Abstract
This article proposes a Markov Chain Monte Carlo (MCMC) rendering algorithm based on a family of guided transition kernels. The kernels exploit properties of ensembles of light transport paths, which are distributed according to the lighting in the scene, and utilize this information to make informed decisions for guiding local path sampling. Critically, our approach does not require caching distributions in world space, saving time and memory, yet it is able to make guided sampling decisions based on whole paths. We show how this can be implemented efficiently by organizing the paths in each ensemble and designing transition kernels for MCMC rendering based on a carefully chosen subset of paths from the ensemble. This algorithm is easy to parallelize and leads to improvements in variance when rendering a variety of scenes.

Abstract
Rendering on conventional computers is capable of generating realistic imagery, but the computational complexity of these light transport algorithms is a limiting factor of image synthesis. Quantum computers have the potential to significantly improve rendering performance through reducing the underlying complexity of the algorithms behind light transport. This article investigates hybrid quantum-classical algorithms for ray tracing, a core component of most rendering techniques. Through a practical implementation of quantum ray tracing in a 3D environment, we show quantum approaches provide a quadratic improvement in query complexity compared to the equivalent classical approach. Based on domain specific knowledge, we then propose algorithms to significantly reduce the computation required for quantum ray tracing through exploiting image space coherence and a principled termination criteria for quantum searching. We show results obtained using a simulator for both Whitted style ray tracing, and for accelerating ray tracing operations when performing classical Monte Carlo integration for area lights and indirect illumination.

Abstract
CFD simulations are a fundamental engineering application, implying huge workloads, often with dynamic behaviour due to runtime mesh refinement. Parallel processing over heterogeneous distributed memory clusters is often used to process such workloads. The execution of dynamic workloads over a set of heterogeneous resources leads to load imbalances that severely impacts execution time, when static uniform load distribution is used. This paper proposes applying dynamic, heterogeneity aware, load balancing techniques within CFD simulations. nSharma, a software package that fully integrates with OpenFOAM, is presented and assessed. Performance gains are demonstrated, achieved by reducing busy times standard deviation among resources, i.e., heterogeneous computing resources are kept busy with useful work due to an effective workload distribution. To best of authors’ knowledge, nSharma is the first implementation and integration of heterogeneity aware load balancing in OpenFOAM and will be made publicly available in order to foster its adoption by the large community of OpenFOAM users.

Abstract
Adaptive protocols enable the construction of more efficient state preparation circuits in variational quantum algorithms (VQAs) by utilizing data obtained from the quantum processor during the execution of the algorithm. This idea originated with Adaptive Derivative-Assembled Problem-Tailored variational quantum eigensolver (ADAPT-VQE), an algorithm that iteratively grows the state preparation circuit operator by operator, with each new operator accompanied by a new variational parameter, and where all parameters acquired thus far are optimized in each iteration. In ADAPT-VQE and other adaptive VQAs that followed it, it has been shown that initializing parameters to their optimal values from the previous iteration speeds up convergence and avoids shallow local traps in the parameter landscape. However, no other data from the optimization performed at one iteration is carried over to the next. In this work, we propose an improved quasi-Newton optimization protocol specifically tailored to adaptive VQAs. The distinctive feature in our proposal is that approximate second derivatives of the cost function are recycled across iterations in addition to optimal parameter values. We implement a quasi-Newton optimizer where an approximation to the inverse Hessian matrix is continuously built and grown across the iterations of an adaptive VQA. The resulting algorithm has the flavor of a continuous optimization where the dimension of the search space is augmented when the gradient norm falls below a given threshold. We show that this inter-optimization exchange of second-order information leads the approximate Hessian in the state of the optimizer to be consistently closer to the exact Hessian. As a result, our method achieves a superlinear convergence rate even in situations where the typical implementation of a quasi-Newton optimizer converges only linearly. Our protocol decreases the measurement costs in implementing adaptive VQAs on quantum hardware as well as the runtime of their classical simulation.

Abstract

Abstract
Reinforcement learning (RL) consists of designing agents that make intelligent decisions without human supervision. When used alongside function approximators such as Neural Networks (NNs), RL is capable of solving extremely complex problems. Deep Q-Learning, a RL algorithm that uses Deep NNs, has been shown to achieve super-human performance in game-related tasks. Nonetheless, it is also possible to use Variational Quantum Circuits (VQCs) as function approximators in RL algorithms. This work empirically studies the performance and trainability of such VQC-based Deep Q-Learning models in classic control benchmark environments. More specifically, we research how data re-uploading affects both these metrics. We show that the magnitude and the variance of the model's gradients remain substantial throughout training even as the number of qubits increases. In fact, both increase considerably in the training's early stages, when the agent needs to learn the most. They decrease later in the training, when the agent should have done most of the learning and started converging to a policy. Thus, even if the probability of being initialized in a Barren Plateau increases exponentially with system size for Hardware-Efficient ansatzes, these results indicate that the VQC-based Deep Q-Learning models may still be able to find large gradients throughout training, allowing for learning.