8,881 research outputs found
Procedures for Converting among Lindblad, Kraus and Matrix Representations of Quantum Dynamical Semigroups
Given an quantum dynamical semigroup expressed as an exponential
superoperator acting on a space of N-dimensional density operators, eigenvalue
methods are presented by which canonical Kraus and Lindblad operator sum
representations can be computed. These methods provide a mathematical basis on
which to develop novel algorithms for quantum process tomography, the
statistical estimation of superoperators and their generators, from a wide
variety of experimental data. Theoretical arguments and numerical simulations
are presented which imply that these algorithms will be quite robust in the
presence of random errors in the data.Comment: RevTeX4, 31 pages, no figures; v4 adds new introduction and a
numerical example illustrating the application of these results to Quantum
Process Tomograph
Seeing Numbers
In 1890 William James listed several “elementary mental categories” that he postulated as having a natural origin. Among them, alongside the ideas of time and space, he also listed the idea of number. A symptomatic feature of Informatics as well as Cognitive Science today is the tendency not to talk so much about ideas as about their representations, either in the computer or in the brain. Taking up somewhat different perspective I will discuss the way natural numbers, viewed as counts of real or imagined objects, may be experienced phenomenally. I put forth even some speculative ideas about mental number processing by numerical savants
A Bloch-Sphere-Type Model for Two Qubits in the Geometric Algebra of a 6-D Euclidean Vector Space
Geometric algebra is a mathematical structure that is inherent in any metric
vector space, and defined by the requirement that the metric tensor is given by
the scalar part of the product of vectors. It provides a natural framework in
which to represent the classical groups as subgroups of rotation groups, and
similarly their Lie algebras. In this article we show how the geometric algebra
of a six-dimensional real Euclidean vector space naturally allows one to
construct the special unitary group on a two-qubit (quantum bit) Hilbert space,
in a fashion similar to that used in the well-established Bloch sphere model
for a single qubit. This is then used to illustrate the Cartan decompositions
and subalgebras of the four-dimensional special unitary group, which have
recently been used by J. Zhang, J. Vala, S. Sastry and K. B. Whaley [Phys. Rev.
A 67, 042313, 2003] to study the entangling capabilities of two-qubit
unitaries.Comment: 14 pages, 2 figures, in press (Proceedings of SPIE Conference on
Defense & Security
Expressing the operations of quantum computing in multiparticle geometric algebra
We show how the basic operations of quantum computing can be expressed and
manipulated in a clear and concise fashion using a multiparticle version of
geometric (aka Clifford) algebra. This algebra encompasses the product operator
formalism of NMR spectroscopy, and hence its notation leads directly to
implementations of these operations via NMR pulse sequences.Comment: RevTeX, 10 pages, no figures; Physics Letters A, in pres
Al-alloy die-castings for automotive industry
Tato rešeršní práce je zaměřena na téma Tlakově lité odlitky z Al slitin pro automobilový průmysl. V teoretické části je toto téma popsáno z hlediska technologie lití pro Al slitiny se zaměřením na vysokotlaké lití, na slitinu hliníku AlSi9Cu3 a na metody zjišťování zbytkové napjatosti. V experimentální části je uvedena ukázka měření zbytkových napětí na vzorcích odlitých ze slitiny AlSi9Cu3.This search is concentrated on Pressure-castings of aluminum alloys for the automotive industry. In the theoretical part of this topic is described in terms of technology for casting aluminum alloys with a focus on high-pressure casting of aluminum alloy AlSi9Cu3 and methods of detecting residual stress. In the experimental section is a sample of residual stress measurements on samples cast alloy AlSi9Cu3.
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