7,553 research outputs found
Improved Quantum Cost for n-bit Toffoli Gates
We present an n-bit Toffoli gate quantum circuit based on the realization
proposed by Barenco, where some of the Toffoli gates in their construction are
replaced with Peres gates. This results in a significant cost reduction. Our
main contribution is a quantum circuit which simulates the (m+1)-bit Toffoli
gate with 32m-96 elementary quantum gates and one garbage bit which is passed
unchanged. This paper is a corrected and expanded version of our recent journal
publication
Propagation of fluctuations in interaction networks governed by the law of mass action
Using an example of physical interactions between proteins, we study how
perturbations propagate in interconnected networks whose equilibrium state is
governed by the law of mass action. We introduce a comprehensive matrix
formalism which predicts the response of this equilibrium to small changes in
total concentrations of individual molecules, and explain it using a heuristic
analogy to a current flow in a network of resistors. Our main conclusion is
that on average changes in free concentrations exponentially decay with the
distance from the source of perturbation. We then study how this decay is
influenced by such factors as the topology of a network, binding strength, and
correlations between concentrations of neighboring nodes. An exact analytic
expression for the decay constant is obtained for the case of uniform
interactions on the Bethe lattice. Our general findings are illustrated using a
real biological network of protein-protein interactions in baker's yeast with
experimentally determined protein concentrations.Comment: 4 pages; 2 figure
Probability Theory Compatible with the New Conception of Modern Thermodynamics. Economics and Crisis of Debts
We show that G\"odel's negative results concerning arithmetic, which date
back to the 1930s, and the ancient "sand pile" paradox (known also as "sorites
paradox") pose the questions of the use of fuzzy sets and of the effect of a
measuring device on the experiment. The consideration of these facts led, in
thermodynamics, to a new one-parameter family of ideal gases. In turn, this
leads to a new approach to probability theory (including the new notion of
independent events). As applied to economics, this gives the correction, based
on Friedman's rule, to Irving Fisher's "Main Law of Economics" and enables us
to consider the theory of debt crisis.Comment: 48p., 14 figs., 82 refs.; more precise mathematical explanations are
added. arXiv admin note: significant text overlap with arXiv:1111.610
On the superfluidity of classical liquid in nanotubes
In 2001, the author proposed the ultra second quantization method. The ultra
second quantization of the Schr\"odinger equation, as well as its ordinary
second quantization, is a representation of the N-particle Schr\"odinger
equation, and this means that basically the ultra second quantization of the
equation is the same as the original N-particle equation: they coincide in
3N-dimensional space.
We consider a short action pairwise potential V(x_i -x_j). This means that as
the number of particles tends to infinity, , interaction is
possible for only a finite number of particles. Therefore, the potential
depends on N in the following way: . If V(y) is finite
with support , then as the support engulfs a finite
number of particles, and this number does not depend on N.
As a result, it turns out that the superfluidity occurs for velocities less
than , where
is the critical Landau velocity and R is the radius of
the nanotube.Comment: Latex, 20p. The text is presented for the International Workshop
"Idempotent and tropical mathematics and problems of mathematical physics",
Independent University of Moscow, Moscow, August 25--30, 2007 and to be
published in the Russian Journal of Mathematical Physics, 2007, vol. 15, #
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