Search results for "complex"
showing 10 items of 5889 documents
The class of languages recognizable by 1-way quantum finite automata is not closed under union
2000
In this paper we develop little further the theory of quantum finite automata (QFA). There are already few properties of QFA known, that deterministic and probabilistic finite automata do not have e.g. they cannot recognize all regular languages. In this paper we show, that class of languages recognizable by QFA is not closed under union, even not under any Boolean operation, where both arguments are significant.
Association of N-(Pyridin-2-yl),N′-substituted Ureas with 2-Amino-1,8-naphthyridines and Benzoates: NMR and Quantum Chemical Studies of the Substitue…
2013
Association of four N-(pyridin-2-yl),N'-R(1)-ureas (R(1) = ethyl, n-butyl, phenyl, and tert-butyl) with substituted 2-amino-1,8-naphthyridines and benzoates were studied by (1)H NMR spectroscopic titrations and quantum chemical calculations. The benzoates and 2-amino-1,8-naphthyridines were selected as representatives of double and triple hydrogen bonding counterparts, respectively. The classical substituent effect on the association was studied. A prerequisite and a crucial step for the complex formation was the breaking of the intramolecular hydrogen bond in urea derivatives. The QTAIM calculation method was employed to explain the hydrogen bonding within complexes. In the case of benzoat…
Chiral condensates from tau decay: a critical reappraisal
2006
The saturation of QCD chiral sum rules is reanalyzed in view of the new and complete analysis of the ALEPH experimental data on the difference between vector and axial-vector correlators (V-A). Ordinary finite energy sum rules (FESR) exhibit poor saturation up to energies below the tau-lepton mass. A remarkable improvement is achieved by introducing pinched, as well as minimizing polynomial integral kernels. Both methods are used to determine the dimension d=6 and d=8 vacuum condensates in the Operator Product Expansion, with the results: {O}_{6}=-(0.00226 \pm 0.00055) GeV^6, and O_8=-(0.0053 \pm 0.0033) GeV^8 from pinched FESR, and compatible values from the minimizing polynomial FESR. Som…
Finite energy chiral sum rules in QCD
2003
The saturation of QCD chiral sum rules of the Weinberg-type is analyzed using ALEPH and OPAL experimental data on the difference between vector and axial-vector correlators (V-A). The sum rules exhibit poor saturation up to current energies below the tau-lepton mass. A remarkable improvement is achieved by introducing integral kernels that vanish at the upper limit of integration. The method is used to determine the value of the finite remainder of the (V-A) correlator, and its first derivative, at zero momentum: $\bar{\Pi}(0) = - 4 \bar{L}_{10} = 0.0257 \pm 0.0003 ,$ and $\bar{\Pi}^{\prime}(0) = 0.065 \pm 0.007 {GeV}^{-2}$. The dimension $d=6$ and $d=8$ vacuum condensates in the Operator P…
QCD Radiative Correction to Zero Recoil Sum Rules for Heavy Flavor Transitions in the Small Velocity Limit.
1995
We consider the small velocity sum rules for heavy flavour semileptonic transitions that are used to estimate the zero recoil values of semileptonic heavy flavour form factors. We analyze the complete O($\alpha _S$) radiative correction to these sum rules. The corrections are universal and influence all "model-independent" bounds previously derived for semileptonic form factors at zero recoil.
Comparison between two strictly local QCD sum rules
1989
Two strictly local QCD sum rules, analytic extrapolation by conformal mapping and analytic continuation by duality, are developed and presented in full detail. They allow the extrapolation of the QCD amplitude to a single point near zero in the complex {ital q}{sup 2} plane. Being orthogonal to the usual QCD sum rules, they present a drastic enlargement of phenomenological applications. In addition, the stability of both methods is shown explicitly, a fact which makes them particularly reliable. The difference between the two methods is illustrated in connection with the determination of the hadronic ({ital g}{minus}2) factor of the muon. Their effectiveness is demonstrated in the calculati…
Multiparton NLO corrections by numerical methods
2013
In this talk we discuss an algorithm for the numerical calculation of one-loop QCD amplitudes and present results at next-to-leading order for jet observables in electron-positron annihilation calculated with the above-mentioned method. The algorithm consists of subtraction terms, approximating the soft, collinear and ultraviolet divergences of QCD one-loop amplitudes, as well as a method to deform the integration contour for the loop integration into the complex plane to match Feynman's i delta rule. The algorithm is formulated at the amplitude level and does not rely on Feynman graphs. Therefore all ingredients of the algorithm can be calculated efficiently using recurrence relations. The…
Grover’s Search with Faults on Some Marked Elements
2018
Grover’s algorithm is a quantum query algorithm solving the unstructured search problem of size [Formula: see text] using [Formula: see text] queries. It provides a significant speed-up over any classical algorithm [3]. The running time of the algorithm, however, is very sensitive to errors in queries. Multiple authors have analysed the algorithm using different models of query errors and showed the loss of quantum speed-up [2, 6]. We study the behavior of Grover’s algorithm in the model where the search space contains both faulty and non-faulty marked elements. We show that in this setting it is indeed possible to find one of marked elements in [Formula: see text] queries. We also analyze…
Quantum Lower Bound for Graph Collision Implies Lower Bound for Triangle Detection
2015
We show that an improvement to the best known quantum lower bound for GRAPH-COLLISION problem implies an improvement to the best known lower bound for TRIANGLE problem in the quantum query complexity model. In GRAPH-COLLISION we are given free access to a graph $(V,E)$ and access to a function $f:V\rightarrow \{0,1\}$ as a black box. We are asked to determine if there exist $(u,v) \in E$, such that $f(u)=f(v)=1$. In TRIANGLE we have a black box access to an adjacency matrix of a graph and we have to determine if the graph contains a triangle. For both of these problems the known lower bounds are trivial ($\Omega(\sqrt{n})$ and $\Omega(n)$, respectively) and there is no known matching upper …
Quantum versus classical query complexity of relation
2011
This paper investigates the computability of mathematical relations in a quantum query model. The important task in complexity theory is to find examples with a large gap between classical and quantum algorithm complexity of the same computational problem. We present new results in quantum query algorithm design that allow achieving a large separation between classical and quantum query complexity of a specific relation. We demonstrate an example where quantum query algorithm for a finite relation needs more than two times fewer queries than the best possible classical analogue. We also show that relation can be extended to infinite family of relations with an input of general size N.