Results 301 to 310 of about 1,857,430 (354)

Accurate BDD-based Unitary Operator Manipulation for Scalable and Robust Quantum Circuit Verification

Design Automation Conference, 2022
Quantum circuit verification is essential, ensuring that quantum program compilation yields a sequence of primitive unitary operators executable correctly and reliably on a quantum processor.
Chun-Yu Wei, Yuan-Hung Tsai, Chiao-Shan Jhang, J. H. Jiang   +3 more
semanticscholar   +1 more source

Unitary Representations of the Affine Group

Journal of Mathematical Physics, 1968
The unitary representations of the affine group, or the group of linear transformations without reflections on the real line, have been found previously by Gel'fand and Naimark. The present paper gives an alternate proof, and presents several properties of the representations which will be used in a later application of this group to continuous ...
Aslaksen, Erik W., Klauder, John R.
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UNITARY BRAID REPRESENTATIONS

International Journal of Modern Physics A, 1992
The original motivation for studying unitarizable representations of the braid group was to construct interesting examples of subfactors of II1 von Neumann factors. This is possible for representations factoring through Hecke algebras or q-Brauer algebras only if the deformation parameter is a root of unity.
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Unitary representations of CM(3)

Journal of Physics A: Mathematical and General, 1994
Summary: Irreducible unitary representations of the group \(CM(3)\), the ``three-dimensional collective motion group', which is the semidirect product of a six-dimensional Abelian group \(T_6\) and \(SL(3, \mathbb{R})\), are constructed. A countable basis is identified in the carrier space of each representation.
Ogura, Hirohumi, Rowe, David J.
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Quantum Codes from Twisted Unitary t-Groups.

Physical Review Letters
We introduce twisted unitary t-groups, a generalization of unitary t-groups under a twisting by an irreducible representation. We then apply representation theoretic methods to the Knill-Laflamme error correction conditions to show that twisted unitary t-
Eric Kubischta, Ian Teixeira
semanticscholar   +1 more source

Unitary representations of the unitary group

Mathematical Proceedings of the Cambridge Philosophical Society, 1969
It is well known that every representation of the group Un of unitary matrices of order n × n is equivalent to a unitary representation (see e.g. Little-wood (6), ch. XI). Our object in the present paper is to discuss some properties of those representations, and to construct a specific unitary representation.
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On the Mixed-Unitary Rank of Quantum Channels

Communications in Mathematical Physics, 2020
In the theory of quantum information, the mixed-unitary quantum channels, for any positive integer dimension n, are those linear maps that can be expressed as a convex combination of conjugations by n×n\documentclass[12pt]{minimal} \usepackage{amsmath ...
Mark W. Girard, D. Leung, Jeremy Levick, Chi-Kwong Li, V. Paulsen, Y. Poon, John Watrous   +6 more
semanticscholar   +1 more source

Dixmier Traces and Unitary Representations

Functional Analysis and Its Applications, 2001
Let \(H_{1}, H_{2}\) be separable Hilbert spaces and let \(L(H_{1},H_{2})\) be the space of all bounded linear mappings from \(H_{1}\) to \(H_{2}\). \(J_{2}(H_{1},H_{2})\) denotes the subspace of \(L(H_{1},H_{2})\) of Hilbert-Schmidt mappings. Let \(G\) be a topological group and \(T_{1}, T_{2}\) be unitary representations of \(G\) into \(H_{1}\) and \(
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Holomorphic Extension of Unitary Representations

Journal of Lie Theory, 1993
Let \(H\) be a complex Hilbert space and \(\pi: G\to U(H)\) is continuous unitary representation of the Lie group \(G\) on \(H\). In this paper the author discusses the problem of extending \(\pi\) holomorphically to a complex manifold which carries the structure of a complex semigroup and which contains \(G\) as its group of units in its boundary ...
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Unitary-group canonical representations

Canadian Journal of Physics, 1989
A procedure based on symmetric-group basis states is constructed to develop and justify the formalism for the computation of unitary-group canonical matrix elements and states, the quantities needed for physical applications to prepare for such applications. It is shown that this method does give the required canonical decomposition.
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