Efficient Quantum State Estimation with Over-complete Tomography

It is widely accepted that the selection of measurement bases can affect the efficiency of quantum state estimation methods, precision of estimating an unknown state can be improved significantly by simply introduce a set of symmetrical measurement bases. Here we compare the efficiencies of estimations with different numbers of measurement bases by numerical simulation and experiment in optical system. The advantages of using a complete set of symmetrical measurement bases are illustrated more clearly

Coevolution of game and network structure: The temptation increases the cooperator density

Most papers about the evolutionary game on graph assume the statistic network structure. However, social interaction could change the relationship of people. And the changing social structure will affect the people's strategy too. We build a coevolutionary model of prisoner's dilemma game and network structure to study the dynamic interaction in the real world. Based on the asynchronous update rule and Monte Carlo simulation, we find that, when players prefer to rewire their links to the richer, the cooperation density will increase. The reason of it has been analyzed.Comment: 7 pages, 6 figure

Super controlled gates and controlled gates in two-qubit gate simulations

In two-qubit gate simulations an entangling gate is used several times together with single qubit gates to simulate another two-qubit gate. We show how a two-qubit gate's simulation power is related to the simulation power of its mirror gate. And we show that an arbitrary two-qubit gate can be simulated by three applications of a super controlled gate together with single qubit gates. We also give the gates set that can be simulated by n applications of a controlled gate in a constructive way. In addition we give some gates which can be used four times to simulate an arbitrary two-qubit gate.Comment: 4 pages, no figure

Totally compatible associative and Lie dialgebras, tridendriform algebras and PostLie algebras

This paper studies the concepts of a totally compatible dialgebra and a totally compatible Lie dialgebra, defined to be a vector space with two binary operations that satisfy individual and mixed associativity conditions and Lie algebra conditions respectively. We show that totally compatible dialgebras are closely related to bimodule algebras and semi-homomorphisms. More significantly, Rota-Baxter operators on totally compatible dialgebras provide a uniform framework to generalize known results that Rota-Baxter related operators give tridendriform algebras. Free totally compatible dialgebras are constructed. We also show that a Rota-Baxter operator on a totally compatible Lie dialgebra gives rise to a PostLie algebra, generalizing the fact that a Rota-Baxter operator on a Lie algebra gives rise to a PostLie algebra.Comment: 17 page

The category and operad of matching dialgebras

This paper gives a systematic study of matching dialgebras corresponding to the operad $As^{(2)}$ in \cite{Zi} as the only Koszul self dual operad there other than the operads of associative algebras and Poisson algebras. The close relationship of matching dialgebras with semi-homomorphisms and matched pairs of associative algebras are established. By anti-symmetrizing, matching dialgerbas are also shown to give compatible Lie algebras, pre-Lie algebras and PostLie algebras. By the rewriting method, the operad of matching dialgebras is shown to be Koszul and the free objects are constructed in terms of tensor algebras. The operadic complex computing the homology of the matching dialgebras is made explicit.Comment: 13 pages, 2 figure

Molecular dynamics simulations of the growth of thin amorphous hydrogenated carbon films on diamond surface

The growth of thin amorphous hydrogenated carbon films (a-C:H) on diamond (111) surface from the bombardment of CH2 radicals is studied using molecular dynamics simulations. The structural analysis shows that the local structure (e.g., the first coordination number of C atoms) of a-C:H depends critically on the content of hydrogen. The increase of kinetic energy of incident radicals leads to the decrease of hydrogen content, which subsequently changes the ratio of sp3 bonded C atoms in a-C:H.Comment: 17 pages, 7 figures, in Chines

Quantum random walk in periodic potential on a line

We investigated the discrete-time quantum random walks on a line in periodic potential. The probability distribution with periodic potential is more complex compared to the normal quantum walks, and the standard deviation $\sigma$ has interesting behaviors for different period $q$ and parameter $\theta$. We studied the behavior of standard deviation with variation in walk steps, period, and $\theta$. The standard deviation increases approximately linearly with $\theta$ and decreases with $1/q$ for $\theta\in(0,\pi/4)$, and increases approximately linearly with $1/q$ for $\theta\in[\pi/4,\pi/2)$. When $q=2$, the standard deviation is lazy for $\theta\in[\pi/4+n\pi,3\pi/4+n\pi],n\in Z$

The Rodriguez-Villegas type congruences for truncated q-hypergeometric functions

We prove some Rodriguez-Villegas type congruences for truncated q-hypergeometric functions.Comment: This is a preliminary draf

Average position in quantum walks with a U(2) coin

We investigated discrete-time quantum walks with an arbitary unitary coin. Here we discover that the average position $=\max( \sin(\alpha+\gamma)$, while the initial state is $1/\sqrt{2}(\mid0L>+i\mid0R>)$. We prove the result and get some symmetry properties of quantum walks with a U(2) coin with $\mid0L>$ and $\mid0R>$ as the initial state

Condition for the adiabatic approximation

We give a sufficient condition for the quantum adiabatic approximation, which is quantitative and can be used to estimate error caused by this approximation. We also discuss when the traditional condition is sufficient.Comment: We give a sufficient condition for the quantum adiabatic approximation, which can be used to resolve the recent criticism on it. Comments are welcom