Abstract
This extended abstract reports on on-going research on quantum algorithmic approaches to the problem of generalised tree search that may exhibit effective quantum speedup, even in the presence of non-constant branching factors. Two strategies are briefly summarised and current work outlined.

Abstract
Reinforcement Learning is at the core of a recent revolution in Artificial Intelligence. Simultaneously, we are witnessing the emergence of a new field: Quantum Machine Learning. In the context of these two major developments, this work addresses the interplay between Quantum Computing and Reinforcement Learning. Learning by interaction is possible in the quantum setting using the concept of oraculization of environments. The paper extends previous oracular instances to address more general stochastic environments. In this setting, we developed a novel quantum algorithm for near-optimal decision-making based on the Reinforcement Learning paradigm known as Sparse Sampling. The proposed algorithm exhibits a quadratic speedup compared to its classical counterpart. To the best of the authors' knowledge, this is the first quantum planning algorithm exhibiting a time complexity independent of the number of states of the environment, which makes it suitable for large state space environments, where planning is otherwise intractable.

Abstract
Bayesian Monte Carlo (BMC) is a promising integration technique which considerably broadens the theoretical tools that can be used to maximize and exploit the information produced by sampling, while keeping the fundamental property of data dimension independence of classical Monte Carlo (CMC). Moreover, BMC uses information that is ignored in the CMC method, such as the position of the samples and prior stochastic information about the integrand, which often leads to better integral estimates. Nevertheless, the use of BMC in computer graphics is still in an incipient phase and its application to more evolved and widely used rendering algorithms remains cumbersome. In this article we propose to apply BMC to a two-level adaptive sampling scheme for illumination integrals. We propose an efficient solution for the second level quadrature computation and show that the proposed method outperforms adaptive quasi-Monte Carlo in terms of image error and high frequency noise. © 2016 The Eurographics Association.

Abstract

Abstract
This paper presents a new, heterogeneous CPU+GPU attacks against lattice-based (post-quantum) cryptosystems based on the Shortest Vector Problem (SVP), a central problem in lattice-based cryptanalysis. To the best of our knowledge, this is the first SVP-attack against lattice-based cryptosystems using CPUs and GPUs simultaneously. We show that Voronoi-cell based CPU+GPU attacks, algorithmically improved in previous work, are suitable for the proposed massively parallel platforms. Results show that 1) heterogeneous platforms are useful in this scenario, as they increment the overall memory available in the system (as GPU's memory can be used effectively), a typical bottleneck for Voronoi-cell algorithms, and we have also been able to increase the performance of the algorithm on such a platform, by successfully using the GPU as a co-processor, 2) this attack can be successfully accelerated using conventional GPUs and 3) we can take advantage of multiple GPUs to attack lattice-based cryptosystems. Experimental results show a speedup up to 7.6x for 2 GPUs hosted by an Intel Xeon E5-2695 v2 CPU (12 cores x2 sockets) using only 1 core and gains in the order of 20% for 2 GPUs hosted by the same machine using all 22 CPU threads (2 are reserved for orchestrating the GPUs), compared to single-CPU execution using the entire 24 threads available.

Abstract
Quantum computing has the potential to provide solutions to many problems which are challenging or out of reach of classical computers. There are several problems in rendering which are amenable to being solved in quantum computers, but these have yet to be demonstrated in practice. This work takes a first step in applying quantum computing to one of the most fundamental operations in rendering: ray casting. This technique computes visibility between two points in a 3D model of the world which is described by a collection of geometric primitives. The algorithm returns, for a given ray, which primitive it intersects closest to its origin. Without a spatial acceleration structure, the classical complexity for this operation is O(N). In this paper, we propose an implementation of Grover's Algorithm (a quantum search algorithm) for ray casting. This provides a quadratic speed up allowing for visibility evaluation for unstructured primitives in O(root N). However, due to technological limitations associated with current quantum computers, in this work the geometrical setup is limited to rectangles and parallel rays (orthographic projection).