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The widespread success of deep neural networks has revealed a surprise in classical machine learning: very complex models often generalize well while simultaneously overfitting training data. This phenomenon of benign overfitting has been studied for a variety of classical models with the goal of better understanding the mechanisms behind deep learning. Characterizing the phenomenon in the context of quantum machine learning might similarly improve our understanding of the relationship between overfitting, overparameterization, and generalization. In this work, we provide a characterization of benign overfitting in quantum models. To do this, we derive the behavior of a classical interpolating Fourier features models for regression on noisy signals, and show how a class of quantum models exhibits analogous features, thereby linking the structure of quantum circuits (such as data-encoding and state preparation operations) to overparameterization and overfitting in quantum models. We intuitively explain these features according to the ability of the quantum model to interpolate noisy data with locally "spiky" behavior and provide a concrete demonstration example of benign overfitting., 41 pages, 6 figures

With near-term quantum devices available and the race for fault-tolerant quantum computers in full swing, researchers became interested in the question of what happens if we replace a supervised machine learning model with a quantum circuit. While such "quantum models" are sometimes called "quantum neural networks", it has been repeatedly noted that their mathematical structure is actually much more closely related to kernel methods: they analyse data in high-dimensional Hilbert spaces to which we only have access through inner products revealed by measurements. This technical manuscript summarises and extends the idea of systematically rephrasing supervised quantum models as a kernel method. With this, a lot of near-term and fault-tolerant quantum models can be replaced by a general support vector machine whose kernel computes distances between data-encoding quantum states. Kernel-based training is then guaranteed to find better or equally good quantum models than variational circuit training. Overall, the kernel perspective of quantum machine learning tells us that the way that data is encoded into quantum states is the main ingredient that can potentially set quantum models apart from classical machine learning models., 26 pages, 9 figures - Version 2 emphasises focus on supervised learning, adds more references to existing literature, deletes section on state discrimination due to a technical error, and updates the comparison between kernel-based and variational training

Quantum classifiers are trainable quantum circuits used as machine learning models. The first part of the circuit implements a quantum feature map that encodes classical inputs into quantum states, embedding the data in a high-dimensional Hilbert space; the second part of the circuit executes a quantum measurement interpreted as the output of the model. Usually, the measurement is trained to distinguish quantum-embedded data. We propose to instead train the first part of the circuit -- the embedding -- with the objective of maximally separating data classes in Hilbert space, a strategy we call quantum metric learning. As a result, the measurement minimizing a linear classification loss is already known and depends on the metric used: for embeddings separating data using the l1 or trace distance, this is the Helstrom measurement, while for the l2 or Hilbert-Schmidt distance, it is a simple overlap measurement. This approach provides a powerful analytic framework for quantum machine learning and eliminates a major component in current models, freeing up more precious resources to best leverage the capabilities of near-term quantum information processors., 11 pages, 6 figures; tutorial available at https://pennylane.ai/qml/app/tutorial_embeddings_metric_learning.html [Version 2 contains minor update]

PennyLane is a Python 3 software framework for differentiable programming of quantum computers. The library provides a unified architecture for near-term quantum computing devices, supporting both qubit and continuous-variable paradigms. PennyLane's core feature is the ability to compute gradients of variational quantum circuits in a way that is compatible with classical techniques such as backpropagation. PennyLane thus extends the automatic differentiation algorithms common in optimization and machine learning to include quantum and hybrid computations. A plugin system makes the framework compatible with any gate-based quantum simulator or hardware. We provide plugins for hardware providers including the Xanadu Cloud, Amazon Braket, and IBM Quantum, allowing PennyLane optimizations to be run on publicly accessible quantum devices. On the classical front, PennyLane interfaces with accelerated machine learning libraries such as TensorFlow, PyTorch, JAX, and Autograd. PennyLane can be used for the optimization of variational quantum eigensolvers, quantum approximate optimization, quantum machine learning models, and many other applications., Code available at https://github.com/XanaduAI/pennylane/ . Significant contributions to the code (new features, new plugins, etc.) will be recognized by the opportunity to be a co-author on this paper

Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into account curvature information and thereby often improves convergence. Here, we develop quantum versions of these iterative optimization algorithms and apply them to polynomial optimization with a unit norm constraint. In each step, multiple copies of the current candidate are used to improve the candidate using quantum phase estimation, an adapted quantum state exponentiation scheme, as well as quantum matrix multiplications and inversions. The required operations perform polylogarithmically in the dimension of the solution vector and exponentially in the number of iterations. Therefore, the quantum algorithm can be useful for high-dimensional problems where a small number of iterations is sufficient., New Journal of Physics, 21 (7), ISSN:1367-2630

It is well known that for certain tasks, quantum computing outperforms classical computing. A growing number of contributions try to use this advantage in order to improve or extend classical machine learning algorithms by methods of quantum information theory. This paper gives a brief introduction into quantum machine learning using the example of pattern classification. We introduce a quantum pattern classification algorithm that draws on Trugenberger's proposal for measuring the Hamming distance on a quantum computer (CA Trugenberger, Phys Rev Let 87, 2001) and discuss its advantages using handwritten digit recognition as from the MNIST database., 14 pages, 3 figures, presented at the 13th Pacific Rim International Conference on Artificial Intelligence

Post-confl ict elections have become an important tool of international confl ict resolution over the last decades. Theoretical studies usually point out that in warto- democracy transitions, military logics of territorial control are transformed into electoral logics of peaceful political contestation. Empirical reality, however, shows that the election process is often accompanied by various forms of violence. This paper analyses post-confl ict elections in war-to-democracy transitions by comparing support structures for confl ict parties as well as their coercive mobilisation strategies in times of violent confl ict and post-confl ict elections. It does so through a single case study of KwaZulu-Natal. This South African province faced a civil war-scale political confl ict in the 80s and early 90s in which the two fi ghting parties – the African National Congress (ANC) and the Inkatha Freedom Party (IFP) – used large-scale violence to establish and protect no-go areas of territorial control. This study finds that in the first decade after South Africa’s miraculous transition, these spatial structures of violence and control persisted at local levels. Violent forms of mobilisation and territorial control thus seem to be able to survive even a successful transition to democracy by many years. Measures to open up the political landscape, deescalate heated-up party antagonisms and overcome geopolitical borders of support structures seem to be crucial elements for post-conflict elections that introduce a pluralist democracy beyond the voting process.African Journal on Conflict Resolution,Volume 13, Number 1, 2013

Background: The emergence of a novel coronavirus, SARS-CoV-2, in December 2019, progressed to become a world pandemic in a few months and reached South Africa at the beginning of March. To investigate introduction and understand the early transmission dynamics of the virus, we formed the South African Network for Genomics Surveillance of COVID (SANGS_COVID), a network of ten government and university laboratories. Here, we present the first results of this effort, which is a molecular epidemiological study of the first twenty-one SARS-CoV-2 whole genomes sampled in the first port of entry, KwaZulu-Natal (KZN), during the first month of the epidemic. By combining this with calculations of the effective reproduction number (R), we aim to shed light on the patterns of infections that define the epidemic in South Africa., Methods: R was calculated using positive cases and deaths from reports provided by the four major provinces. Molecular epidemiology investigation involved sequencing viral genomes from patients in KZN using ARCTIC protocols and assembling whole genomes using meticulous alignment methods. Phylogenetic analysis was performed using maximum likelihood (ML) and Bayesian trees, lineage classification and molecular clock calculations., Findings: The epidemic in South Africa has been very heterogeneous. Two of the largest provinces, Gauteng, home of the two large metropolis Johannesburg and Pretoria, and KwaZulu-Natal, home of the third largest city in the country Durban, had a slow growth rate on the number of detected cases. Whereas, Western Cape, home of Cape Town, and the Eastern Cape provinces the epidemic is spreading fast. Our estimates of transmission potential for South Africa suggest a decreasing transmission potential towards R=1 since the first cases and deaths have been reported. However, between 06 May and 18 May 2020, we estimate that R was on average 1.39 (1.04 - 2.15, 95% CI). We also demonstrate that early transmission in KZN, and most probably in all main regions of SA, was associated with multiple international introductions and dominated by lineages B1 and B. The study also provides evidence for locally acquired infections in a hospital in Durban within the first month of the epidemic, which inflated early mortality in KZN., Interpretation: This first report of SANGS_COVID consortium focuses on understanding the epidemic heterogeneity and introduction of SARS-CoV-2 strains in the first month of the epidemic in South Africa. The early introduction of SARS-CoV-2 in KZN included caused a localized outbreak in a hospital, provides potential explanations for the initially high death rates in the province. The current high rate of transmission of COVID-19 in the Western Cape and Eastern Cape highlights the crucial need to strength local genomic surveillance in South Africa., Funding: UKZN Flagship Program entitled: Afrocentric Precision Approach to Control Health Epidemic, by a research Flagship grant from the South African Medical Research Council (MRC-RFA-UFSP-01-2013/UKZN HIVEPI, by the the Technology Innovation Agency and the the Department of Science and Innovation and by National Human Genome Re- search Institute of the National Institutes of Health under Award Number U24HG006941. H3ABioNet is an initiative of the Human Health and Heredity in Africa Consortium (H3Africa).