Abstract Modern machine learning (ML) methods typically fail to adequately capture causal information. Consequently, such models do not handle data distributional shifts, are vulnerable to adversarial examples, and often learn spurious correlations (Schölkopf and von Kügelgen 2022 (arXiv:2204.00607) [cs.AI]). Causal ML, or causal inference, aims to solve these issues by estimating the expected outcome of counterfactual events, using observational and/or interventional data, where causal relationships are typically depicted as directed acyclic graphs. It is an open question as to whether these causal algorithms provide opportunities for quantum enhancement. In this paper we consider a recently developed family of non-parametric, continuous causal estimators and derive quantum algorithms for these tasks. Kernel evaluation and large matrix inversion are critical sub-routines of these classical algorithms, which makes them particularly amenable to a quantum treatment. Unlike other quantum ML algorithms, closed form solutions for the estimators exist, negating the need for gradient evaluation and variational learning. We describe several new hybrid quantum–classical algorithms and show that uniform consistency of the estimators is retained. Furthermore, if one is satisfied with a quantum state output that is proportional to the true causal estimand, then these algorithms inherit the exponential complexity advantages given by quantum linear system solvers.
Abstract Modern machine learning (ML) methods typically fail to adequately capture causal information. Consequently, such models do not handle data distributional shifts, are vulnerable to adversarial examples, and often learn spurious correlations (Schölkopf and von Kügelgen 2022 (arXiv:2204.00607) [cs.AI]). Causal ML, or causal inference, aims to solve these issues by estimating the expected outcome of counterfactual events, using observational and/or interventional data, where causal relationships are typically depicted as directed acyclic graphs. It is an open question as to whether these causal algorithms provide opportunities for quantum enhancement. In this paper we consider a recently developed family of non-parametric, continuous causal estimators and derive quantum algorithms for these tasks. Kernel evaluation and large matrix inversion are critical sub-routines of these classical algorithms, which makes them particularly amenable to a quantum treatment. Unlike other quantum ML algorithms, closed form solutions for the estimators exist, negating the need for gradient evaluation and variational learning. We describe several new hybrid quantum–classical algorithms and show that uniform consistency of the estimators is retained. Furthermore, if one is satisfied with a quantum state output that is proportional to the true causal estimand, then these algorithms inherit the exponential complexity advantages given by quantum linear system solvers.
In this thesis, I present several results on quantum statistical inference in the following two directions. Firstly, I demonstrate that quantum algorithms can be applied to enhance the computing and training of Gaussian processes (GPs), a powerful model widely used in classical statistical inference and supervised machine learning. A crucial component of the quantum GP algorithm is solving linear systems with quantum computers, for which I present a novel algorithm that achieves a provable advantage over previously known methods. I will also explicitly address the task of encoding the classical data into a quantum state for machine learning applications. I then apply the quantum enhanced GPs to Bayesian deep learning and present an experimental demonstration on contemporary hardware and simulators. Secondly, I look into the notion of quantum causality and apply it to inferring spatial and temporal quantum correlations, and present an analytical toolkit for causal inference in quantum data. I will also make the connection between causality and quantum communications, and present a general bound for the quantum capacity of noisy communication channels.
Quantum computers acting as ML accelerators have attracted considerable interest as a promising avenue for addressing the limitations of classical computing confronted with solving complex, high-dimensional problems and handling large data sets. The most exciting aspect of quantum computing lies in its quantum advantage via techniques such as quantum parallelism, superposition, and entanglement which allows not only for rapid data processing, but also a means to resolve complex optimization problems beyond the capacity of classical algorithms. Nevertheless, the usage of quantum computing in machine learning is still a fledgling domain, with challenges concerning quantum noise, hardware restrictions, and algorithmic development. In particular, this research is concerned with the development of and study on hybrid quantum-classical algorithms that target to improve ML models in terms of computational capabilities by making use of the best of both worlds. To address this, researchers are developing hybrid algorithms that leverage the strengths of quantum computing for specific tasks, like optimization and pattern recognition, while still relying on classical computing for more flexible and larger-scale processing, ultimately achieving more efficient machine learning systems that can handle large datasets and complex problem-solving more effectively. It includes potential hybrid approaches like quantum-enhanced optimization algorithms, quantum neural networks, and quantum support vector machines, and examines how such algorithms can be used for practical ML problems including data classification, regression and clustering. Furthermore, the paper proposes that hybrid quantum algorithms offer several advantages over their classical counterparts, such as faster convergence rates, higher accuracy in high-dimensional spaces, and improved handling of non-linear and complex problem landscapes. Key advancements in the area of data processing speed and efficiency in problem-solving with and without quantum in the machine learning workflow are also highlighted in the research through comparative analysis and simulation studies. Lastly, the paper concludes by outlining the obstacles yet to be surmounted and the opportunities that lie ahead for hybrid quantum-classical algorithms, such as further improvement of quantum hardware and error mitigation methods, as well as the design of new algorithmic paradigms that seamlessly integrates the classical and quantum computing spaces.
Anomaly detection (AD) underpins fraud prevention, network security, industrial condition monitoring, medical diagnosis, and searches for new physics. However, it remains challenging due to rare anomalies, scarce labeled data, and the high dimensionality and strong correlation of sensor data. Many classical machine learning (ML) algorithms are designed to address AD in various settings, but the growth of quantum computing opens a new path for these problems. Quantum machine learning (QML) offers new tools, from exploring exponentially large Hilbert spaces and promising speed-ups to the native processing of quantum data. Thus, this review connects the two fields. We first present the basics of quantum computing, quantum algorithms, and QML with the most influential literature, and formalize the classical anomaly scores that quantum methods inherit. We then systematically review 30 primary studies of quantum anomaly detection (QAD) published between 2018 and 2026, express each method family through its anomaly score, and organize the field into a taxonomy of six families: quantum kernel methods, quantum autoencoders, quantum generative models, variational quantum classifiers, quantum linear-algebra methods, and detectors for quantum data. A cross-study analysis shows that the field has moved from asymptotic speed-up proposals to small hybrid experiments, that kernels and autoencoders dominate, that only nine studies run on gate-based hardware, and that none yet demonstrates a robust, practically relevant advantage over well-tuned classical detectors. We close with the main obstacles, such as data embedding, barren plateaus, kernel concentration, and weak baselines, and a research roadmap that prioritizes quantum data, fair benchmarks against classical baselines, and robust detectors for sequential and distributed data.
Quantum machine learning (QML), an emerging discipline with applications in various domains, has the potential to dramatically improve deep learning while reducing model complexity. Quantum computers are well suited for machine learning (ML) tasks, especially because ML models are rapidly growing and require large amounts of data to learn. For example, classical computers that train large language and foundation models typically require supercomputers. If a need exists to double the number of model parameters, one will have to double the size of the supercomputer needed to train it. A quantum computer's parameter or state space grows exponentially with the number of qubits. This means doubling the number of model parameters only requires adding one quantum bit. Another advantage is that quantum computers can use entanglement and interference to potentially learn patterns with less data. Currently, no existing solutions compares the performance of classical and quantum machine learning algorithms for a workflow comprised of multiple ML tasks. This poster presents a QML workspace to explore and verify these QML algorithms with different available quantum frameworks such as Qisklt, CUDA Quantum, and PennyLane in a consistent, reproducible, and theoretically sound way and provide a comparison with similar classical machine learning algorithms.
This dissertation presents a study of quantum algorithms for problems that can be posed as matrix function tasks. In Chapter 1 we demonstrate a simple unifying framework for implementing of smooth functions of matrices on a quantum computer. This framework captures a variety of problems that can be solved by evaluating properties of some function of a matrix, and we identify speedups over classical algorithms for some problem classes. The analysis combines ideas from the classical theory of function approximation with the quantum algorithmic primitive of implementing linear combinations of unitary operators. In Chapter 2 we continue this study by looking at the role of sparsity of input matrices in constructing efficient quantum algorithms. We show that classically pre-processing an input matrix by spectral sparsification can be profitable for quantum Hamiltonian simulation algorithms, without compromising the simulation error or complexity. Such preprocessing incurs a one time cost linear in the size of the matrix, but can be exploited to exponentially speed up subsequent subroutines such as inversion. In Chapter 3, we give an application of this theory of matrix functions to the problem of estimating the Renyi entropy of an unknown quantum state. We combine matrix function techniques with mixed state quantum computation in the one-clean qubit model, and are able to bound of the expected runtime of our algorithm in terms of the unknown target quantity. In addition to the theme of analysing the complexity of our algorithms, we also identify instances that are of practical relevance, leading us to some problems of machine learning. In Chapter 4 we investigate kernel based learning methods using random features. We work with the QRAM input model suitable for big data, and show how matrix functions and the quantum Fourier transform can be used to devise a quantum algorithm for sampling random features that are optimised for given input data and choice of kernel. We obtain a potential exponential speedup over the best known classical algorithm even without explicit assumptions of sparsity or low rank. Finally in Chapter 5 we consider the technique of beamsearch decoding used in natural language processing. We work in the query model, and show how quantum search with advice can be used to construct a quantum search decoder that can find the optimal parse (which may for instance be a best translation, or text-to-speech transcript) at least quadratically faster than the best known classical algorithms, and obtain super-quadratic speedups in the expected runtime.
There has been remarkable development in the data-driven decision-making domain of Artificial Intelligence (AI). However, the complexity of the AI models and the amount of data have shown some drawbacks with conventional computing models. One of the interdisciplinary branches of quantum computing and machine learning is Quantum Machine Learning (QML), which is a combination of quantum computing and machine learning and relies on the unique characteristics of quantum computing, such as superposition, entanglement, and quantum parallelism, to enhance the performance of the machines. This review provides a comprehensive description of theory, architectures, algorithms, implementational approaches, applications, problems, and future directions of QML. The core concepts of quantum computing and machine learning are introduced. Different representations of quantum states, quantum data encoding, variational quantum circuits, quantum kernel methods, and hybrid quantum or classical optimization are discussed. Significant QML algorithms like Quantum Support Vector Machines, Quantum Neural Networks, Variational Quantum Eigen solvers, Quantum Approximate Optimization Algorithms, and Quantum reinforcement learning are explored and evaluated for computational power and applications. The scaling up of quantum computer sizes, data encoding overhead, complexity of optimizations, benchmarking, and decoherence are discussed in detail, as well as recent developments in fault-tolerant quantum computing and hybrid learning approaches. Finally, a conceptual framework is given to demonstrate the unification of classical computation and quantum computation to intelligently process data. This review demonstrates how QML could be the next-generation computational method to accelerate scientific advancements and enable new advanced AI technologies.