2024 David gross hudson theorem clifford

David gross hudson theorem clifford

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August undefined, 2024

http://www.stat.yale.edu/~pollard/Courses/251.spring04/Handouts/Hammersley-Clifford.pdf WebClifford's theorem has led to a branch of representation theory in its own right, now known as Clifford theory. This is particularly relevant to the representation theory of finite …

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WebSep 26, 2016 · The Clifford group fails gracefully to be a unitary 4-design Authors: Huangjun Zhu Richard Kueng Markus Grassl University of Gdansk David Gross Abstract A unitary t-design is a set of... WebFigure 1. Circuit diagram of SWAP implementation using SUM and QFT gates. The QFT gates are labeled accordingly, and the SUM gates are indicated by a vertical line, with the solid dot on the control qudit and a ⊕ on the target qudit. - "An ideal characterization of the Clifford operators" green and yellow jordan 5

1. MarkovrandomﬁeldsandGibbsdistributions - Yale University

WebFeb 9, 2024 · David Gross, Sepehr Nezami, and Michael Walter, ``Schur–Weyl Duality for the Clifford Group with Applications: Property Testing, a Robust Hudson Theorem, and de Finetti Representations'' Communications in Mathematical Physics 385, 1325–1393 (2024). WebMay 6, 2024 · The result constitutes a robust generalization of the discrete Hudson theorem. (4) We show that complex projective designs of arbitrary order can be obtained from a finite number (independent of the number of qudits) of Clifford orbits. To prove this result, we give explicit formulas for arbitrary moments of random stabilizer states. flowers bread store crestview fl

Multiqubit Clifford groups are unitary 3-designs – arXiv Vanity

WebClifford's theorem has led to a branch of representation theory in its own right, now known as Clifford theory. This is particularly relevant to the representation theory of finite solvable groups, where normal subgroups usually abound. For more general finite groups, Clifford theory often allows representation-theoretic questions to be reduced ... WebDavid J. Gross. The Nobel Prize in Physics 2004. Born: 19 February 1941, Washington, D.C., USA. Affiliation at the time of the award: University of California, Kavli Institute for … green and yellow jordan 1 midWebAug 31, 2024 · This short chapter introduces Clifford theory, which is the subject of comparing the representation theories of a finite group and a normal subgroup of it. We prove Clifford’s theorem in the first section. The rest of the chapter discusses how to go from the representations of the normal subgroup and the quotient to representations of … flowers bread company near me

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David gross hudson theorem clifford

WebAug 1, 2024 · discrete Hudson theorem. • W e show that complex projective designs of arbitrary order can be obtained from a ﬁnite number (independent of the number of … WebThe Clifford group is identiﬁed as the set of unitary operations which preserve positivity. The result can be seen as a discrete version of Hudson’s Theorem. Hudson established that for continuous variable systems, the Wigner function of a pure state has no negative values if and only if the state is Gaussian.

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WebMar 21, 2024 · Gross: "Hudson's Theorem for finite-dimensional quantum systems" (2006) Neuhauser: "An Explicit Construction of the Metaplectic Representation over a Finite Field" (2002) Bolt, Room, and Wall: "On the Clifford collineation, transform and similarity groups. II." (1960) Zhu: "Permutation Symmetry Determines the Discrete Wigner Function" (2016) WebJun 29, 2024 · Schur–Weyl Duality for the Clifford Group with Applications: Property Testing, a Robust Hudson Theorem, and de Finetti Representations. David Gross 1,2, …

WebDec 15, 2006 · The Clifford group is identified as the set of unitary operations which preserve positivity. The result can be seen as a discrete version of Hudson's theorem. … WebApr 13, 2024 · David Gross. ``Hudson’s theorem for finite-dimensional quantum systems''. Journal of Mathematical Physics 47, 122107 (2006). doi: 10.1063/ 1.2393152. arXiv:quant-ph/ 0602001. ... Zak Webb. ``The clifford group forms a unitary 3-design''. Quantum Information and Computation 16, 1379–1400 (2016). doi: 10.26421/ QIC16.15-16-8. …

WebFeb 15, 2024 · David Gross, in full David Jonathan Gross, (born February 19, 1941, Washington, D.C., U.S.), American physicist who, with H. David Politzer and Frank … WebIn this work, we describe a similar duality theory for tensor powers of Clifford unitaries. The Clifford group is a central object in many subfields of quantum information, most prominently in the theory of fault-tolerance. The duality theory has a simple and clean description in terms of finite geometries.

WebFeb 16, 2024 · David Gross, Sepehr Nezami & Michael Walter. Fault-tolerant quantum computation with non-binary systems ... (i.e., the degree that a state cannot be approximately generated by Clifford gates) thus become ... Walter, M.: Schur-Weyl duality for the Clifford group with applications: property testing, a robust Hudson theorem, and …

WebDavid Gross Bell's Theorem shows that quantum mechanical correlations can violate the constraints that the causal structure of certain experiments impose on any classical … green and yellow in spanishWebMay 27, 2024 · 1. Let V be an irreducible representation of a finite group G over the field C (we can take any field in fact). Let H be a normal subgroup of G. Look at V as representation of H; it may not be irreducible, so take an H -irreducible subspace W of V. Next, consider subspaces g W. It can be shown that H acts on g W (due to normality) irreducibly. green and yellow imagesWebThe Hammersley-Clifford Theorem asserts that the process {X t: t ∈ T} is a Markov random ﬁeld if and only if the corresponding Q is a Gibbs distribution. It is mostly a matter of bookkeeping to show that every Gibbs distribution deﬁnes a Markov random ﬁeld. <3> Example. With only a slight abuse of notation, we may write V A(x) as V A(x ... flowers bread store eden ncWebAug 31, 2024 · This short chapter introduces Clifford theory, which is the subject of comparing the representation theories of a finite group and a normal subgroup of it. We … flowers bread company locationsWebDec 19, 2006 · The Clifford group is identified as the set of unitary operations which preserve positivity. The result can be seen as a discrete version of Hudson’s theorem. … flowers bread store farmville vaWebDavid Gross, University of Cologne With: Sepehr Nezami, Michael Walter, Felipe Montealegre, Huangjun Zhu ... Application 2: Robust Hudson Thm. [Nezami, Walter, DG … flowers bread store hoursWebWe show that, on a Hilbert space of odd dimension, the only pure states to possess a non-negative Wigner function are stabilizer states. The Clifford group is identified as the set … flowers bread company brands