Quantum Computing for Fusion Energy Science Applications

This is a review of recent research exploring and extending present-day quantum computing capabilities for fusion energy science applications. We begin with a brief tutorial on both ideal and open quantum dynamics, universal quantum computation, and quantum algorithms. Then, we explore the topic of using quantum computers to simulate both linear and nonlinear dynamics in greater detail. Because quantum computers can only efficiently perform linear operations on the quantum state, it is challenging to perform nonlinear operations that are generically required to describe the nonlinear differential equations of interest. In this work, we extend previous results on embedding nonlinear systems within linear systems by explicitly deriving the connection between the Koopman evolution operator, the Perron-Frobenius evolution operator, and the Koopman-von Neumann evolution (KvN) operator. We also explicitly derive the connection between the Koopman and Carleman approaches to embedding. Extension of the KvN framework to the complex-analytic setting relevant to Carleman embedding, and the proof that different choices of complex analytic reproducing kernel Hilbert spaces depend on the choice of Hilbert space metric are covered in the appendices. Finally, we conclude with a review of recent quantum hardware implementations of algorithms on present-day quantum hardware platforms that may one day be accelerated through Hamiltonian simulation. We discuss the simulation of toy models of wave-particle interactions through the simulation of quantum maps and of wave-wave interactions important in nonlinear plasma dynamics.Comment: 42 pages; 12 figures; invited paper at the 2021-2022 International Sherwood Fusion Theory Conferenc

Quantum walks: a comprehensive review

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing Journa

Quantum information processing in continuous time

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2004.Includes bibliographical references (p. 127-138) and index.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Quantum mechanical computers can solve certain problems asymptotically faster than any classical computing device. Several fast quantum algorithms are known, but the nature of quantum speedup is not well understood, and inventing new quantum algorithms seems to be difficult. In this thesis, we explore two approaches to designing quantum algorithms based on continuous-time Hamiltonian dynamics. In quantum computation by adiabatic evolution, the computer is prepared in the known ground state of a simple Hamiltonian, which is slowly modified so that its ground state encodes the solution to a problem. We argue that this approach should be inherently robust against low-temperature thermal noise and certain control errors, and we support this claim using simulations. We then show that any adiabatic algorithm can be implemented in a different way, using only a sequence of measurements of the Hamiltonian. We illustrate how this approach can achieve quadratic speedup for the unstructured search problem. We also demonstrate two examples of quantum speedup by quantum walk, a quantum mechanical analog of random walk. First, we consider the problem of searching a region of space for a marked item. Whereas a classical algorithm for this problem requires time proportional to the number of items regardless of the geometry, we show that a simple quantum walk algorithm can find the marked item quadratically faster for a lattice of dimension greater than four, and almost quadratically faster for a four-dimensional lattice. We also show that by endowing the walk with spin degrees of freedom, the critical dimension can be lowered to two. Second, we construct an oracular problem that a quantum walk can solve exponentially faster than any classical algorithm.(cont.) This constitutes the only known example of exponential quantum speedup not based on the quantum Fourier transform. Finally, we consider bipartite Hamiltonians as a model of quantum channels and study their ability to process information given perfect local control. We show that any interaction can simulate any other at a nonzero rate, and that tensor product Hamiltonians can simulate each other reversibly. We also calculate the optimal asymptotic rate at which certain Hamiltonians can generate entanglement.by Andrew MacGregor Childs.Ph.D

Quantum Cryptography Beyond Quantum Key Distribution

Quantum cryptography is the art and science of exploiting quantum mechanical effects in order to perform cryptographic tasks. While the most well-known example of this discipline is quantum key distribution (QKD), there exist many other applications such as quantum money, randomness generation, secure two- and multi-party computation and delegated quantum computation. Quantum cryptography also studies the limitations and challenges resulting from quantum adversaries---including the impossibility of quantum bit commitment, the difficulty of quantum rewinding and the definition of quantum security models for classical primitives. In this review article, aimed primarily at cryptographers unfamiliar with the quantum world, we survey the area of theoretical quantum cryptography, with an emphasis on the constructions and limitations beyond the realm of QKD.Comment: 45 pages, over 245 reference

Algorithmes incrémentaux pour la théorie de la fonctionnelle de la densité

The ability to model molecular systems on a computer has become a crucial tool for chemists. Indeed molecular simulations have helped to understand and predict properties of nanoscopic world, and during the last decades have had large impact on domains like biology, electronic or materials development. Particle simulation is a classical method of molecular dynamic. In particle simulation, molecules are split into atoms, their inter-atomic interactions are computed, and their time trajectories are derived step by step. Unfortunately, inter-atomic interactions computation costs prevent large systems to be modeled in a reasonable time. In this context, our research team looks for new accurate and efficient molecular simulation models. One of our team's focus is the search and elimination of useless calculus in dynamical simulations. Hence has been proposed a new adaptively restrained dynamical model in which the slowest particles movement is frozen, computational time is saved if the interaction calculus method do not compute again interactions between static atoms. The team also developed several interaction models that benefit from a restrained dynamical model, they often updates interactions incrementally using the previous time step results and the knowledge of which particle have moved.In the wake of our team's work, we propose in this thesis an incremental First-principles interaction models. Precisely, we have developed an incremental Orbital-Free Density Functional Theory method that benefits from an adaptively restrained dynamical model. The new OF-DFT model keeps computation in Real-Space, so can adaptively focus computations where they are necessary. The method is first proof-tested, then we show its ability to speed up computations when a majority of particle are static and with a restrained particle dynamic model. This work is a first step toward a combination of incremental First-principle interaction models and adaptively restrained particle dynamic models.In the wake of our team's work, we propose in this thesis an incremental First-principles interaction models. Precisely, we have developed an incremental Orbital-Free Density Functional Theory method that benefits from an adaptively restrained dynamical model. The new OF-DFT model keeps computation in Real-Space, so can adaptively focus computations where they are necessary. The method is first proof-tested, then we show its ability to speed up computations when a majority of particle are static and with a restrained particle dynamic model. This work is a first step toward a combination of incremental First-principle interaction models and adaptively restrained particle dynamic models.L'informatique est devenue un outil incontournable de la chimie. En effet la capacité de simuler des molécules sur ordinateur a aidé à la compréhension du monde nanoscopic et à la prédiction de ses propriétés. La simulation moléculaire a eu ces dernières décennies un impact scientifique énorme en biologie, en électronique, en science des matériaux ... La simulation de particules est une des méthodes classiques de dynamique moléculaire, les molécules y sont divisées en atomes, leurs interactions relatives calculées et leurs trajectoires déduites pas à pas. Malheureusement un calcul précis des interactions entre atomes demande énormément d'opérations et donc de temps, ce qui limite la portée de la simulation moléculaire à des systèmes de taille raisonnable. C'est dans ce contexte que notre équipe recherche de nouveaux modèles de simulation moléculaire rapide et précis. Un des angles de recherche est l'élimination des calculs inutiles des simulations. L'équipe a ainsi proposé un modèle de dynamique moléculaire dite restreinte de manière adaptative dans lequel le mouvement des particules les plus lentes est bloqué. Si la simulation ne recalcule pas les interactions inchangées entre atomes bloqués, le calcul des interactions est plus rapide. L'équipe a aussi développé plusieurs modèles d'interactions plus efficaces pour des modèles de dynamique restreinte de particules, ils mettent à jour les interactions de façon incrémentale en utilisant les résultats du pas de temps précédent et la liste des particules mobiles. Dans le sillage des travaux de notre équipe de recherche, nous proposons dans cette thèse une méthode incrémentale pour calculer des interactions interatomique basées sur les modèles de Théorie de la Fonctionnelle de la Densité Sans Orbitale. La nouvelle méthode garde les calculs dans l'espace réel et peut ainsi concentrer les calculs où cela est nécessaire. Dans ce manuscrit nous vérifions cette méthode, puis nous évaluons les gains de vitesse lorsqu'une majorité de particule est bloquée, avec un modèle de dynamique restreinte. Ces travaux sont un pas vers la l'intégration de modèles d'interactions Premier-principes pour des modèles dynamiques restreint de manière adaptative

Fast algorithm for real-time rings reconstruction

The GAP project is dedicated to study the application of GPU in several contexts in which real-time response is important to take decisions. The definition of real-time depends on the application under study, ranging from answer time of μs up to several hours in case of very computing intensive task. During this conference we presented our work in low level triggers [1] [2] and high level triggers [3] in high energy physics experiments, and specific application for nuclear magnetic resonance (NMR) [4] [5] and cone-beam CT [6]. Apart from the study of dedicated solution to decrease the latency due to data transport and preparation, the computing algorithms play an essential role in any GPU application. In this contribution, we show an original algorithm developed for triggers application, to accelerate the ring reconstruction in RICH detector when it is not possible to have seeds for reconstruction from external trackers