada, FRSC is a Canadian theoretical physicist and founder and until mid 2017, was the director of the Institute for Quantum Computing at the University of Waterloo. He is also a professor in the Department of Physics and Astronomy at the University of Waterloo and an associate faculty member at Perimeter Institute for Theoretical Physics. Laflamme is currently a Canada Research Chair in Quantum Information. In December 2017, he was named as one of the appointees to the Order of Canada. As Stephen Hawking's PhD student, he first became famous for convincing Hawking that time does not reverse in a contracting universe, along with Don Page (physicist), Don Page. Hawking told the story of how this happened in his famous book A Brief History of Time in the chapter The Arrow of Time. Later on Laflamme made a name for himself in quantum computing and Quantum information, quantum information theory, whic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perturbation Theory (quantum Mechanics)
In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an additional "perturbing" Hamiltonian representing a weak disturbance to the system. If the disturbance is not too large, the various physical quantities associated with the perturbed system (e.g. its energy levels and eigenstates) can be expressed as "corrections" to those of the simple system. These corrections, being small compared to the size of the quantities themselves, can be calculated using approximate methods such as asymptotic series. The complicated system can therefore be studied based on knowledge of the simpler one. In effect, it is describing a complicated unsolved system using a simple, solvable system. Approximate Hamiltonians Perturbation theory is an important tool for de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Daniel Lidar
Daniel Amihud Lidar is the holder of the Viterbi Professorship of Engineering at the University of Southern California, where he is a Professor of Electrical Engineering, Chemistry, Physics & Astronomy. He is the Director and co-founder of the USC Center for Quantum Information Science & Technology (CQIST) as well as Scientific Director of the USC-Lockheed Martin Quantum Computing Center, notable for his research on control of quantum systems and quantum information processing. Education He is a class of 1986 graduate of the Armand Hammer United World College of the American West. He obtained his PhD from the Hebrew University of Jerusalem in 1997 under Robert Benny Gerber and Ofer Biham, with a thesis entitled ''Structural Characterization of Disordered Systems''. Career In 1997–2000, he was a postdoc at UC Berkeley, having been awarded Rothschild Foundation and Fulbright Program fellowships (the latter of which he declined); in 2000–2005, he was an assistant professor an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
