9,702 research outputs found
Semantics for a Quantum Programming Language by Operator Algebras
This paper presents a novel semantics for a quantum programming language by
operator algebras, which are known to give a formulation for quantum theory
that is alternative to the one by Hilbert spaces. We show that the opposite
category of the category of W*-algebras and normal completely positive
subunital maps is an elementary quantum flow chart category in the sense of
Selinger. As a consequence, it gives a denotational semantics for Selinger's
first-order functional quantum programming language QPL. The use of operator
algebras allows us to accommodate infinite structures and to handle classical
and quantum computations in a unified way.Comment: In Proceedings QPL 2014, arXiv:1412.810
The state sum invariant of lens spaces
In this paper, we calculate the values of the state sum invariants for
the lens spaces . In particular, we show that the values of the
invariants are determined by and . As a corollary,
we show that the state sum is a homotopy invariant for the oriented lens
spaces.Comment: 6 pages, 0 figure
Minimal model theory for relatively trivial log canonical pairs
We study relative log canonical pairs with relatively trivial log canonical
divisors. We fix such a pair and establish the minimal model
theory for the pair assuming the minimal model theory for all
Kawamata log terminal pairs whose dimension is not greater than .
We also show the finite generation of log canonical rings for log canonical
pairs of dimension five which are not of log general type.Comment: 38 pages, final version. The statement of Theorem 1.2 was replaced by
that of Theorem 4.2, which was equivalent to Theorem 1.2. Accompanied by
this, Lemma 4.1 and Theorem 4.2 was removed. Numbering of definitions and
others in Section 2 and Section 4 was changed. Other minor changes. To appear
in Ann. Inst. Fourier (Grenoble
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