Laplacian spectral characterization of roses

A rose graph is a graph consisting of cycles that all meet in one vertex. We show that except for two specific examples, these rose graphs are determined by the Laplacian spectrum, thus proving a conjecture posed by Lui and Huang [F.J. Liu and Q.X. Huang, Laplacian spectral characterization of 3-rose graphs, Linear Algebra Appl. 439 (2013), 2914--2920]. We also show that if two rose graphs have a so-called universal Laplacian matrix with the same spectrum, then they must be isomorphic. In memory of Horst Sachs (1927-2016), we show the specific case of the latter result for the adjacency matrix by using Sachs' theorem and a new result on the number of matchings in the disjoint union of paths

Quantum Oracle Interrogation: Getting all information for almost half the price

Consider a quantum computer in combination with a binary oracle of domain size N. It is shown how N/2+sqrt(N) calls to the oracle are sufficient to guess the whole content of the oracle (being an N bit string) with probability greater than 95%. This contrasts the power of classical computers which would require N calls to achieve the same task. From this result it follows that any function with the N bits of the oracle as input can be calculated using N/2+sqrt(N) queries if we allow a small probability of error. It is also shown that this error probability can be made arbitrary small by using N/2+O(sqrt(N)) oracle queries. In the second part of the article `approximate interrogation' is considered. This is when only a certain fraction of the N oracle bits are requested. Also for this scenario does the quantum algorithm outperform the classical protocols. An example is given where a quantum procedure with N/10 queries returns a string of which 80% of the bits are correct. Any classical protocol would need 6N/10 queries to establish such a correctness ratio.Comment: 11 pages LaTeX2e, 1 postscript figure; error analysis added; new section on approximate interrogation adde

Quantum Algorithms for Weighing Matrices and Quadratic Residues

In this article we investigate how we can employ the structure of combinatorial objects like Hadamard matrices and weighing matrices to device new quantum algorithms. We show how the properties of a weighing matrix can be used to construct a problem for which the quantum query complexity is ignificantly lower than the classical one. It is pointed out that this scheme captures both Bernstein & Vazirani's inner-product protocol, as well as Grover's search algorithm. In the second part of the article we consider Paley's construction of Hadamard matrices, which relies on the properties of quadratic characters over finite fields. We design a query problem that uses the Legendre symbol chi (which indicates if an element of a finite field F_q is a quadratic residue or not). It is shown how for a shifted Legendre function f_s(i)=chi(i+s), the unknown s in F_q can be obtained exactly with only two quantum calls to f_s. This is in sharp contrast with the observation that any classical, probabilistic procedure requires more than log(q) + log((1-e)/2) queries to solve the same problem.Comment: 18 pages, no figures, LaTeX2e, uses packages {amssymb,amsmath}; classical upper bounds added, presentation improve

Comment on "Quantum identification schemes with entanglements"

In a recent paper, [Phys. Rev. A 65, 052326 (2002)], Mihara presented several cryptographic protocols that were claimed to be quantum mechanical in nature. In this comment it is pointed out that these protocols can be described in purely classical terms. Hence, the security of these schemes does not rely on the usage of entanglement or any other quantum mechanical property.Comment: 2 pages, revtex

Options for sustainability improvement and biomass use in Malaysia : Palm oil production chain and biorefineries for non-food use of residues and by-products including other agricultural crops

The Division Biobased Products of the WUR institute A&F was approached by the Dutch Ministry of Agriculture, Nature and Food Quality with a policy support question about the potential of Bio-based economic developments in Malaysia. Malaysia is one of the major international trade partners of the Netherlands. Annually 4.500 – 5.000 million euro’s worth of goods are imported from Malaysia. The Netherlands are Malaysia’s most important trading partner within the EU. The volume of agricultural commodities and especially palm oil products are substantial and the use of biobased resources for the generation of energy or biofuel has created a fierce debate on the sustainability of expansion of use of the biomass resources. In the context of the international policy to support the transition towards a biobased economy the potential resources that can be used for production of materials, chemicals and energy needs to be indentified. This report is reviewing the options that the current Malaysian agro-forestry sector may provide for sustainable developments. The main conclusions are that especially the currently underutilized residues and polluting wastes from the palm oil production have big potential for value addition and technical product development that also could substantially contribute to the reduction of greenhouse gas emissions. Examples can be found in fermentation of residues and effluents to produce bio-gas / ethanol or bioplastics but also fibre boards and building materials. Demonstration on pilot scale of such technologies could create new business and bilateral interactions between Malaysia and The Netherlands

Two Classical Queries versus One Quantum Query

In this note we study the power of so called query-limited computers. We compare the strength of a classical computer that is allowed to ask two questions to an NP-oracle with the strength of a quantum computer that is allowed only one such query. It is shown that any decision problem that requires two parallel (non-adaptive) SAT-queries on a classical computer can also be solved exactly by a quantum computer using only one SAT-oracle call, where both computations have polynomial time-complexity. Such a simulation is generally believed to be impossible for a one-query classical computer. The reduction also does not hold if we replace the SAT-oracle by a general black-box. This result gives therefore an example of how a quantum computer is probably more powerful than a classical computer. It also highlights the potential differences between quantum complexity results for general oracles when compared to results for more structured tasks like the SAT-problem.Comment: 6 pages, LaTeX2e, no figures, minor changes and correction