Quantum Generative Adversarial Networks for Learning and Loading Random Distributions

Quantum algorithms have the potential to outperform their classical counterparts in a variety of tasks. The realization of the advantage often requires the ability to load classical data efficiently into quantum states. However, the best known methods require $\mathcal{O}\left(2^n\right)$ gates to load an exact representation of a generic data structure into an $n$-qubit state. This scaling can easily predominate the complexity of a quantum algorithm and, thereby, impair potential quantum advantage. Our work presents a hybrid quantum-classical algorithm for efficient, approximate quantum state loading. More precisely, we use quantum Generative Adversarial Networks (qGANs) to facilitate efficient learning and loading of generic probability distributions -- implicitly given by data samples -- into quantum states. Through the interplay of a quantum channel, such as a variational quantum circuit, and a classical neural network, the qGAN can learn a representation of the probability distribution underlying the data samples and load it into a quantum state. The loading requires $\mathcal{O}\left(poly\left(n\right)\right)$ gates and can, thus, enable the use of potentially advantageous quantum algorithms, such as Quantum Amplitude Estimation. We implement the qGAN distribution learning and loading method with Qiskit and test it using a quantum simulation as well as actual quantum processors provided by the IBM Q Experience. Furthermore, we employ quantum simulation to demonstrate the use of the trained quantum channel in a quantum finance application.Comment: 14 pages, 13 figure

Option Pricing using Quantum Computers

We present a methodology to price options and portfolios of options on a gate-based quantum computer using amplitude estimation, an algorithm which provides a quadratic speedup compared to classical Monte Carlo methods. The options that we cover include vanilla options, multi-asset options and path-dependent options such as barrier options. We put an emphasis on the implementation of the quantum circuits required to build the input states and operators needed by amplitude estimation to price the different option types. Additionally, we show simulation results to highlight how the circuits that we implement price the different option contracts. Finally, we examine the performance of option pricing circuits on quantum hardware using the IBM Q Tokyo quantum device. We employ a simple, yet effective, error mitigation scheme that allows us to significantly reduce the errors arising from noisy two-qubit gates.Comment: Fixed a typo. This article has been accepted in Quantu

Distribution of Random Streams for Simulation Practitioners

International audienceThere is an increasing interest in the distribution of parallel random number streamsin the high-performance computing community particularly, with the manycore shift. Even ifwe have at our disposal statistically sound random number generators according to the latestand thorough testing libraries, their parallelization can still be a delicate problem. Indeed, aset of recent publications shows it still has to be mastered by the scientific community. Withthe arrival of multi-core and manycore processor architectures on the scientist desktop, modelerswho are non-specialists in parallelizing stochastic simulations need help and advice in distributingrigorously their experimental plans and replications according to the state of the art in pseudo-random numbers parallelization techniques. In this paper, we discuss the different partitioningtechniques currently in use to provide independent streams with their corresponding software. Inaddition to the classical approaches in use to parallelize stochastic simulations on regular processors,this paper also presents recent advances in pseudo-random number generation for general-purposegraphical processing units. The state of the art given in this paper is written for simulationpractitioners

iQIST : An open source continuous-time quantum Monte Carlo impurity solver toolkit

Quantum impurity solvers have a broad range of applications in theoretical studies of strongly correlated electron systems. Especially, they play a key role in dynamical mean-field theory calculations of correlated lattice models and realistic materials. Therefore, the development and implementation of efficient quantum impurity solvers is an important task. In this paper, we present an open source interacting quantum impurity solver toolkit (dubbed iQIST). This package contains several highly optimized quantum impurity solvers which are based on the hybridization expansion continuous-time quantum Monte Carlo algorithm, as well as some essential pre- and post-processing tools. We first introduce the basic principle of continuous-time quantum Monte Carlo algorithm and then discuss the implementation details and optimization strategies. The software framework, major features, and installation procedure for iQIST are also explained. Finally, several simple tutorials are presented in order to demonstrate the usage and power of iQIST

A Brief Review on Mathematical Tools Applicable to Quantum Computing for Modelling and Optimization Problems in Engineering

Since its emergence, quantum computing has enabled a wide spectrum of new possibilities and advantages, including its efficiency in accelerating computational processes exponentially. This has directed much research towards completely novel ways of solving a wide variety of engineering problems, especially through describing quantum versions of many mathematical tools such as Fourier and Laplace transforms, differential equations, systems of linear equations, and optimization techniques, among others. Exploration and development in this direction will revolutionize the world of engineering. In this manuscript, we review the state of the art of these emerging techniques from the perspective of quantum computer development and performance optimization, with a focus on the most common mathematical tools that support engineering applications. This review focuses on the application of these mathematical tools to quantum computer development and performance improvement/optimization. It also identifies the challenges and limitations related to the exploitation of quantum computing and outlines the main opportunities for future contributions. This review aims at offering a valuable reference for researchers in fields of engineering that are likely to turn to quantum computing for solutions. Doi: 10.28991/ESJ-2023-07-01-020 Full Text: PD

Probabilistic structural mechanics research for parallel processing computers

Aerospace structures and spacecraft are a complex assemblage of structural components that are subjected to a variety of complex, cyclic, and transient loading conditions. Significant modeling uncertainties are present in these structures, in addition to the inherent randomness of material properties and loads. To properly account for these uncertainties in evaluating and assessing the reliability of these components and structures, probabilistic structural mechanics (PSM) procedures must be used. Much research has focused on basic theory development and the development of approximate analytic solution methods in random vibrations and structural reliability. Practical application of PSM methods was hampered by their computationally intense nature. Solution of PSM problems requires repeated analyses of structures that are often large, and exhibit nonlinear and/or dynamic response behavior. These methods are all inherently parallel and ideally suited to implementation on parallel processing computers. New hardware architectures and innovative control software and solution methodologies are needed to make solution of large scale PSM problems practical

Photonic integrated circuit design in a foundry+fabless ecosystem

A foundry-based photonic ecosystem is expected to become necessary with increasing demand and adoption of photonics for commercial products. To make foundry-enabled photonics a real success, the photonic circuit design flow should adopt known concepts from analog and mixed signal electronics. Based on the similarities and differences between the existing photonic and the standardized electronics design flow, we project the needs and evolution of the photonic design flow, such as schematic driven design, accurate behavioral models, and yield prediction in the presence of fabrication variability

Optimization in Quasi-Monte Carlo Methods for Derivative Valuation

Computational complexity in financial theory and practice has seen an immense rise recently. Monte Carlo simulation has proved to be a robust and adaptable approach, well suited for supplying numerical solutions to a large class of complex problems. Although Monte Carlo simulation has been widely applied in the pricing of financial derivatives, it has been argued that the need to sample the relevant region as uniformly as possible is very important. This led to the development of quasi-Monte Carlo methods that use deterministic points to minimize the integration error. A major disadvantage of low-discrepancy number generators is that they tend to lose their ability of homogeneous coverage as the dimensionality increases. This thesis develops a novel approach to quasi-Monte Carlo methods to evaluate complex financial derivatives more accurately by optimizing the sample coordinates in such a way so as to minimize the discrepancies that appear when using lowdiscrepancy sequences. The main focus is to develop new methods to, optimize the sample coordinate vector, and to test their performance against existing quasi-Monte Carlo methods in pricing complicated multidimensional derivatives. Three new methods are developed, the Gear, the Simulated Annealing and the Stochastic Tunneling methods. These methods are used to evaluate complex multi-asset financial derivatives (geometric average and rainbow options) for dimensions up to 2000. It is shown that the two stochastic methods, Simulated Annealing and Stochastic Tunneling, perform better than existing quasi-Monte Carlo methods, Faure' and Sobol'. This difference in performance is more evident in higher dimensions, particularly when a low number of points is used in the Monte Carlo simulations. Overall, the Stochastic Tunneling method yields the smallest percentage root mean square relative error and requires less computational time to converge to a global solution, proving to be the most promising method in pricing complex derivativesImperial Users onl