Applying Grover's algorithm to AES: quantum resource estimates

We present quantum circuits to implement an exhaustive key search for the Advanced Encryption Standard (AES) and analyze the quantum resources required to carry out such an attack. We consider the overall circuit size, the number of qubits, and the circuit depth as measures for the cost of the presented quantum algorithms. Throughout, we focus on Clifford$+T$ gates as the underlying fault-tolerant logical quantum gate set. In particular, for all three variants of AES (key size 128, 192, and 256 bit) that are standardized in FIPS-PUB 197, we establish precise bounds for the number of qubits and the number of elementary logical quantum gates that are needed to implement Grover's quantum algorithm to extract the key from a small number of AES plaintext-ciphertext pairs.Comment: 13 pages, 3 figures, 5 tables; to appear in: Proceedings of the 7th International Conference on Post-Quantum Cryptography (PQCrypto 2016

Experimental magic state distillation for fault-tolerant quantum computing

Any physical quantum device for quantum information processing is subject to errors in implementation. In order to be reliable and efficient, quantum computers will need error correcting or error avoiding methods. Fault-tolerance achieved through quantum error correction will be an integral part of quantum computers. Of the many methods that have been discovered to implement it, a highly successful approach has been to use transversal gates and specific initial states. A critical element for its implementation is the availability of high-fidelity initial states such as |0> and the Magic State. Here we report an experiment, performed in a nuclear magnetic resonance (NMR) quantum processor, showing sufficient quantum control to improve the fidelity of imperfect initial magic states by distilling five of them into one with higher fidelity

Verification of Quantum Computation and the Price of Trust

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Robust Detection of Hierarchical Communities from Escherichia coli Gene Expression Data

Determining the functional structure of biological networks is a central goal of systems biology. One approach is to analyze gene expression data to infer a network of gene interactions on the basis of their correlated responses to environmental and genetic perturbations. The inferred network can then be analyzed to identify functional communities. However, commonly used algorithms can yield unreliable results due to experimental noise, algorithmic stochasticity, and the influence of arbitrarily chosen parameter values. Furthermore, the results obtained typically provide only a simplistic view of the network partitioned into disjoint communities and provide no information of the relationship between communities. Here, we present methods to robustly detect coregulated and functionally enriched gene communities and demonstrate their application and validity for Escherichia coli gene expression data. Applying a recently developed community detection algorithm to the network of interactions identified with the context likelihood of relatedness (CLR) method, we show that a hierarchy of network communities can be identified. These communities significantly enrich for gene ontology (GO) terms, consistent with them representing biologically meaningful groups. Further, analysis of the most significantly enriched communities identified several candidate new regulatory interactions. The robustness of our methods is demonstrated by showing that a core set of functional communities is reliably found when artificial noise, modeling experimental noise, is added to the data. We find that noise mainly acts conservatively, increasing the relatedness required for a network link to be reliably assigned and decreasing the size of the core communities, rather than causing association of genes into new communities.Comment: Due to appear in PLoS Computational Biology. Supplementary Figure S1 was not uploaded but is available by contacting the author. 27 pages, 5 figures, 15 supplementary file

Non-Linear Neuronal Responses as an Emergent Property of Afferent Networks: A Case Study of the Locust Lobula Giant Movement Detector

In principle it appears advantageous for single neurons to perform non-linear operations. Indeed it has been reported that some neurons show signatures of such operations in their electrophysiological response. A particular case in point is the Lobula Giant Movement Detector (LGMD) neuron of the locust, which is reported to locally perform a functional multiplication. Given the wide ramifications of this suggestion with respect to our understanding of neuronal computations, it is essential that this interpretation of the LGMD as a local multiplication unit is thoroughly tested. Here we evaluate an alternative model that tests the hypothesis that the non-linear responses of the LGMD neuron emerge from the interactions of many neurons in the opto-motor processing structure of the locust. We show, by exposing our model to standard LGMD stimulation protocols, that the properties of the LGMD that were seen as a hallmark of local non-linear operations can be explained as emerging from the dynamics of the pre-synaptic network. Moreover, we demonstrate that these properties strongly depend on the details of the synaptic projections from the medulla to the LGMD. From these observations we deduce a number of testable predictions. To assess the real-time properties of our model we applied it to a high-speed robot. These robot results show that our model of the locust opto-motor system is able to reliably stabilize the movement trajectory of the robot and can robustly support collision avoidance. In addition, these behavioural experiments suggest that the emergent non-linear responses of the LGMD neuron enhance the system's collision detection acuity. We show how all reported properties of this neuron are consistently reproduced by this alternative model, and how they emerge from the overall opto-motor processing structure of the locust. Hence, our results propose an alternative view on neuronal computation that emphasizes the network properties as opposed to the local transformations that can be performed by single neurons

Verification of Quantum Computation: An Overview of Existing Approaches

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Ephrin-A5 Suppresses Neurotrophin Evoked Neuronal Motility, ERK Activation and Gene Expression

During brain development, growth cones respond to attractive and repulsive axon guidance cues. How growth cones integrate guidance instructions is poorly understood. Here, we demonstrate a link between BDNF (brain derived neurotrophic factor), promoting axonal branching and ephrin-A5, mediating axonal repulsion via Eph receptor tyrosine kinase activation. BDNF enhanced growth cone filopodial dynamics and neurite branching of primary neurons. We show that ephrin-A5 antagonized this BDNF-evoked neuronal motility. BDNF increased ERK phosphorylation (P-ERK) and nuclear ERK entry. Ephrin-A5 suppressed BDNF-induced ERK activity and might sequester P-ERK in the cytoplasm. Neurotrophins are well established stimulators of a neuronal immediate early gene (IEG) response. This is confirmed in this study by e.g. c-fos, Egr1 and Arc upregulation upon BDNF application. This BDNF-evoked IEG response required the transcription factor SRF (serum response factor). Notably, ephrin-A5 suppressed a BDNF-evoked neuronal IEG response, suggesting a role of Eph receptors in modulating gene expression. In opposite to IEGs, long-term ephrin-A5 application induced cytoskeletal gene expression of tropomyosin and actinin. To uncover specific Eph receptors mediating ephrin-As impact on neurotrophin signaling, EphA7 deficient mice were analyzed. In EphA7 deficient neurons alterations in growth cone morphology were observed. However, ephrin-A5 still counteracted neurotrophin signaling suggesting that EphA7 is not required for ephrin and BDNF crosstalk. In sum, our data suggest an interaction of ephrin-As and neurotrophin signaling pathways converging at ERK signaling and nuclear gene activity. As ephrins are involved in development and function of many organs, such modulation of receptor tyrosine kinase signaling and gene expression by Ephs might not be limited to the nervous system

I-Louvain: An Attributed Graph Clustering Method

International audienceModularity allows to estimate the quality of a partition into communities of a graph composed of highly interconnected vertices. In this article, we introduce a complementary measure, based on inertia, and specially conceived to evaluate the quality of a partition based on real attributes describing the vertices. We propose also I-Louvain, a graph nodes clustering method which uses our criterion , combined with Newman's modularity, in order to detect communities in attributed graph where real attributes are associated with the vertices. Our experiments show that combining the relational information with the attributes allows to detect the communities more efficiently than using only one type of information. In addition, our method is more robust to data degradation