17 research outputs found
Scale-Dependent Functions, Stochastic Quantization and Renormalization
We consider a possibility to unify the methods of regularization, such as the
renormalization group method, stochastic quantization etc., by the extension of
the standard field theory of the square-integrable functions to the theory of functions that depend on coordinate
and resolution . In the simplest case such field theory turns out to be a
theory of fields defined on the affine group ,
, which consists of dilations and translation of
Euclidean space. The fields are constructed using the
continuous wavelet transform. The parameters of the theory can explicitly
depend on the resolution . The proper choice of the scale dependence
makes such theory free of divergences by construction.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
Towards a feasible implementation of quantum neural networks using quantum dots
We propose an implementation of quantum neural networks using an array of
quantum dots with dipole-dipole interactions. We demonstrate that this
implementation is both feasible and versatile by studying it within the
framework of GaAs based quantum dot qubits coupled to a reservoir of acoustic
phonons. Using numerically exact Feynman integral calculations, we have found
that the quantum coherence in our neural networks survive for over a hundred ps
even at liquid nitrogen temperatures (77 K), which is three orders of magnitude
higher than current implementations which are based on SQUID-based systems
operating at temperatures in the mK range.Comment: revtex, 5 pages, 2 eps figure
Quantum hierarchic models for information processing
Both classical and quantum computations operate with the registers of bits.
At nanometer scale the quantum fluctuations at the position of a given bit,
say, a quantum dot, not only lead to the decoherence of quantum state of this
bit, but also affect the quantum states of the neighboring bits, and therefore
affect the state of the whole register. That is why the requirement of reliable
separate access to each bit poses the limit on miniaturization, i.e, constrains
the memory capacity and the speed of computation. In the present paper we
suggest an algorithmic way to tackle the problem of constructing reliable and
compact registers of quantum bits. We suggest to access the states of quantum
register hierarchically, descending from the state of the whole register to the
states of its parts. Our method is similar to quantum wavelet transform, and
can be applied to information compression, quantum memory, quantum
computations.Comment: 14 pages, LaTeX, 1 eps figur
Wavelet-Based Quantum Field Theory
The Euclidean quantum field theory for the fields , which depend on both the position and the resolution , constructed in SIGMA 2 (2006), 046, on the base of the continuous wavelet transform, is considered. The Feynman diagrams in such a theory become finite under the assumption there should be no scales in internal lines smaller than the minimal of scales of external lines. This regularisation agrees with the existing calculations of radiative corrections to the electron magnetic moment. The transition from the newly constructed theory to a standard Euclidean field theory is achieved by integration over the scale arguments