176 research outputs found

    Neural Networks and the Search for a Quadratic Residue Detector

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    This paper investigates the feasibility of employing artificial neural network techniques for solving fundamental cryptography problems, taking quadratic residue detection as an example. The problem of quadratic residue detection is one which is well known in both number theory and cryptography. While it garners less attention than problems such as factoring or discrete logarithms, it is similar in both difficulty and importance. No polynomial—time algorithm is currently known to the public by which the quadratic residue status of one number modulo another may be determined. This work leverages machine learning algorithms in an attempt to create a detector capable of solving instances of the problem more efficiently. A variety of neural networks, currently at the forefront of machine learning methodologies, were compared to see if any were capable of consistently outperforming random guessing as a mechanism for detection. Surprisingly, neural networks were repeatably able to achieve accuracies well in excess of random guessing on numbers up to 20 bits in length. Unfortunately, this performance was only achieved after a super—polynomial amount of network training, and therefore we do not believe that the system as implemented could scale to cryptographically relevant inputs of 500 to 1000 bits. This nonetheless suggests a new avenue of attack in the search for solutions to the quadratic residues problem, where future work focused on feature set refinement could potentially reveal the components necessary to construct a true closed—form solution

    High-energy electronic excitations in Sr2_2IrO4_4 observed by Raman scattering

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    Spin-orbit interaction in Sr2_2IrO4_4 leads to the realization of the JeffJ_{\mathrm{eff}} = 1/2 state and also induces an insulating behavior. Using large-shift Raman spectroscopy, we found two high-energy excitations of the d-shell multipletat at 690 meV and 680 meV with A1gA_{1g} and B1gB_{1g} symmetry respectively. As temperature decreases, the A1gA_{1g} and B1gB_{1g} peaks narrow, and the A1gA_{1g} peak shifts to higher energy while the energy of the B1gB_{1g} peak remains the same. When 25%\% of Ir is substituted with Rh the A1gA_{1g} peak softens by 10%\% but the B1gB_{1g} peak does not. We show that both pseudospin-flip and non-pseudosin-flip dd electronic transitions are Raman active, but only the latter are observed

    Entanglement and the Speed of Evolution in Mixed States

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    Entanglement speeds up evolution of a pure bipartite spin state, in line with the time energy uncertainty. However if the state is mixed this is not necessarily the case. We provide a counter example and point to other factors affecting evolution in mixed states, including classical correlations and entropy

    Failed attempt to escape from the quantum pigeon conundrum

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    A recent criticism by Kunstatter et al. [Phys. Lett. A 384, 126686 (2020)] of a quantum setup violating the pigeon counting principle [Aharonov et al. PNAS 113, 532 (2016)] is refuted. The quantum nature of the violation of the pigeonhole principle with pre- and postselection is clarified.Comment: to be published in Physics Letters

    High-Energy Electronic Excitations in Sr\u3csub\u3e2\u3c/sub\u3eIrO\u3csub\u3e4\u3c/sub\u3e Observed by Raman Scattering

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    Spin-orbit interaction in Sr2IrO4 leads to the realization of the Jeff=1/2 state and also induces an insulating behavior. Using large-shift Raman spectroscopy, we found two high-energy excitations of the d-shell multiplet at 690 and 680 meV with A1g and B1g symmetry, respectively. As temperature decreases, the A1g and B1g peaks narrow, and the A1g peak shifts to higher energy while the energy of the B1g peak remains the same. When 25% of Ir is substituted with Rh the A1g peak softens by 10% but the B1g peak does not. We show that both pseudospin-flip and non-pseudo-spin-flip d-d electronic transitions are Raman active, but only the latter are observed. Our experiments and analysis place significant new constraints on the possible electronic structure of Sr2IrO4
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