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Quantum machine learning promises to efficiently solve important problems. There are two persistent challenges in classical machine learning: the lack of labeled data, and the limit of computational power. We propose a novel framework that resolves both issues: quantum semi-supervised learning. Moreover, we provide a protocol in systematically designing quantum machine learning algorithms with quantum supremacy, which can be extended beyond quantum semi-supervised learning. In the meantime, we show that naive quantum matrix product estimation algorithm outperforms the best known classical matrix multiplication algorithm. We showcase two concrete quantum semi-supervised learning algorithms: a quantum self-training algorithm named the propagating nearest-neighbor classifier, and the quantum semi-supervised K-means clustering algorithm. By doing time complexity analysis, we conclude that they indeed possess quantum supremacy.

Variational quantum algorithms have been introduced as a promising class of quantum-classical hybrid algorithms that can already be used with the noisy quantum computing hardware available today by employing parameterized quantum circuits. Considering the non-trivial nature of quantum circuit compilation and the subtleties of quantum computing, it is essential to verify that these parameterized circuits have been compiled correctly. Established equivalence checking procedures that handle parameter-free circuits already exist. However, no methodology capable of handling circuits with parameters has been proposed yet. This work fills this gap by showing that verifying the equivalence of parameterized circuits can be achieved in a purely symbolic fashion using an equivalence checking approach based on the ZX-calculus. At the same time, proofs of inequality can be efficiently obtained with conventional methods by taking advantage of the degrees of freedom inherent to parameterized circuits. We implemented the corresponding methods and proved that the resulting methodology is complete. Experimental evaluations (using the entire parametric ansatz circuit library provided by Qiskit as benchmarks) demonstrate the efficacy of the proposed approach. The implementation is open source and publicly available as part of the equivalence checking tool QCEC (//github.com/cda-tum/qcec) which is part of the Munich Quantum Toolkit (MQT).

Even after decades of quantum computing development, examples of generally useful quantum algorithms with exponential speedups over classical counterparts are scarce. Recent progress in quantum algorithms for linear-algebra positioned quantum machine learning (QML) as a potential source of such useful exponential improvements. Yet, in an unexpected development, a recent series of "dequantization" results has equally rapidly removed the promise of exponential speedups for several QML algorithms. This raises the critical question whether exponential speedups of other linear-algebraic QML algorithms persist. In this paper, we study the quantum-algorithmic methods behind the algorithm for topological data analysis of Lloyd, Garnerone and Zanardi through this lens. We provide evidence that the problem solved by this algorithm is classically intractable by showing that its natural generalization is as hard as simulating the one clean qubit model -- which is widely believed to require superpolynomial time on a classical computer -- and is thus very likely immune to dequantizations. Based on this result, we provide a number of new quantum algorithms for problems such as rank estimation and complex network analysis, along with complexity-theoretic evidence for their classical intractability. Furthermore, we analyze the suitability of the proposed quantum algorithms for near-term implementations. Our results provide a number of useful applications for full-blown, and restricted quantum computers with a guaranteed exponential speedup over classical methods, recovering some of the potential for linear-algebraic QML to become one of quantum computing's killer applications.

In this paper, we present Q# implementations for arbitrary single-variabled fixed-point arithmetic operations for a gate-based quantum computer based on lookup tables (LUTs). In general, this is an inefficent way of implementing a function since the number of inputs can be large or even infinite. However, if the input domain can be bounded and there can be some error tolerance in the output (both of which are often the case in practical use-cases), the quantum LUT implementation of certain quantum arithmetic functions can be more efficient than their corresponding reversible arithmetic implementations. We discuss the implementation of the LUT using Q\# and its approximation errors. We then show examples of how to use the LUT to implement quantum arithmetic functions and compare the resources required for the implementation with the current state-of-the-art bespoke implementations of some commonly used arithmetic functions. The implementation of the LUT is designed for use by practitioners to use when implementing end-to-end quantum algorithms. In addition, given its well-defined approximation errors, the LUT implementation makes for a clear benchmark for evaluating the efficiency of bespoke quantum arithmetic circuits .

Solving large systems of equations is a challenge for modeling natural phenomena, such as simulating subsurface flow. To avoid systems that are intractable on current computers, it is often necessary to neglect information at small scales, an approach known as coarse-graining. For many practical applications, such as flow in porous, homogenous materials, coarse-graining offers a sufficiently-accurate approximation of the solution. Unfortunately, fractured systems cannot be accurately coarse-grained, as critical network topology exists at the smallest scales, including topology that can push the network across a percolation threshold. Therefore, new techniques are necessary to accurately model important fracture systems. Quantum algorithms for solving linear systems offer a theoretically-exponential improvement over their classical counterparts, and in this work we introduce two quantum algorithms for fractured flow. The first algorithm, designed for future quantum computers which operate without error, has enormous potential, but we demonstrate that current hardware is too noisy for adequate performance. The second algorithm, designed to be noise resilient, already performs well for problems of small to medium size (order 10 to 1000 nodes), which we demonstrate experimentally and explain theoretically. We expect further improvements by leveraging quantum error mitigation and preconditioning.

The field of quantum machine learning (QML) explores how quantum computers can be used to more efficiently solve machine learning problems. As an application of hybrid quantum-classical algorithms, it promises a potential quantum advantages in the near term. In this thesis, we use the ZXW-calculus to diagrammatically analyse two key problems that QML applications face. First, we discuss algorithms to compute gradients on quantum hardware that are needed to perform gradient-based optimisation for QML. Concretely, we give new diagrammatic proofs of the common 2- and 4-term parameter shift rules used in the literature. Additionally, we derive a novel, generalised parameter shift rule with 2n terms that is applicable to gates that can be represented with n parametrised spiders in the ZXW-calculus. Furthermore, to the best of our knowledge, we give the first proof of a conjecture by Anselmetti et al. by proving a no-go theorem ruling out more efficient alternatives to the 4-term shift rule. Secondly, we analyse the gradient landscape of quantum ans\"atze for barren plateaus using both empirical and analytical techniques. Concretely, we develop a tool that automatically calculates the variance of gradients and use it to detect likely barren plateaus in commonly used quantum ans\"atze. Furthermore, we formally prove the existence or absence of barren plateaus for a selection of ans\"atze using diagrammatic techniques from the ZXW-calculus.

Existing recommender systems extract the user preference based on learning the correlation in data, such as behavioral correlation in collaborative filtering, feature-feature, or feature-behavior correlation in click-through rate prediction. However, regretfully, the real world is driven by causality rather than correlation, and correlation does not imply causation. For example, the recommender systems can recommend a battery charger to a user after buying a phone, in which the latter can serve as the cause of the former, and such a causal relation cannot be reversed. Recently, to address it, researchers in recommender systems have begun to utilize causal inference to extract causality, enhancing the recommender system. In this survey, we comprehensively review the literature on causal inference-based recommendation. At first, we present the fundamental concepts of both recommendation and causal inference as the basis of later content. We raise the typical issues that the non-causality recommendation is faced. Afterward, we comprehensively review the existing work of causal inference-based recommendation, based on a taxonomy of what kind of problem causal inference addresses. Last, we discuss the open problems in this important research area, along with interesting future works.

Advances in artificial intelligence often stem from the development of new environments that abstract real-world situations into a form where research can be done conveniently. This paper contributes such an environment based on ideas inspired by elementary Microeconomics. Agents learn to produce resources in a spatially complex world, trade them with one another, and consume those that they prefer. We show that the emergent production, consumption, and pricing behaviors respond to environmental conditions in the directions predicted by supply and demand shifts in Microeconomics. We also demonstrate settings where the agents' emergent prices for goods vary over space, reflecting the local abundance of goods. After the price disparities emerge, some agents then discover a niche of transporting goods between regions with different prevailing prices -- a profitable strategy because they can buy goods where they are cheap and sell them where they are expensive. Finally, in a series of ablation experiments, we investigate how choices in the environmental rewards, bartering actions, agent architecture, and ability to consume tradable goods can either aid or inhibit the emergence of this economic behavior. This work is part of the environment development branch of a research program that aims to build human-like artificial general intelligence through multi-agent interactions in simulated societies. By exploring which environment features are needed for the basic phenomena of elementary microeconomics to emerge automatically from learning, we arrive at an environment that differs from those studied in prior multi-agent reinforcement learning work along several dimensions. For example, the model incorporates heterogeneous tastes and physical abilities, and agents negotiate with one another as a grounded form of communication.

Properly handling missing data is a fundamental challenge in recommendation. Most present works perform negative sampling from unobserved data to supply the training of recommender models with negative signals. Nevertheless, existing negative sampling strategies, either static or adaptive ones, are insufficient to yield high-quality negative samples --- both informative to model training and reflective of user real needs. In this work, we hypothesize that item knowledge graph (KG), which provides rich relations among items and KG entities, could be useful to infer informative and factual negative samples. Towards this end, we develop a new negative sampling model, Knowledge Graph Policy Network (KGPolicy), which works as a reinforcement learning agent to explore high-quality negatives. Specifically, by conducting our designed exploration operations, it navigates from the target positive interaction, adaptively receives knowledge-aware negative signals, and ultimately yields a potential negative item to train the recommender. We tested on a matrix factorization (MF) model equipped with KGPolicy, and it achieves significant improvements over both state-of-the-art sampling methods like DNS and IRGAN, and KG-enhanced recommender models like KGAT. Further analyses from different angles provide insights of knowledge-aware sampling. We release the codes and datasets at //github.com/xiangwang1223/kgpolicy.