Neural Networks for Predicting Algorithm Runtime Distributions

Many state-of-the-art algorithms for solving hard combinatorial problems in artificial intelligence (AI) include elements of stochasticity that lead to high variations in runtime, even for a fixed problem instance. Knowledge about the resulting runtime distributions (RTDs) of algorithms on given problem instances can be exploited in various meta-algorithmic procedures, such as algorithm selection, portfolios, and randomized restarts. Previous work has shown that machine learning can be used to individually predict mean, median and variance of RTDs. To establish a new state-of-the-art in predicting RTDs, we demonstrate that the parameters of an RTD should be learned jointly and that neural networks can do this well by directly optimizing the likelihood of an RTD given runtime observations. In an empirical study involving five algorithms for SAT solving and AI planning, we show that neural networks predict the true RTDs of unseen instances better than previous methods, and can even do so when only few runtime observations are available per training instance

Calculating Unknown Eigenvalues with a Quantum Algorithm

Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct the algorithm. We have implemented the complete quantum phase estimation algorithm for a single qubit unitary in which the answer is calculated by the algorithm. We use a new approach to implementing the controlled-unitary operations that lie at the heart of the majority of quantum algorithms that is more efficient and does not require the eigenvalues of the unitary to be known. These results point the way to efficient quantum simulations and quantum metrology applications in the near term, and to factoring large numbers in the longer term. This approach is architecture independent and thus can be used in other physical implementations

A New Cryptosystem Based On Hidden Order Groups

Let $G_1$ be a cyclic multiplicative group of order $n$. It is known that the Diffie-Hellman problem is random self-reducible in $G_1$ with respect to a fixed generator $g$ if $\phi(n)$ is known. That is, given $g, g^x\in G_1$ and having oracle access to a `Diffie-Hellman Problem' solver with fixed generator $g$, it is possible to compute $g^{1/x} \in G_1$ in polynomial time (see theorem 3.2). On the other hand, it is not known if such a reduction exists when $\phi(n)$ is unknown (see conjuncture 3.1). We exploit this ``gap'' to construct a cryptosystem based on hidden order groups and present a practical implementation of a novel cryptographic primitive called an \emph{Oracle Strong Associative One-Way Function} (O-SAOWF). O-SAOWFs have applications in multiparty protocols. We demonstrate this by presenting a key agreement protocol for dynamic ad-hoc groups.Comment: removed examples for multiparty key agreement and join protocols, since they are redundan

Implementing Shor's algorithm on Josephson Charge Qubits

We investigate the physical implementation of Shor's factorization algorithm on a Josephson charge qubit register. While we pursue a universal method to factor a composite integer of any size, the scheme is demonstrated for the number 21. We consider both the physical and algorithmic requirements for an optimal implementation when only a small number of qubits is available. These aspects of quantum computation are usually the topics of separate research communities; we present a unifying discussion of both of these fundamental features bridging Shor's algorithm to its physical realization using Josephson junction qubits. In order to meet the stringent requirements set by a short decoherence time, we accelerate the algorithm by decomposing the quantum circuit into tailored two- and three-qubit gates and we find their physical realizations through numerical optimization.Comment: 12 pages, submitted to Phys. Rev.