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Do Ngoc Diep

Publications and source records attributed to Do Ngoc Diep.

At least 19 recordsLinked to original sources
arXiv2020

Nonparametric Regression Quantum Neural Networks

In two pervious papers \cite{dndiep3}, \cite{dndiep4}, the first author constructed the least square quantum neural networks (LS-QNN), and ploynomial interpolation quantum neural networks ( PI-QNN), parametrico-stattistical QNN like: leanr regrassion quantum neural networks (LR-QNN), polynomial regression quantum neural networks (PR-QNN), chi-squared quantum neural netowrks ($χ^2$-QNN). We observed that the method works also in the cases by using nonparametric statistics. In this paper we analyze and implement the nonparametric tests on QNN such as: linear nonparametric regression quantum neural networks (LNR-QNN), polynomial nonparametric regression quantum neural networks (PNR-QNN). The implementation is constructed through the Gauss-Jordan Elimination quantum neural networks (GJE-QNN).The training rule is to use the high probability confidence regions or intervals.

cs.ET↗
arXiv2020

Statistical Tests and Confidential Intervals as Thresholds for Quantum Neural Networks

Some basic quantum neural networks were analyzed and constructed in the recent work of the author \cite{dndiep3}, published in International Journal of Theoretical Physics (2020). In particular the Least Quare Problem (LSP) and the Linear Regression Problem (LRP) was discussed. In this second paper we continue to analyze and construct the least square quantum neural network (LS-QNN), the polynomial interpolation quantum neural network (PI-QNN), the polynomial regression quantum neural network (PR-QNN) and chi-squared quantum neural network ($χ^2$-QNN). We use the corresponding solution or tests as the threshold for the corresponding training rules.

cs.ET↗
arXiv2017

Multiparty Quantum Telecommunication Using Quantum Fourier Transforms

Consider the problem: Alice wishes to send the same key to $n-1$ users (Bob, Carol,. . . , Nathan), while preventing eavesdropper Eve from acquiring information without being detected. The problem has no solution in the classical cryptography but in quantum telecommunication there are some codes to solve the problem. In the paper \cite{zengetall}, Guo-Jyun Zeng, Kuan-Hung Chen, Zhe-Hua Chang, Yu-Shan Yang, and Yao-Hsin Chou from one side and Cabello in \cite{cabello} from other side, used Hadamard gates, Pauli gates in providing the quantum communication code for two-partity telecommunication with 3 persons and then generalized it to the case of arbitrary number of participants, indicating the position of measurements of participants. We remark that the Hadamard gate with precising the position of measurement is the same as Fourier transform for two qubits and hence use the general Fourier transform for $n$ entangled qubits, in place of Hadamard gates. The result is more natural for arbitrary $n$ qudits.

quant-ph↗
arXiv2017

Quantization of Fields and Automorphic Representations

In this paper we use the quantization of fields based on Geometric Langlands Correspondence \cite{diep1} to realize the automorphic representations of some concrete series of groups: for the affine Heisenberg (loop) groups it is reduced to the construction of the affine Kac-Moody representation by the Weyl relations in Fock spaces. For the solvable and nilpotent groups following the construction we show that it is the result of applying the constructions of irreducible unitary representation via the geometric quantization and the construction of positive energy representations and finally, for the semi-simple or reductive Lie groups, using the Geometric Langlands Correspondence, we show that a repeated application of the construction give all the automorphic representations of reductive Lie groups: first we show that every representation of the fundamental group of Riemann surface into the dual Langlands groups ${}^LG$ of $G$ corresponds to a representation of the fundamental group of the surface into the reductive group $G$, what is corresponding to a quantum inducing bundle of the geometric quantization of finite dimensional reductive Lie groups and then apply the construction of positive energy representation of loop groups.

math.RT↗
arXiv2016

$\ell$-adic Poisson Formula and Endoscopy for $p$-Adic Reductive Groups

For two distinguished prime $\ell$ and $p$, we prove a $\ell$-adic version of the Poisson formula for reductive $p$-adic groups. In order to do this we write an identity for the trace of regular representation and orbital integrals. Next we reduce them to orbital integrals for endoscopy groups and look at this as the special value of $L$-function at $s=0$. And finally show that it is equal to the special value of motivic $L$-function at $s=0$.

math.RT↗
arXiv2016

Poisson Summation and Endoscopy for SU(2,1)

In this paper we analyze the endoscopy for $SU(2,1)$. The new results are a precise realization of the discrete series representations (in Section 2), a computation of their traces (Section 3) and an exact formula for the Poisson summation and endoscopy for this group (in Section 4).

math.RT↗
arXiv2016

On the Twisted KK-Theory and Positive Scalar Curvature Problem

Positiveness of scalar curvature and Ricci curvature requires vanishing the obstruction $θ(M)$ which is computed in some KK-theory of C*-algebras index as a pairing of spin Dirac operator and Mishchenko bundle associated to the manifold. U. Pennig had proved that the obstruction $θ(M)$ does not vanish if $M$ is an enlargeable closed oriented smooth manifold of even dimension larger than or equals to 3, the universal cover of which admits a spin structure. Using the equivariant cohomology of holonomy groupoids we prove the theorem in the general case without restriction of evenness of dimension. Our groupoid method is different from the method used by B. Hanke and T. Schick in reduction to the case of even dimension.

math.KT↗
arXiv2014

Poisson Summation and Endoscopy for $Sp(4,\mathbb R)$

In this paper we analyze the endoscopy for $\Sp(4,\mathbb R)$. The new results are a precise realization of the discrete series representations (in Section 2), a computation of their traces (Section 3) and an exact formula for the noncommutative Poisson summation and endoscopy of for this group (in Sections 4,5).

math.QA↗
arXiv2014

Poisson Summation and Endoscopy for $SL(3,\mathbb R)$

The group is interesting as the first example of split rank 2 semisimple group, all the irreducible unitary representations of which are known. We make a precise realization of the discrete series representations (in Section 2) by using the Orbit Method and Geometric Quantization, a computation of their traces (Section 3) and an exact formula for the noncommutative Poisson summation and endoscopy of for this group (in Section 4).

math.QA↗
arXiv2014

Automorphic Representations of $\SL(2,\mathbb R)$ and Quantization of Fields

In this paper we make a clear relationship between the automorphic representations and the quantization through the Geometric Langlands Correspondence. We observe that the discrete series representation are realized in the sum of eigenspaces of Cartan generator, and then present the automorphic representations in form of induced representations with inducing quantum bundle over a Riemann surface and then use the loop group representation construction to realize the automorphic representations. The Lanlands picture of automorphic representations is precised by using the Poisson summation formula.

math.RT↗
arXiv2007

Quantum Gauss Jordan Elimination

In this paper we construct the Quantum GaußJordan Elimination (QGJE) Algorithm and estimate the complexity time of computation of Reduced Row Echelon Form (RREF) of an $N\times N$ matrix using QGJE procedure. The main theorem asserts that QGJE has computation time of order $2^{N/2}$.

quant-ph↗
arXiv2007

Category of Noncommutative CW complexes. III

We prove in this paper a noncommutative version of Leray Spectral Sequence Theorem and then Leray-Serre Spectral Theorem for noncommutative Serre fibrations: for NC Serre fibration there are converging spectral sequences with $\E^2$ terms as $\E^2_{p,q} = \HP_p(A; \HP_q(B,A)) \Longrightarrow \HP_{p+q}(B)$ and $\E^2_{p,q} = \HP_p(A;\K_q(B,A)) \Longrightarrow \K_{p+q}(B)$.

math.QA↗
arXiv2007

Category of Noncommutative CW Complexes

We expose the notion of noncommutative CW (NCCW) complexes, define noncommutative (NC) mapping cylinder and NC mapping cone, and prove the noncommutative Approximation Theorem. The long exact homotopy sequences associated with arbitrary morphisms are also deduced.

math.QA↗
arXiv2007

Category of Noncommutative CW Complexes. II

We introduce in this paper the notion of noncommutative Serre fibration (shortly, NCSF) and show that up to homotopy, every NCCW complex morphism is some noncommutative Serre fibration. We then deduce a six-term exact sequence for the periodic cyclic homology and for K-theory of an arbitrary noncommutative Serre fibration. We also show how to use this technique to compute K-theory and cyclic theory of some noncommutative quotients.

math.QA↗
arXiv2003

The Noncommutative Chern-Connes Character of the Locally Compact Quantum Normalizer of SU(1,1) in SL(2,C)

We observe that the von Neumann envelope of the quantum algebra of functions on the normalizer of thegroup $\SU(1,1)\cong \SL(2,\mathbb R)$ in $\SL(2,\mathbb C)$ via deformation quantization contains the von Neumann algebraic quantum normalizer of $\SU(1,1)$ in the frame work of Waronowicz-Korogodsky. We then use the technique of reduction to the maximal subgroup to compute the K-theory, the periodic cyclic homology and the corresponding Chern-Connes character.

math.QA↗