Scalable Neural Network Decoders for Higher Dimensional Quantum Codes

Machine learning has the potential to become an important tool in quantum error correction as it allows the decoder to adapt to the error distribution of a quantum chip. An additional motivation for using neural networks is the fact that they can be evaluated by dedicated hardware which is very fast and consumes little power. Machine learning has been previously applied to decode the surface code. However, these approaches are not scalable as the training has to be redone for every system size which becomes increasingly difficult. In this work the existence of local decoders for higher dimensional codes leads us to use a low-depth convolutional neural network to locally assign a likelihood of error on each qubit. For noiseless syndrome measurements, numerical simulations show that the decoder has a threshold of around $7.1\%$ when applied to the 4D toric code. When the syndrome measurements are noisy, the decoder performs better for larger code sizes when the error probability is low. We also give theoretical and numerical analysis to show how a convolutional neural network is different from the 1-nearest neighbor algorithm, which is a baseline machine learning method

Using Output Codes for Two-class Classification Problems

Error-correcting output codes (ECOCs) have been widely used in many applications for multi-class classification problems. The problem is that ECOCs cannot be ap- plied directly on two-class datasets. The goal of this thesis is to design and evaluate an approach to solve this problem, and then investigate whether the approach can yield better classification models. To be able to use ECOCs, we turn two-class datasets into multi-class datasets first, by using clustering. With the resulting multi-class datasets in hand, we evalu- ate three different encoding methods for ECOCs: exhaustive coding, random coding and a “pre-defined” code that is found using random search. The exhaustive coding method has the highest error-correcting abilities. However, this method is limited due to the exponential growth of bit columns in the codeword matrix precluding it from being used for problems with large numbers of classes. Random coding can be used to cover situations with large numbers of classes in the data. To improve on completely random matrices, “pre-defined” codeword matrices can be generated by using random search that optimizes row separation yielding better error correction than a purely random matrix. To speed up the process of finding good matrices, GPU parallel programming is investigated in this thesis. From the empirical results, we can say that the new algorithm, which applies multi-class ECOCs on two-class data using clustering, does improve the performance for some base learners, when compared to applying them directly to the original two- class datasets

AUTOSIM: An automated repetitive software testing tool

AUTOSIM is a software tool which automates the repetitive run testing of software. This tool executes programming tasks previously performed by a programmer with one year of programming experience. Use of the AUTOSIM tool requires a knowledge base containing information about known faults, code fixes, and the fault diagnosis-correction process. AUTOSIM can be considered as an expert system which replaces a low level of programming expertise. Reference information about the design and implementation of the AUTOSIM software test tool provides flowcharts to assist in maintaining the software code and a description of how to use the tool