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We show how to translate a subset of RISC-V machine code compiled from a subset of C to quadratic unconstrained binary optimization (QUBO) models that may be solved by a quantum annealing machine: given a bound $n$, there is input $I$ to a program $P$ such that $P$ runs into a given program state $E$ executing no more than $n$ machine instructions if and only if the QUBO model of $P$ for $n$ evaluates to 0 on $I$. Thus, with more qubits on the machine than variables in the QUBO model, quantum annealing the model reaches 0 (ground) energy in constant time with high probability on some input $I$ that is part of the ground state if and only if $P$ runs into $E$ on $I$ executing no more than $n$ instructions. Translation takes $\mathcal{O}(n^2)$ time effectively turning a quantum annealer into a polynomial-time symbolic execution engine and bounded model checker, eliminating their path and state explosion problems. Here, we take advantage of the fact that any machine instruction may only increase the size of the program state by a constant amount of bits. Translation time comes down from $\mathcal{O}(n^2)$ to $\mathcal{O}(n\cdot|P|)$ if memory consumption of $P$ is bounded by a constant, establishing a linear (quadratic) upper bound on quantum space, in number of qubits on a quantum annealer, in terms of algorithmic time (space) in classical computing. The construction provides a non-relativizing argument for $NP\subseteq BQP$, without violating the optimality of Grover's algorithm, also on gate-model quantum machines, and motivates a temporal and spatial metric of quantum advantage. Our prototypical open-source toolchain translates machine code that runs on real RISC-V hardware to models that can be solved by real quantum annealing hardware, as shown in our experiments.

The Solovay-Kitaev algorithm is a fundamental result in quantum computation. It gives an algorithm for efficiently compiling arbitrary unitaries using universal gate sets: any unitary can be approximated by short gates sequences, whose length scales merely poly-logarithmically with accuracy. As a consequence, the choice of gate set is typically unimportant in quantum computing. However, the Solovay-Kitaev algorithm requires the gate set to be inverse-closed. It has been a longstanding open question if efficient algorithmic compilation is possible without this condition. In this work, we provide the first inverse-free Solovay-Kitaev algorithm, which makes no assumption on the structure within a gate set beyond universality, answering this problem in the affirmative, and providing an efficient compilation algorithm in the absence of inverses for both $\text{SU}(d)$ and $\text{SL}(d, \mathbb{C})$. The algorithm works by showing that approximate gate implementations of the generalized Pauli group can self-correct their errors.

The guesswork quantifies the minimum number of queries needed to guess the state of a quantum ensemble if one is allowed to query only one state at a time. Previous approaches to the computation of the guesswork were based on standard semi-definite programming techniques and therefore lead to approximated results. In contrast, our main result is an algorithm that, upon the input of any qubit ensemble over a discrete ring and with uniform probability distribution, after finitely many steps outputs the exact closed-form analytic expression of its guesswork. The complexity of our guesswork-computing algorithm is factorial in the number of states, with a more-than-quadratic speedup for symmetric ensembles. To find such symmetries, we provide an algorithm that, upon the input of any point set over a discrete ring, after finitely many steps outputs its exact symmetries. The complexity of our symmetries-finding algorithm is polynomial in the number of points. As examples, we compute the guesswork of regular and quasi-regular sets of qubit states.

Demonstrating quantum advantage requires experimental implementation of a computational task that is hard to achieve using state-of-the-art classical systems. One approach is to perform sampling from a probability distribution associated with a class of highly entangled many-body wavefunctions. It has been suggested that this approach can be certified with the Linear Cross-Entropy Benchmark (XEB). We critically examine this notion. First, in a "benign" setting where an honest implementation of noisy quantum circuits is assumed, we characterize the conditions under which the XEB approximates the fidelity. Second, in an "adversarial" setting where all possible classical algorithms are considered for comparison, we show that achieving relatively high XEB values does not imply faithful simulation of quantum dynamics. We present an efficient classical algorithm that, with 1 GPU within 2s, yields high XEB values, namely 2-12% of those obtained in experiments. By identifying and exploiting several vulnerabilities of the XEB, we achieve high XEB values without full simulation of quantum circuits. Remarkably, our algorithm features better scaling with the system size than noisy quantum devices for commonly studied random circuit ensembles. To quantitatively explain the success of our algorithm and the limitations of the XEB, we use a theoretical framework in which the average XEB and fidelity are mapped to statistical models. We illustrate the relation between the XEB and the fidelity for quantum circuits in various architectures, with different gate choices, and in the presence of noise. Our results show that XEB's utility as a proxy for fidelity hinges on several conditions, which must be checked in the benign setting but cannot be assumed in the adversarial setting. Thus, the XEB alone has limited utility as a benchmark for quantum advantage. We discuss ways to overcome these limitations.

The dominating NLP paradigm of training a strong neural predictor to perform one task on a specific dataset has led to state-of-the-art performance in a variety of applications (eg. sentiment classification, span-prediction based question answering or machine translation). However, it builds upon the assumption that the data distribution is stationary, ie. that the data is sampled from a fixed distribution both at training and test time. This way of training is inconsistent with how we as humans are able to learn from and operate within a constantly changing stream of information. Moreover, it is ill-adapted to real-world use cases where the data distribution is expected to shift over the course of a model's lifetime. The first goal of this thesis is to characterize the different forms this shift can take in the context of natural language processing, and propose benchmarks and evaluation metrics to measure its effect on current deep learning architectures. We then proceed to take steps to mitigate the effect of distributional shift on NLP models. To this end, we develop methods based on parametric reformulations of the distributionally robust optimization framework. Empirically, we demonstrate that these approaches yield more robust models as demonstrated on a selection of realistic problems. In the third and final part of this thesis, we explore ways of efficiently adapting existing models to new domains or tasks. Our contribution to this topic takes inspiration from information geometry to derive a new gradient update rule which alleviate catastrophic forgetting issues during adaptation.

Classic machine learning methods are built on the $i.i.d.$ assumption that training and testing data are independent and identically distributed. However, in real scenarios, the $i.i.d.$ assumption can hardly be satisfied, rendering the sharp drop of classic machine learning algorithms' performances under distributional shifts, which indicates the significance of investigating the Out-of-Distribution generalization problem. Out-of-Distribution (OOD) generalization problem addresses the challenging setting where the testing distribution is unknown and different from the training. This paper serves as the first effort to systematically and comprehensively discuss the OOD generalization problem, from the definition, methodology, evaluation to the implications and future directions. Firstly, we provide the formal definition of the OOD generalization problem. Secondly, existing methods are categorized into three parts based on their positions in the whole learning pipeline, namely unsupervised representation learning, supervised model learning and optimization, and typical methods for each category are discussed in detail. We then demonstrate the theoretical connections of different categories, and introduce the commonly used datasets and evaluation metrics. Finally, we summarize the whole literature and raise some future directions for OOD generalization problem. The summary of OOD generalization methods reviewed in this survey can be found at //out-of-distribution-generalization.com.

Minimizing cross-entropy over the softmax scores of a linear map composed with a high-capacity encoder is arguably the most popular choice for training neural networks on supervised learning tasks. However, recent works show that one can directly optimize the encoder instead, to obtain equally (or even more) discriminative representations via a supervised variant of a contrastive objective. In this work, we address the question whether there are fundamental differences in the sought-for representation geometry in the output space of the encoder at minimal loss. Specifically, we prove, under mild assumptions, that both losses attain their minimum once the representations of each class collapse to the vertices of a regular simplex, inscribed in a hypersphere. We provide empirical evidence that this configuration is attained in practice and that reaching a close-to-optimal state typically indicates good generalization performance. Yet, the two losses show remarkably different optimization behavior. The number of iterations required to perfectly fit to data scales superlinearly with the amount of randomly flipped labels for the supervised contrastive loss. This is in contrast to the approximately linear scaling previously reported for networks trained with cross-entropy.

Quantum hardware and quantum-inspired algorithms are becoming increasingly popular for combinatorial optimization. However, these algorithms may require careful hyperparameter tuning for each problem instance. We use a reinforcement learning agent in conjunction with a quantum-inspired algorithm to solve the Ising energy minimization problem, which is equivalent to the Maximum Cut problem. The agent controls the algorithm by tuning one of its parameters with the goal of improving recently seen solutions. We propose a new Rescaled Ranked Reward (R3) method that enables stable single-player version of self-play training that helps the agent to escape local optima. The training on any problem instance can be accelerated by applying transfer learning from an agent trained on randomly generated problems. Our approach allows sampling high-quality solutions to the Ising problem with high probability and outperforms both baseline heuristics and a black-box hyperparameter optimization approach.

Machine Learning models become increasingly proficient in complex tasks. However, even for experts in the field, it can be difficult to understand what the model learned. This hampers trust and acceptance, and it obstructs the possibility to correct the model. There is therefore a need for transparency of machine learning models. The development of transparent classification models has received much attention, but there are few developments for achieving transparent Reinforcement Learning (RL) models. In this study we propose a method that enables a RL agent to explain its behavior in terms of the expected consequences of state transitions and outcomes. First, we define a translation of states and actions to a description that is easier to understand for human users. Second, we developed a procedure that enables the agent to obtain the consequences of a single action, as well as its entire policy. The method calculates contrasts between the consequences of a policy derived from a user query, and of the learned policy of the agent. Third, a format for generating explanations was constructed. A pilot survey study was conducted to explore preferences of users for different explanation properties. Results indicate that human users tend to favor explanations about policy rather than about single actions.

Quantum machine learning is expected to be one of the first potential general-purpose applications of near-term quantum devices. A major recent breakthrough in classical machine learning is the notion of generative adversarial training, where the gradients of a discriminator model are used to train a separate generative model. In this work and a companion paper, we extend adversarial training to the quantum domain and show how to construct generative adversarial networks using quantum circuits. Furthermore, we also show how to compute gradients -- a key element in generative adversarial network training -- using another quantum circuit. We give an example of a simple practical circuit ansatz to parametrize quantum machine learning models and perform a simple numerical experiment to demonstrate that quantum generative adversarial networks can be trained successfully.