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In uncertainty quantification, variance-based global sensitivity analysis quantitatively determines the effect of each input random variable on the output by partitioning the total output variance into contributions from each input. However, computing conditional expectations can be prohibitively costly when working with expensive-to-evaluate models. Surrogate models can accelerate this, yet their accuracy depends on the quality and quantity of training data, which is expensive to generate (experimentally or computationally) for complex engineering systems. Thus, methods that work with limited data are desirable. We propose a diffeomorphic modulation under observable response preserving homotopy (D-MORPH) regression to train a polynomial dimensional decomposition surrogate of the output that minimizes the number of training data. The new method first computes a sparse Lasso solution and uses it to define the cost function. A subsequent D-MORPH regression minimizes the difference between the D-MORPH and Lasso solution. The resulting D-MORPH surrogate is more robust to input variations and more accurate with limited training data. We illustrate the accuracy and computational efficiency of the new surrogate for global sensitivity analysis using mathematical functions and an expensive-to-simulate model of char combustion. The new method is highly efficient, requiring only 15% of the training data compared to conventional regression.

Quantum algorithms for factorization, search, and simulation obtain computational advantage by performing control flow such as branching and iteration based on the value of quantum data in superposition. Complicating realization of these algorithms is the fact that in predominant quantum machine models, all control flow as embodied by the program counter is classical, and cannot exist in superposition. In this work, we identify that an alternative model to enable a program counter in superposition faces an obstacle -- no such machine can correctly support control flow constructs with non-injective semantics, including the conventional conditional jump. In fact, prior attempts to support this instruction cause programs to inappropriately collapse the superposition of data, meaning that quantum advantage is lost. We prove that in general, control flow abstractions with non-injective transition semantics, such as the conventional conditional jump or the $\lambda$-calculus, cannot operate over quantum data while preserving its superposition and the computational advantage of the quantum algorithm. This theorem explains why quantum programming languages to date have been unable to directly leverage the classical concept of programs as data to support the rich control flow abstractions known in classical programming. As an alternative, we present a new quantum machine model featuring variants of conditional jump with inherently injective semantics, which sidesteps our impossibility theorem and correctly enables both quantum effects on data and data-dependent control flow. We identify the necessary condition for programs for such a machine to preserve superposition of data, and show that expressible programs coincide with the unitary quantum circuits, with examples for phase estimation, quantum walk, and physical simulation.

The introduction of the European Union's (EU) set of comprehensive regulations relating to technology, the General Data Protection Regulation, grants EU citizens the right to explanations for automated decisions that have significant effects on their life. This poses a substantial challenge, as many of today's state-of-the-art algorithms are generally unexplainable black boxes. Simultaneously, we have seen an emergence of the fields of quantum computation and quantum AI. Due to the fickle nature of quantum information, the problem of explainability is amplified, as measuring a quantum system destroys the information. As a result, there is a need for post-hoc explanations for quantum AI algorithms. In the classical context, the cooperative game theory concept of the Shapley value has been adapted for post-hoc explanations. However, this approach does not translate to use in quantum computing trivially and can be exponentially difficult to implement if not handled with care. We propose a novel algorithm which reduces the problem of accurately estimating the Shapley values of a quantum algorithm into a far simpler problem of estimating the true average of a binomial distribution in polynomial time.

We consider a cooperative multi-agent system consisting of a team of agents with decentralized information. Our focus is on the design of symmetric (i.e. identical) strategies for the agents in order to optimize a finite horizon team objective. We start with a general information structure and then consider some special cases. The constraint of using symmetric strategies introduces new features and complications in the team problem. For example, we show in a simple example that randomized symmetric strategies may outperform deterministic symmetric strategies. We also discuss why some of the known approaches for reducing agents' private information in teams may not work under the constraint of symmetric strategies. We then adopt the common information approach for our problem and modify it to accommodate the use of symmetric strategies. This results in a common information based dynamic program where each step involves minimization over a single function from the space of an agent's private information to the space of probability distributions over actions. We present specialized models where private information can be reduced using simple dynamic program based arguments.

Online polarization research currently focuses on studying single-issue opinion distributions or computing distance metrics of interaction network structures. Limited data availability often restricts studies to positive interaction data, which can misrepresent the reality of a discussion. We introduce a novel framework that aims at combining these three aspects, content and interactions, as well as their nature (positive or negative), while challenging the prevailing notion of polarization as an umbrella term for all forms of online conflict or opposing opinions. In our approach, built on the concepts of cleavage structures and structural balance of signed social networks, we factorize polarization into two distinct metrics: Antagonism and Alignment. Antagonism quantifies hostility in online discussions, based on the reactions of users to content. Alignment uses signed structural information encoded in long-term user-user relations on the platform to describe how well user interactions fit the global and/or traditional sides of discussion. We can analyse the change of these metrics through time, localizing both relevant trends but also sudden changes that can be mapped to specific contexts or events. We apply our methods to two distinct platforms: Birdwatch, a US crowd-based fact-checking extension of Twitter, and DerStandard, an Austrian online newspaper with discussion forums. In these two use cases, we find that our framework is capable of describing the global status of the groups of users (identification of cleavages) while also providing relevant findings on specific issues or in specific time frames. Furthermore, we show that our four metrics describe distinct phenomena, emphasizing their independent consideration for unpacking polarization complexities.

We investigate a framework for binary image denoising via restricted Boltzmann machines (RBMs) that introduces a denoising objective in quadratic unconstrained binary optimization (QUBO) form and is well-suited for quantum annealing. The denoising objective is attained by balancing the distribution learned by a trained RBM with a penalty term for derivations from the noisy image. We derive the statistically optimal choice of the penalty parameter assuming the target distribution has been well-approximated, and further suggest an empirically supported modification to make the method robust to that idealistic assumption. We also show under additional assumptions that the denoised images attained by our method are, in expectation, strictly closer to the noise-free images than the noisy images are. While we frame the model as an image denoising model, it can be applied to any binary data. As the QUBO formulation is well-suited for implementation on quantum annealers, we test the model on a D-Wave Advantage machine, and also test on data too large for current quantum annealers by approximating QUBO solutions through classical heuristics.

Quantum networks are complex systems formed by the interaction among quantum processors through quantum channels. Analogous to classical computer networks, quantum networks allow for the distribution of quantum operations among quantum processors. In this work, we describe a Quantum Walk Control Protocol (QWCP) to perform distributed quantum operations in a quantum network. We consider a generalization of the discrete-time coined quantum walk model that accounts for the interaction between quantum walks in the network graph with quantum registers inside the network nodes. QWCP allows for the implementation of networked quantum services, such as distributed quantum computing and entanglement distribution, abstracting hardware implementation and the transmission of quantum information through channels. Multiple interacting quantum walks can be used to propagate entangled control signals across the network in parallel. We demonstrate how to use QWCP to perform distributed multi-qubit controlled gates, which shows the universality of the protocol for distributed quantum computing. Furthermore, we apply the QWCP to the task of entanglement distribution in a quantum network.

The performance of a quantum information processing protocol is ultimately judged by distinguishability measures that quantify how distinguishable the actual result of the protocol is from the ideal case. The most prominent distinguishability measures are those based on the fidelity and trace distance, due to their physical interpretations. In this paper, we propose and review several algorithms for estimating distinguishability measures based on trace distance and fidelity. The algorithms can be used for distinguishing quantum states, channels, and strategies (the last also known in the literature as "quantum combs"). The fidelity-based algorithms offer novel physical interpretations of these distinguishability measures in terms of the maximum probability with which a single prover (or competing provers) can convince a verifier to accept the outcome of an associated computation. We simulate many of these algorithms by using a variational approach with parameterized quantum circuits. We find that the simulations converge well in both the noiseless and noisy scenarios, for all examples considered. Furthermore, the noisy simulations exhibit a parameter noise resilience. Finally, we establish a strong relationship between various quantum computational complexity classes and distance estimation problems.

Quantum Internetworking is a recent field that promises numerous interesting applications, many of which require the distribution of entanglement between arbitrary pairs of users. This work deals with the problem of scheduling in an arbitrary entanglement swapping quantum network - often called first generation quantum network - in its general topology, multicommodity, loss-aware formulation. We introduce a linear algebraic framework that exploits quantum memory through the creation of intermediate entangled links. The framework is then employed to mathematically derive a natural class of quadratic scheduling policies for quantum networks by applying Lyapunov Drift Minimization, a standard technique in classical network science. Moreover, an additional class of Max-Weight inspired policies is proposed and benchmarked, reducing significantly the computation cost, at the price of a slight performance degradation. The policies are compared in terms of information availability, localization and overall network performance through an ad-hoc simulator that admits user-provided network topologies and scheduling policies in order to showcase the potential application of the provided tools to quantum network design.

Several distributions and families of distributions are proposed to model skewed data, think, e.g., of skew-normal and related distributions. Lambert W random variables offer an alternative approach where, instead of constructing a new distribution, a certain transform is proposed (Goerg, 2011). Such an approach allows the construction of a Lambert W skewed version from any distribution. We choose Lambert W normal distribution as a natural starting point and also include Lambert W exponential distribution due to the simplicity and shape of the exponential distribution, which, after skewing, may produce a reasonably heavy tail for loss models. In the theoretical part, we focus on the mathematical properties of obtained distributions, including the range of skewness. In the practical part, the suitability of corresponding Lambert W transformed distributions is evaluated on real insurance data. The results are compared with those obtained using common loss distributions.