Gradient-free quantum optimization on NISQ devices

Variational Quantum Eigensolvers (VQEs) have recently attracted considerable attention. Yet, in practice, they still suffer from the efforts for estimating cost function gradients for large parameter sets or resource-demanding reinforcement strategies. Here, we therefore consider recent advances in weight-agnostic learning and propose a strategy that addresses the trade-off between finding appropriate circuit architectures and parameter tuning. We investigate the use of NEAT-inspired algorithms which evaluate circuits via genetic competition and thus circumvent issues due to exceeding numbers of parameters. Our methods are tested both via simulation and on real quantum hardware and are used to solve the transverse Ising Hamiltonian and the Sherrington-Kirkpatrick spin model.Comment: 13 pages, 6 figures, comments welcome

Quantum Genetic Algorithms for Computer Scientists

Genetic algorithms (GAs) are a class of evolutionary algorithms inspired by Darwinian natural selection. They are popular heuristic optimisation methods based on simulated genetic mechanisms, i.e., mutation, crossover, etc. and population dynamical processes such as reproduction, selection, etc. Over the last decade, the possibility to emulate a quantum computer (a computer using quantum-mechanical phenomena to perform operations on data) has led to a new class of GAs known as “Quantum Genetic Algorithms” (QGAs). In this review, we present a discussion, future potential, pros and cons of this new class of GAs. The review will be oriented towards computer scientists interested in QGAs “avoiding” the possible difficulties of quantum-mechanical phenomena

Solving Travelling Salesman Problem by Using Optimization Algorithms

This paper presents the performances of different types of optimization techniques used in artificial intelligence (AI), these are Ant Colony Optimization (ACO), Improved Particle Swarm Optimization with a new operator (IPSO), Shuffled Frog Leaping Algorithms (SFLA) and modified shuffled frog leaping algorithm by using a crossover and mutation operators. They were used to solve the traveling salesman problem (TSP) which is one of the popular and classical route planning problems of research and it is considered  as one of the widely known of combinatorial optimization. Combinatorial optimization problems are usually simple to state but very difficult to solve. ACO, PSO, and SFLA are intelligent meta-heuristic optimization algorithms with strong ability to analyze the optimization problems and find the optimal solution. They were tested on benchmark problems from TSPLIB and the test results were compared with each other.Keywords: Ant colony optimization, shuffled frog leaping algorithms, travelling salesman problem, improved particle swarm optimizatio

Symbolic Regression in Materials Science: Discovering Interatomic Potentials from Data

Particle-based modeling of materials at atomic scale plays an important role in the development of new materials and understanding of their properties. The accuracy of particle simulations is determined by interatomic potentials, which allow to calculate the potential energy of an atomic system as a function of atomic coordinates and potentially other properties. First-principles-based ab initio potentials can reach arbitrary levels of accuracy, however their aplicability is limited by their high computational cost. Machine learning (ML) has recently emerged as an effective way to offset the high computational costs of ab initio atomic potentials by replacing expensive models with highly efficient surrogates trained on electronic structure data. Among a plethora of current methods, symbolic regression (SR) is gaining traction as a powerful "white-box" approach for discovering functional forms of interatomic potentials. This contribution discusses the role of symbolic regression in Materials Science (MS) and offers a comprehensive overview of current methodological challenges and state-of-the-art results. A genetic programming-based approach for modeling atomic potentials from raw data (consisting of snapshots of atomic positions and associated potential energy) is presented and empirically validated on ab initio electronic structure data.Comment: Submitted to the GPTP XIX Workshop, June 2-4 2022, University of Michigan, Ann Arbor, Michiga

Adaptive Double Chain Quantum Genetic Algorithm for Constrained Optimization Problems

Optimization problems are often highly constrained and evolutionary algorithms (EAs) are effective methods to tackle this kind of problems. To further improve search efficiency and convergence rate of EAs, this paper presents an adaptive double chain quantum genetic algorithm (ADCQGA) for solving constrained optimization problems. ADCQGA makes use of double-individuals to represent solutions that are classified as feasible and infeasible solutions. Fitness (or evaluation) functions are defined for both types of solutions. Based on the fitness function, three types of step evolution (SE) are defined and utilized for judging evolutionary individuals. An adaptive rotation is proposed and used to facilitate updating individuals in different solutions. To further improve the search capability and convergence rate, ADCQGA utilizes an adaptive evolution process (AEP), adaptive mutation and replacement techniques. ADCQGA was first tested on a widely used benchmark function to illustrate the relationship between initial parameter values and the convergence rate/search capability. Then the proposed ADCQGA is successfully applied to solve other twelve benchmark functions and five well-known constrained engineering design problems. Multi-aircraft cooperative target allocation problem is a typical constrained optimization problem and requires efficient methods to tackle. Finally, ADCQGA is successfully applied to solving the target allocation problem

Quantum annealing for vehicle routing and scheduling problems

Metaheuristic approaches to solving combinatorial optimization problems have many attractions. They sidestep the issue of combinatorial explosion; they return good results; they are often conceptually simple and straight forward to implement. There are also shortcomings. Optimal solutions are not guaranteed; choosing the metaheuristic which best fits a problem is a matter of experimentation; and conceptual differences between metaheuristics make absolute comparisons of performance difficult. There is also the difficulty of configuration of the algorithm - the process of identifying precise values for the parameters which control the optimization process. Quantum annealing is a metaheuristic which is the quantum counterpart of the well known classical Simulated Annealing algorithm for combinatorial optimization problems. This research investigates the application of quantum annealing to the Vehicle Routing Problem, a difficult problem of practical significance within industries such as logistics and workforce scheduling. The work devises spin encoding schemes for routing and scheduling problem domains, enabling an effective quantum annealing algorithm which locates new solutions to widely used benchmarks. The performance of the metaheuristic is further improved by the development of an enhanced tuning approach using fitness clouds as behaviour models. The algorithm is shown to be further enhanced by taking advantage of multiprocessor environments, using threading techniques to parallelize the optimization workload. The work also shows quantum annealing applied successfully in an industrial setting to generate solutions to complex scheduling problems, results which created extra savings over an incumbent optimization technique. Components of the intellectual property rendered in this latter effort went on to secure a patent-protected status

Variational quantum architectures. Applications for noisy intermediate-scale quantum computers

[eng] Quantum algorithms showing promising speedups with respect to their classical counterparts already exist. However, noise limits the quantum circuit depth, making the practical implementation of many such quantum algorithms impossible nowadays. In this sense, variational quantum algorithms offer a new approach, reducing the requisites of quantum computational resources at the expense of classical optimization. Disciplines in which variational quantum algorithms may have practical applications include simulation of quantum systems, solving large systems of linear equations, combinatorial optimization, data compression, quantum state diagonalization, among others. This thesis studies different variational quantum algorithm applications. In Chapter 1, we introduce the main building blocks of variational quantum algorithms. In Chapter 2, we benchmark the seminal variational quantum eigensolver algorithm for condensed matter systems. In Chapter 3, we explore how the task of compressing quantum information is affected by data encoding in variational quantum circuits. In Chapter 4, we propose a novel variational quantum algorithm to compute the singular values of pure bipartite states. In Chapter 5, we develop a new variational quantum algorithm to solve linear systems of equations. Finally, in Chapter 6, we implement quantum generative adversarial networks for generative modeling tasks. The conclusions of this thesis are exposed in Chapter 7. Furthermore, supplementary material can be found in the appendices. Appendix A provides an introduction to Qibo, a framework for quantum simulation. Appendix B presents some results related to the Solovay-Kitaev theorem. Extra results from Chapter 5 and Chapter 6 can be found in Appendix C and Appendix D, respectively.[spa] Algoritmos cuánticos mostrando prometedoras ventajas respecto sus contrapartes clásicas ya existen. Sin embargo, el ruido limita la profundidad de los circuitos cuánticos, lo que hace imposible la aplicación práctica de muchos de estos algoritmos cuánticos en la actualidad. En este sentido, los algoritmos cuánticos variacionales ofrecen un nuevo enfoque, reduciendo los requisitos de recursos computacionales cuánticos a expensas de optimización clásica. Disciplinas en las que los algoritmos cuánticos variacionales pueden tener aplicaciones prácticas incluyen la simulación de sistemas cuánticos, la resolución de grandes sistemas de ecuaciones lineales, la optimización combinatoria, la compresión de datos y la diagonalización de estados cuánticos, entre otras. Esta tesis estudia diferentes aplicaciones de los algoritmos cuánticos variacionales. En el Capítulo 1, presentamos los principales bloques de construcción de los algoritmos cuánticos variacionales. En el Capítulo 2, evaluamos el algoritmo “variational quantum eigensolver” para sistemas de materia condensada. En el capítulo 3, exploramos cómo la tarea de comprimir la información cuántica se ve afectada por la codificación de datos en los circuitos cuánticos variacionales. En el Capítulo 4, proponemos un novedoso algoritmo cuántico variacional para calcular los valores singulares de los estados bipartitos puros. En el Capítulo 5, desarrollamos un nuevo algoritmo cuántico variacional para resolver sistemas lineales de ecuaciones. Finalmente, en el Capítulo 6, implementamos redes generativas adversarias cuánticas para tareas de modelado generativo. Las conclusiones de esta tesis se exponen en el Capítulo 7. Además, se puede encontrar material complementario en los apéndices. El Apéndice A ofrece una introducción a Qibo, un software para la simulación cuántica. El Apéndice B presenta algunos resultados relacionados con el teorema de Solovay-Kitaev. En el Apéndice C y en el Apéndice D se pueden encontrar resultados adicionales del Capítulo 5 y del Capítulo 6, respectivamente