Multistart Methods for Quantum Approximate Optimization

Hybrid quantum-classical algorithms such as the quantum approximate optimization algorithm (QAOA) are considered one of the most promising approaches for leveraging near-term quantum computers for practical applications. Such algorithms are often implemented in a variational form, combining classical optimization methods with a quantum machine to find parameters to maximize performance. The quality of the QAOA solution depends heavily on quality of the parameters produced by the classical optimizer. Moreover, the presence of multiple local optima in the space of parameters makes it harder for the classical optimizer. In this paper we study the use of a multistart optimization approach within a QAOA framework to improve the performance of quantum machines on important graph clustering problems. We also demonstrate that reusing the optimal parameters from similar problems can improve the performance of classical optimization methods, expanding on similar results for MAXCUT

An algorithm for maximum likelihood estimation using an efficient method for approximating sensitivities

An algorithm for maximum likelihood (ML) estimation is developed primarily for multivariable dynamic systems. The algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). The method determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort compared with integrating the analytically determined sensitivity equations or using a finite-difference method. Different surface-fitting methods are discussed and demonstrated. Aircraft estimation problems are solved by using both simulated and real-flight data to compare MNRES with commonly used methods; in these solutions MNRES is found to be equally accurate and substantially faster. MNRES eliminates the need to derive sensitivity equations, thus producing a more generally applicable algorithm

Training Single Walled Carbon Nanotube based Materials to perform computation

This thesis illustrates the use of Single Walled Carbon Nanotube based materials for the solution of various computational problems by using the process of computer controlled evolution. The study aims to explore and identify three dimensions of a form of unconventional computing called, `Evolution-in-materio'. First, it focuses on identifying suitable materials for computation. Second, it explores suitable methods, i.e. optimisation and evolutionary algorithms to train these materials to perform computation. And third, it aims to identify suitable computational problems to test with these materials. Different carbon based materials, mainly single walled carbon nano-tubes with their varying concentrations in polymers have been studied to be trained for different computational problems using the principal of `evolution-in-materio'. The conductive property of the materials is used to train these materials to perform some meaningful computation. The training process is formulated as an optimisation problem with hardware in loop. It involves the application of an external stimuli (voltages) on the material which brings changes in its electrical properties. In order to train the material for a specific computational problem, a large number of configuration signals need to be tested to find the one that transforms the incident signal in such a way that a meaningful computation can be extracted from the material. An evolutionary algorithm is used to identify this configuration data and using a hardware platform, this data is transformed into incident signals. Depending on the computational problem, the specific voltages signals when applied at specific points on to the material, as identified by an evolutionary algorithm, can make the material behave as a Logic gate, a tone discriminator or a data classifier. The problem is implemented on two types of hardware platforms, one a more simple implementation using mbed ( a micro- controller) and other is a purpose-built platform for `Evolution-in-materio" called Mecobo. The results of this study showed that the single walled carbon nanotube composites can be trained to perform simple computational tasks (such as tone discriminator, AND, OR logic gates and a Half adder circuit), as well as complex computational problems such as Full Adder circuit and various binary and multiple class machine learning problems. The study has also identified the suitability of using evolutionary algorithms such as Particle Swarm Optimisation algorithm (PSO) and Differential evolution for finding solutions of complex computational problems such as complex logic gates and various machine learning classification problems. The implementation of classification problem with the carbon nanotube based materials also identified the role of a classifier. It has been found that K-nearest neighbour method and its variant kNN ball tree algorithm are more suitable to train carbon nanotube based materials for different classification problems. The study of varying concentrations of single walled carbon nanotubes in fixed polymer ratio for the solution of different computational problems provided an indication of the link between single walled carbon nanotubes concentration and ability to solve computational problem. The materials used in this study showed stability in the results for all the considered computational problems. These material systems can compliment the current electronic technology and can be used to create a new type of low energy and low cost electronic devices. This offers a promising new direction for evolutionary computation