Prime Factorization in the Duality Computer

We give algorithms to factorize large integers in the duality computer. We provide three duality algorithms for factorization based on a naive factorization method, the Shor algorithm in quantum computing, and the Fermat's method in classical computing. All these algorithms are polynomial in the input size.Comment: 4 page

Tight Kernel Bounds for Problems on Graphs with Small Degeneracy

In this paper we consider kernelization for problems on d-degenerate graphs, i.e. graphs such that any subgraph contains a vertex of degree at most $d$. This graph class generalizes many classes of graphs for which effective kernelization is known to exist, e.g. planar graphs, H-minor free graphs, and H-topological-minor free graphs. We show that for several natural problems on d-degenerate graphs the best known kernelization upper bounds are essentially tight.Comment: Full version of ESA 201

General-Purpose Parallel Simulator for Quantum Computing

With current technologies, it seems to be very difficult to implement quantum computers with many qubits. It is therefore of importance to simulate quantum algorithms and circuits on the existing computers. However, for a large-size problem, the simulation often requires more computational power than is available from sequential processing. Therefore, the simulation methods using parallel processing are required. We have developed a general-purpose simulator for quantum computing on the parallel computer (Sun, Enterprise4500). It can deal with up-to 30 qubits. We have performed Shor's factorization and Grover's database search by using the simulator, and we analyzed robustness of the corresponding quantum circuits in the presence of decoherence and operational errors. The corresponding results, statistics and analyses are presented.Comment: 15 pages, 15 figure

Gravitational Correction and Weak Gravity Conjecture

We consider the gravitational correction to the running of gauge coupling. Weak gravity conjecture implies that the gauge theories break down when the gravitational correction becomes greater than the contribution from gauge theories. This observation can be generalized to non-Abelian gauge theories in diverse dimensions and the cases with large extra dimensions.Comment: 8 pages; minor correction and refs adde

Controlled order rearrangement encryption for quantum key distribution

A novel technique is devised to perform orthogonal state quantum key distribution. In this scheme, entangled parts of a quantum information carrier are sent from Alice to Bob through two quantum channels. However before the transmission, the orders of the quantum information carrier in one channel is reordered so that Eve can not steal useful information. At the receiver's end, the order of the quantum information carrier is restored. The order rearrangement operation in both parties is controlled by a prior shared control key which is used repeatedly in a quantum key distribution session.Comment: 5 pages and 2 figure

Vanishing Effective Mass of the Neutrinoless Double Beta Decay?

We stress that massive neutrinos may be Majorana particles even if the effective mass of the neutrinoless double beta decay m_ee vanishes. We show that current neutrino oscillation data do allow m_ee = 0 to hold, if the Majorana CP-violating phases lie in two specific regions. Strong constraints on three neutrino masses can then be obtained. We find that the neutrino mass spectrum performs a normal hierarchy: m_1 < m_2 < m_3. A possible texture of the neutrino mass matrix is also illustrated under the m_ee = 0 condition.Comment: RevTex 9 pages (2 PS figures included). More discussions and references added. Results partly changed. To appear in Phys. Rev.

A Model of Fermion Masses and Flavor Mixings with Family Symmetry SU(3)⊗U(1)SU(3)\otimes U(1)

The family symmetry $SU(3)\otimes U(1)$ is proposed to solve flavor problems about fermion masses and flavor mixings. It's breaking is implemented by some flavon fields at the high-energy scale. In addition a discrete group $Z_{2}$ is introduced to generate tiny neutrino masses, which is broken by a real singlet scalar field at the middle-energy scale. The low-energy effective theory is elegantly obtained after all of super-heavy fermions are integrated out and decoupling. All the fermion mass matrices are regularly characterized by four fundamental matrices and thirteen parameters. The model can perfectly fit and account for all the current experimental data about the fermion masses and flavor mixings, in particular, it finely predicts the first generation quark masses and the values of $\theta^{\,l}_{13}$ and $J_{CP}^{\,l}$ in neutrino physics. All of the results are promising to be tested in the future experiments.Comment: 14 pages, 1 figure, to make a few of corrections to the old version. arXiv admin note: substantial text overlap with arXiv:1011.457

Prediction of Ue3U_{e3} in Neutrino Mass Matrix with Two Zeros

We have discussed predictions of $|U_{e3}|$ and $J_{CP}$ in the framework of the neutrino mass matrix with two zeros. In the case of the best fit values of $\tan^2\theta_{12}$, $\tan^2\theta_{23}$, $\Delta m^2_{\rm sun}$ and $\Delta m_{\rm atm}^2$, the prediction of $|U_{e3}|$ is $0.11\sim 0.14$. The lower bound of $|U_{e3}|$ is 0.05, which depends on $\tan\theta_{12}$ and $\tan\theta_{23}$. We have investigated the stability of these predictions taking account of small corrections to zeros, which may come from radiative corrections or off-diagonal elements of the charged lepton massmatrix. The lower bound of $|U_{e3}|$ comes down considerably due to the small corrections to zeros.Comment: Figures and discussions are adde

Isotope effect in impure high T_c superconductors

The influence of various kinds of impurities on the isotope shift exponent \alpha of high temperature superconductors has been studied. In these materials the dopant impurities, like Sr in La_{2-x}Sr_xCuO_4, play different role and usually occupy different sites than impurities like Zn, Fe, Ni {\it etc} intentionally introduced into the system to study its superconducting properties. In the paper the in-plane and out-of-plane impurities present in layered superconductors have been considered. They differently affect the superconducting transition temperature T_c. The relative change of isotope shift coefficient, however, is an universal function of T_c/T_{c0} (T_{c0} reffers to impurity free system) {\it i.e.} for angle independent scattering rate and density of states function it does not depend whether the change of T_c is due to in- or out-of-plane impurities. The role of the anisotropic impurity scattering in changing oxygen isotope coefficient of superconductors with various symmetries of the order parameter is elucidated. The comparison of the calculated and experimental dependence of \alpha/\alpha_0, where \alpha_0 is the clean system isotope shift coefficient, on T_c/T_{c0} is presented for a number of cases studied. The changes of \alpha calculated within stripe model of superconductivity in copper oxides resonably well describe the data on La_{1.8}Sr_{0.2}Cu_{1-x}(Fe,Ni)_xO_4, without any fitting parameters.Comment: 8 pages, 6 figures, Phys. Rev. B67 (2003) accepte